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johndcook.com


5. 11. 2024Maybe Copernicus isn’t coming – johndcook.com
5. 11. 2024Trigonometric interpolation – johndcook.com
5. 11. 2024Moments with Laplace – johndcook.com
4. 11. 2024The impossible puzzle – johndcook.com
4. 11. 2024When do moments determine a function? – johndcook.com
1. 11. 2024Floating point: Everything old is new again – johndcook.com
31. 10. 2024How hard is constraint programming? – johndcook.com
28. 10. 2024Band-limited expansion – johndcook.com
26. 10. 2024Delay differential equations – johndcook.com
25. 10. 2024Laplace transform inversion theorems – johndcook.com
25. 10. 2024Mellin transform and Riemann zeta – johndcook.com
24. 10. 2024Sawtooth waves – johndcook.com
22. 10. 2024Pioneering work is ugly – johndcook.com
21. 10. 2024New Mersenne prime found – johndcook.com
19. 10. 2024Channel capacity of a telegraph – johndcook.com
17. 10. 2024Squares, triangles, and octal – johndcook.com
16. 10. 2024RNG, PRNG, CSPRNG – johndcook.com
16. 10. 2024Triangle circle maximization problem – johndcook.com
15. 10. 2024Relating six properties of a triangle in one equation – johndcook.com
15. 10. 2024Preprocessing text to make it more compressible – johndcook.com
13. 10. 2024Why does FM sound better than AM? – johndcook.com
13. 10. 2024Shifted reciprocal – johndcook.com
11. 10. 2024Triangles to Triangles – johndcook.com
10. 10. 2024Golden ellipse – johndcook.com
10. 10. 2024Areal coordinates and ellipse area – johndcook.com
9. 10. 2024Average number of divisors – johndcook.com
8. 10. 2024Lucas numbers and Lucas pseudoprimes – johndcook.com
30. 9. 2024Identifying hash algorithms – johndcook.com
28. 9. 2024Testing random number generators – johndcook.com
28. 9. 2024Limitations on Venn diagrams – johndcook.com
27. 9. 2024Edit distance – johndcook.com
27. 9. 2024Birthday problem approximation – johndcook.com
26. 9. 2024(1 − z) / (1 + z) – johndcook.com
22. 9. 2024Error in Ramanujan’s approximation for ellipse perimeter – johndcook.com
19. 9. 2024The Cauchy distribution’s counter-intuitive behavior – johndcook.com
17. 9. 2024Arithmetic, Geometry, Harmony, and Gold – johndcook.com
14. 9. 2024Ceva, cevians, and Routh’s theorem – johndcook.com
14. 9. 2024Moments of inertia mnemonic – johndcook.com
13. 9. 2024Binomial bound – johndcook.com
10. 9. 2024Separable functions in different contexts – johndcook.com
8. 9. 2024Body roundness index – johndcook.com
7. 9. 2024A couple more variations on an ancient theme – johndcook.com
7. 9. 2024Finding pi in the alphabet – johndcook.com
3. 9. 2024Optimal rational approximation – johndcook.com
2. 9. 2024Pell is to silver as Fibonacci is to gold – johndcook.com
1. 9. 2024Miles to kilometers – johndcook.com
31. 8. 2024Ancient accurate approximation for sine – johndcook.com
31. 8. 2024Mentally multiply by π – johndcook.com
31. 8. 2024A better integral for the normal distribution – johndcook.com
30. 8. 2024Drawing with a compass on a globe – johndcook.com
29. 8. 2024The negative binomial distribution and Pascal’s triangle – johndcook.com
29. 8. 2024A strange take on the harmonic series – johndcook.com
26. 8. 2024Variance matters more than mean in the extremes – johndcook.com
24. 8. 2024Increasing speed due to friction – johndcook.com
24. 8. 2024Ptolemy’s theorem – johndcook.com
20. 8. 2024Rule for converting trig identities into hyperbolic identities – johndcook.com
19. 8. 2024Interpolation and the cotanc function – johndcook.com
18. 8. 2024Binomial coefficients with non-integer arguments – johndcook.com
18. 8. 2024Bessel, Everett, and Lagrange interpolation – johndcook.com
17. 8. 2024Compression and interpolation – johndcook.com
16. 8. 2024Chebyshev polynomials as distorted cosines – johndcook.com
13. 8. 2024Math’s base 32 versus Linux’s base 32 – johndcook.com
11. 8. 2024Editing a file without an editor – johndcook.com
9. 8. 2024Interpolating the gamma function – johndcook.com
4. 8. 2024Too clever Monte Carlo – johndcook.com
3. 8. 2024Evaluating a class of infinite sums in closed form – johndcook.com
30. 7. 2024Sphere spilling out – johndcook.com
26. 7. 2024A variation on Rock, Paper, Scissors – johndcook.com
23. 7. 2024q-analog of rising powers – johndcook.com
22. 7. 2024Solvability of linear systems over finite fields – johndcook.com
22. 7. 2024Why do medical tests always have error rates? – johndcook.com
13. 7. 2024Rényi’s parking constant – johndcook.com
6. 7. 2024Calculating when a planet will appear to move backwards – johndcook.com
2. 7. 2024Do incremental improvements add, multiply, or something else? – johndcook.com
1. 7. 2024The Clausen function – johndcook.com
27. 6. 2024Limit of a doodle – johndcook.com
27. 6. 2024National Provider Identifier (NPI) and its checksum – johndcook.com
25. 6. 2024Getting some (algorithmic) SAT-isfaction – johndcook.com
25. 6. 2024Computing Γ(z) for complex z with tables – johndcook.com
25. 6. 2024Calculating trig functions from tables – johndcook.com
20. 6. 2024Rapidly convergent series for ellipse perimeter – johndcook.com
20. 6. 2024Kepler’s ellipse perimeter approximations – johndcook.com
12. 6. 2024Power method and centrality – johndcook.com
10. 6. 2024The search for the perfect prompt – johndcook.com
8. 6. 2024Eigenvector centrality – johndcook.com
5. 6. 2024Fitting a line without an intercept term – johndcook.com
3. 6. 2024Solutions to tan(x) = x – johndcook.com
3. 6. 2024Computing logarithms of complex numbers – johndcook.com
3. 6. 2024Using a table of logarithms – johndcook.com
1. 6. 2024Duct tape value creation – johndcook.com
28. 5. 2024Condition on your data – johndcook.com
28. 5. 2024Can you look at experimental results along the way or not? – johndcook.com
27. 5. 2024One-liner to troubleshoot LaTeX references – johndcook.com
22. 5. 2024A “well-known” series – johndcook.com
21. 5. 2024Probability, cryptography, and naïveté – johndcook.com
20. 5. 2024Thinking by playing around – johndcook.com
13. 5. 2024Approximation by prime powers – johndcook.com
12. 5. 2024Logarithm approximation curiosity – johndcook.com
11. 5. 2024Iterated Mersenne primes – johndcook.com
10. 5. 2024Small probabilities add, big ones don’t – johndcook.com
8. 5. 2024Logistic regression quick takes – johndcook.com
7. 5. 2024Numerical application of mean value theorem – johndcook.com
7. 5. 2024Numerical differentiation with a complex step – johndcook.com
7. 5. 2024MCMC and the coupon collector problem – johndcook.com
4. 5. 2024Up and down the abstraction ladder – johndcook.com
1. 5. 2024Making documents with makefiles – johndcook.com
1. 5. 2024Applied abstraction – johndcook.com
30. 4. 2024A deck of cards – johndcook.com
28. 4. 2024What can JWST see? – johndcook.com
27. 4. 2024Fizz buzz walk – johndcook.com
25. 4. 2024Closed-form solutions to nonlinear PDEs – johndcook.com
24. 4. 2024Choosing a Computer Language for a Project – johndcook.com
22. 4. 2024On greedy algorithms and rodeo clowns – johndcook.com
20. 4. 2024Finding strings in binary files – johndcook.com
20. 4. 2024Extract text from a PDF – johndcook.com
19. 4. 2024Length of a general Archimedean spiral – johndcook.com
18. 4. 2024How big will a carpet be when you roll or unroll it? – johndcook.com
17. 4. 2024Approximating a spiral by rings – johndcook.com
17. 4. 2024Hypergeometric function of a large negative argument – johndcook.com
16. 4. 2024More is less – johndcook.com
12. 4. 2024Precise answers to useless questions – johndcook.com
11. 4. 2024Pairs in poker – johndcook.com
10. 4. 2024Solar system means – johndcook.com
9. 4. 2024Earth : Jupiter :: Jupiter : Sun – johndcook.com
9. 4. 2024Gravity on Jupiter – johndcook.com
5. 4. 2024Are guidance documents laws? – johndcook.com
2. 4. 2024More Laguerre images – johndcook.com
28. 3. 2024A Bayesian approach to proving you’re human – johndcook.com
27. 3. 2024Antenna length: Another rule of 72 – johndcook.com
26. 3. 2024Hallucinations of AI Science Models – johndcook.com
25. 3. 2024Double super factorial – johndcook.com
22. 3. 2024Laguerre’s root finding method – johndcook.com
21. 3. 2024Breach Safe Harbor – johndcook.com
21. 3. 2024MD5 hash collision example – johndcook.com
16. 3. 2024Distance from a point to a line – johndcook.com
15. 3. 2024Experiences with Thread Programming in Microsoft Windows – johndcook.com
14. 3. 2024Accelerating Archimedes – johndcook.com
9. 3. 2024How much will a cable sag? A simple approximation – johndcook.com
9. 3. 2024Unique letter patterns in words – johndcook.com
9. 3. 2024How to Organize Technical Research? – johndcook.com
8. 3. 2024A surprising result about surprise index – johndcook.com
8. 3. 2024Estimating an author’s vocabulary – johndcook.com
7. 3. 2024Detecting the language of encrypted text – johndcook.com
7. 3. 2024Blow up in finite time – johndcook.com
5. 3. 2024Normal subgroups are subtle – johndcook.com
4. 3. 2024Finite differences and Pascal’s triangle – johndcook.com
4. 3. 2024Archiving data on paper – johndcook.com
2. 3. 2024Emails moved to Substack – johndcook.com
2. 3. 2024What’s the Best Code Editor? – johndcook.com
29. 2. 2024Bounding the perimeter of a triangle between circles – johndcook.com
28. 2. 2024Music of the spheres – johndcook.com
28. 2. 2024The Real Book – johndcook.com
27. 2. 2024Substack replacing email subscription – johndcook.com
26. 2. 2024Determinant of an infinite matrix – johndcook.com
25. 2. 2024Area of quadrilateral as a determinant – johndcook.com
24. 2. 2024A very accurate logarithm approximation – johndcook.com
24. 2. 2024Handy approximation for roots of fractions – johndcook.com
23. 2. 2024Uncovering names masked with stars – johndcook.com
23. 2. 2024Almost ASCII – johndcook.com
23. 2. 2024A knight’s tour of an infinite chessboard – johndcook.com
22. 2. 2024Natural one-liners – johndcook.com
22. 2. 2024When is less data less private? – johndcook.com
20. 2. 2024Additive functions – johndcook.com
17. 2. 2024Frequency analysis – johndcook.com
15. 2. 2024Security by obscurity – johndcook.com
14. 2. 2024Advanced questions about a basic diagram – johndcook.com
13. 2. 2024How much metadata is in a photo? – johndcook.com
13. 2. 2024The Borwein integrals – johndcook.com
12. 2. 2024Avoiding Multiprocessing Errors in Bash Shell – johndcook.com
10. 2. 2024This-way-up and Knuth arrows – johndcook.com
10. 2. 2024Factoring pseudoprimes – johndcook.com
8. 2. 2024Do comments in a LaTeX file change the output? – johndcook.com
8. 2. 2024Your PDF may reveal more than you intend – johndcook.com
8. 2. 2024If you save a file as PDF twice, you get two different files – johndcook.com
6. 2. 2024Is Low Precision Arithmetic Safe? – johndcook.com
6. 2. 2024How likely is a random variable to be far from its center? – johndcook.com
3. 2. 2024Connecting the FFT and quadratic reciprocity – johndcook.com
2. 2. 2024Two-digit zip codes – johndcook.com
31. 1. 2024Bessel zero spacing – johndcook.com
30. 1. 2024Coloring the queen’s graph – johndcook.com
29. 1. 2024Regex to match SWIFT-BIC codes – johndcook.com
27. 1. 2024Bad takes on chaos theory – johndcook.com
26. 1. 2024New Ways To Make Code Run Faster – johndcook.com
25. 1. 2024Brute force cryptanalysis – johndcook.com
25. 1. 2024Straddling checkerboard encryption – johndcook.com
23. 1. 2024Email subscription changes – johndcook.com
20. 1. 2024Beta inequality symmetries – johndcook.com
18. 1. 2024When is a function of two variables separable? – johndcook.com
18. 1. 2024Applications of Bernoulli differential equations – johndcook.com
16. 1. 2024The IQ Test That AI Can’t Pass – johndcook.com
16. 1. 2024New Twitter account for cryptography – johndcook.com
16. 1. 2024Means of means bounding the logarithmic mean – johndcook.com
15. 1. 2024Base 64 encoding remainder problem – johndcook.com
13. 1. 2024Binary to text to binary – johndcook.com
12. 1. 2024Why “a caret, euro, trademark” ’ in a file? – johndcook.com
12. 1. 2024A valid character to represent an invalid character – johndcook.com
12. 1. 2024When zeros at natural numbers implies zero everywhere – johndcook.com
10. 1. 2024When High Performance Computing Is Not High Performance – johndcook.com
9. 1. 2024Leading zeros – johndcook.com
9. 1. 2024Ky Fan’s inequality – johndcook.com
6. 1. 2024Previous digital signature standard expires next month – johndcook.com
6. 1. 2024Integral representations of means – johndcook.com
6. 1. 2024Sierpiński’s inequality – johndcook.com
5. 1. 2024The Five Safes data privacy framework – johndcook.com
4. 1. 2024A curious pattern in January exponential sums – johndcook.com
3. 1. 2024The Million Dollar Matrix Multiply – johndcook.com
3. 1. 2024Is there an elliptic curve with 2024 points? – johndcook.com
1. 1. 2024Computing inverse factorial – johndcook.com
1. 1. 2024Square root factorial – johndcook.com
1. 1. 2024Computing square root floor – johndcook.com
1. 1. 2024Groups of order 2024 – johndcook.com
31. 12. 2023Weak encryption and surveillance – johndcook.com
29. 12. 2023Randomize, then humanize – johndcook.com
28. 12. 2023An unusual introduction to manifolds – johndcook.com
28. 12. 2023Example of memorizing a 256-bit private key – johndcook.com
27. 12. 2023Top twelve posts of 2023 – johndcook.com
26. 12. 2023Doomsday 2024 – johndcook.com
20. 12. 2023Addition theorems for Dixon functions – johndcook.com
19. 12. 2023Fermat curve – johndcook.com
19. 12. 2023Conformal map between disk and equilateral triangle – johndcook.com
18. 12. 2023Integrals involving secants and tangents – johndcook.com
15. 12. 2023What is the point of a public key fingerprint? – johndcook.com
13. 12. 2023Fine-grained file differences – johndcook.com
12. 12. 2023The ed line editor: bravado, utility, and history – johndcook.com
12. 12. 2023sin(cos(x)) versus cos(sin(x)) – johndcook.com
11. 12. 2023Rectangles to Rectangles – johndcook.com
11. 12. 2023ASCII armor: send encrypted data in plain text – johndcook.com
7. 12. 2023Why not reuse passwords? – johndcook.com
7. 12. 2023The world’s sneakiest substitution – johndcook.com
6. 12. 2023f(g(x)) versus g(f(x)) – johndcook.com
4. 12. 2023Constellations in Mathematica – johndcook.com
2. 12. 2023222nd Carnival of Mathematics – johndcook.com
2. 12. 2023Bounding complex roots by a positive root – johndcook.com
1. 12. 2023Convergent subsequence – johndcook.com
30. 11. 2023How to memorize the periodic table – johndcook.com
28. 11. 2023Solving a triangle the size of Argentina – johndcook.com
27. 11. 2023Unix linguistics – johndcook.com
26. 11. 2023Numerical integral with a singularity – johndcook.com
26. 11. 2023Radius of a stretched spring – johndcook.com
25. 11. 2023Wrapping Christmas lights around a tree trunk – johndcook.com
23. 11. 2023Database reconstruction attacks – johndcook.com
21. 11. 2023Number of groups of squarefree order – johndcook.com
21. 11. 2023Estimating number of groups of a given order – johndcook.com
20. 11. 2023Period of a nonlinear pendulum – johndcook.com
20. 11. 2023Kepler triangle – johndcook.com
19. 11. 2023Decoupling formal theorem proving effort – johndcook.com
19. 11. 2023Partitioning dots and dashes – johndcook.com
18. 11. 2023Schwarz lemma, Schwarz-Pick theorem, and Poincare metric – johndcook.com
18. 11. 2023Factored random numbers – johndcook.com
18. 11. 2023DICOM image data – johndcook.com
17. 11. 2023Personal information in digital photos – johndcook.com
17. 11. 2023What can you learn from a phone number? – johndcook.com
14. 11. 2023Rational solution to Korteweg–De Vries equation – johndcook.com
13. 11. 2023Ruzsa distance and Ruzsa entropy warmup – johndcook.com
12. 11. 2023US Census area hierarchy – johndcook.com
8. 11. 2023USPS tracking numbers – johndcook.com
8. 11. 2023Zero-Concentrated Differential Privacy – johndcook.com
8. 11. 2023Differentially private stochastic gradient descent – johndcook.com
8. 11. 2023Using dimensional analysis to check probability calculations – johndcook.com
8. 11. 2023Randomized response and local differential privacy – johndcook.com
8. 11. 2023PATE framework for differentially private machine learning – johndcook.com
6. 11. 2023Earth mover’s distance – johndcook.com
5. 11. 2023KL divergence from normal to normal – johndcook.com
4. 11. 2023Normal approximation to normal – johndcook.com
4. 11. 2023Logistic / Normal approximation – johndcook.com
3. 11. 2023Fax machines in the 21st century – johndcook.com
3. 11. 2023Blog RSS feed – johndcook.com
3. 11. 2023Solitons and the KdV equation – johndcook.com
2. 11. 2023A disk around Paris – johndcook.com
1. 11. 2023Using classical statistics to avoid regulatory burden – johndcook.com
1. 11. 2023Executive order on differential privacy – johndcook.com
1. 11. 2023Differential entropy and privacy – johndcook.com
31. 10. 2023Positive polynomials revisited – johndcook.com
30. 10. 2023Identifiers depend on context – johndcook.com
29. 10. 2023Country and language abbreviations – johndcook.com
28. 10. 2023Certifying that a system of polynomial equations has no solution – johndcook.com
27. 10. 2023Time difference – johndcook.com
24. 10. 2023Best of N series – johndcook.com
24. 10. 2023Lessons from Skylab – johndcook.com
24. 10. 2023Curvature: principal, Gauss, and mean – johndcook.com
24. 10. 2023An algebraic superegg – johndcook.com
23. 10. 2023Nonlinear algebra – johndcook.com
22. 10. 2023Stability of a superegg – johndcook.com
22. 10. 2023Best-of-five versus Best-of-seven – johndcook.com
20. 10. 2023The 19th rule of HIPAA Safe Harbor – johndcook.com
19. 10. 2023Bluesky – johndcook.com
18. 10. 2023Portable sed -i across MacOS and Linux – johndcook.com
16. 10. 2023Nearest, easiest, and most accessible – johndcook.com
15. 10. 2023Johnson circle theorem – johndcook.com
14. 10. 2023Newton line – johndcook.com
12. 10. 2023Homework problems are rigged – johndcook.com
11. 10. 2023Python code for means – johndcook.com
11. 10. 2023More ways of splitting the octave – johndcook.com
11. 10. 2023Maclaurin’s inequality – johndcook.com
11. 10. 2023Newton’s inequality and log concave sequences – johndcook.com
10. 10. 2023U statistics and a new paper by Terence Tao – johndcook.com
10. 10. 2023Detecting fraud with the GRIM test – johndcook.com
10. 10. 2023Tritone – johndcook.com
10. 10. 2023When a function cannot be extended – johndcook.com
7. 10. 2023Tanh and elementary symmetric polynomials – johndcook.com
6. 10. 2023Addition theorems – johndcook.com
6. 10. 2023Hyperbolic tangent sum – johndcook.com
5. 10. 2023Tangent sum – johndcook.com
5. 10. 2023Enriched categories – johndcook.com
5. 10. 2023p-norm trig functions and “squigonometry” – johndcook.com
5. 10. 2023Geometric derivation of hyperbolic trig functions – johndcook.com
4. 10. 2023Lemniscate functions – johndcook.com
4. 10. 2023Generalized trigonometry – johndcook.com
3. 10. 2023From graph theory to category theory – johndcook.com
3. 10. 2023Test functions – johndcook.com
3. 10. 2023Groups vs Abelian groups: Pedantic or profound? – johndcook.com
2. 10. 2023Supereggs, squigonometry, and squircles – johndcook.com
2. 10. 2023Corny AI – johndcook.com
2. 10. 2023Today’s star – johndcook.com
30. 9. 2023Consecutive coupon collector problem – johndcook.com
29. 9. 2023Regular solids and Monte Carlo integration – johndcook.com
28. 9. 2023Cross-platform way to enter Unicode characters – johndcook.com
28. 9. 2023Using Unicode on MacOS – johndcook.com
27. 9. 2023Circular coordinate art – johndcook.com
26. 9. 2023When there is only one group of a given size – johndcook.com
26. 9. 2023Analogy between prime numbers and simple groups – johndcook.com
26. 9. 2023Normal and non-normal subgroups – johndcook.com
24. 9. 2023Mersenne primes are unsafe – johndcook.com
24. 9. 2023Victorian public key cryptography – johndcook.com
23. 9. 2023Navigating a LaTeX file – johndcook.com
23. 9. 2023HTML entity data – johndcook.com
23. 9. 2023Double-struck capital letters – johndcook.com
22. 9. 2023Primes, weeds, and military precision – johndcook.com
22. 9. 2023Continued fractions as matrix products – johndcook.com
22. 9. 2023Fractional linear and linear – johndcook.com
21. 9. 2023Naming Awk – johndcook.com
18. 9. 2023Geometric mean on unit circle – johndcook.com
18. 9. 2023Gauss map, Euclidean algorithm, and continued fractions – johndcook.com
18. 9. 2023An elliptic curve is a functor – johndcook.com
17. 9. 2023Elliptic curve addition formulas – johndcook.com
17. 9. 2023Rational height functions – johndcook.com
15. 9. 2023Timing attacks – johndcook.com
15. 9. 2023Elliptic curve Diffie-Hellman key exchange – johndcook.com
15. 9. 2023Finite field Diffie Hellman primes – johndcook.com
14. 9. 2023Chinese Remainder Theorem synthesis algorithm – johndcook.com
14. 9. 2023Gaining efficiency by working modulo factors – johndcook.com
14. 9. 2023Group theory and RSA encryption – johndcook.com
11. 9. 2023Hyperellipsoid surface area – johndcook.com
11. 9. 2023Solve for ellipse axes given perimeter – johndcook.com
11. 9. 2023Possible and actual football scores – johndcook.com
10. 9. 2023How you define center matters a lot – johndcook.com
9. 9. 2023Belt around an elliptical waist – johndcook.com
9. 9. 2023Recursive triangle subdivision – johndcook.com
8. 9. 2023Justifiable sample size – johndcook.com
6. 9. 2023Checksum polynomials – johndcook.com
4. 9. 2023Jordan normal form: 1’s above or below diagonal? – johndcook.com
4. 9. 2023Eigenvectors of the DFT matrix – johndcook.com
3. 9. 2023DFT conventions: NumPy vs Mathematica – johndcook.com
2. 9. 2023DFT mandalas – johndcook.com
31. 8. 2023Sonnets are square – johndcook.com
30. 8. 2023First time seeing a rare event – johndcook.com
29. 8. 2023Stellar magnitude – johndcook.com
29. 8. 2023Area codes – johndcook.com
27. 8. 2023Curvature at Cairo – johndcook.com
27. 8. 2023Calculating the intersection of two circles – johndcook.com
26. 8. 2023A small programming language – johndcook.com
26. 8. 2023Quadrature rules and an impossibility theorem – johndcook.com
24. 8. 2023Jigs – johndcook.com
21. 8. 2023Can the chi squared test detect fake primes? – johndcook.com
21. 8. 2023Mastodon account – johndcook.com
21. 8. 2023Fake primes – johndcook.com
18. 8. 2023Do 5% less – johndcook.com
17. 8. 2023Tracking and the Euler rotation theorem – johndcook.com
17. 8. 2023Using WordNet to create a PAO system – johndcook.com
17. 8. 2023Memorizing four-digit numbers – johndcook.com
17. 8. 2023The numerical range ellipse – johndcook.com
15. 8. 2023Random slices of a sphube – johndcook.com
15. 8. 2023Twin stars and twin primes – johndcook.com
12. 8. 2023Simple way to distribute points on a sphere – johndcook.com
12. 8. 2023Spherical coordinate Rosetta Stone – johndcook.com
10. 8. 2023Creating a Traveling Salesman Tour of Texas with Mathematica – johndcook.com
10. 8. 2023Area and volume of hypersphere cap – johndcook.com
10. 8. 2023Random points in a high-dimensional orthant – johndcook.com
9. 8. 2023Cosine similarity does not satisfy the triangle inequality – johndcook.com
9. 8. 2023Angles between words – johndcook.com
8. 8. 2023Productive constraints – johndcook.com
8. 8. 2023Möbius transformations over a finite field – johndcook.com
7. 8. 2023Sort and remove duplicates – johndcook.com
6. 8. 2023Swish function and a Swiss mathematician – johndcook.com
6. 8. 2023Swish, mish, and serf – johndcook.com
5. 8. 2023Generating and inspecting an RSA private key – johndcook.com
5. 8. 2023RSA encryption in practice – johndcook.com
5. 8. 2023Code to convert words to Major system numbers – johndcook.com
4. 8. 2023Software and the Allee effect – johndcook.com
4. 8. 2023Solved problems becoming unsolved – johndcook.com
4. 8. 2023The cobbler’s son – johndcook.com
3. 8. 2023Date sequence from the command line – johndcook.com
31. 7. 2023Up-down permutations – johndcook.com
31. 7. 2023Variance of binned data – johndcook.com
31. 7. 2023Ancient estimate of π and modern numerical analysis – johndcook.com
30. 7. 2023ARPAbet and the Major mnemonic system – johndcook.com
29. 7. 2023Ruzsa distance – johndcook.com
28. 7. 2023Finding the imaginary part of an analytic function from the real part – johndcook.com
27. 7. 2023Every Japanese prefecture shrinking – johndcook.com
27. 7. 2023Named entity recognition – johndcook.com
26. 7. 2023Jaccard index and jazz albums – johndcook.com
25. 7. 2023Trying NLP on Middle English – johndcook.com
25. 7. 2023Extending harmonic numbers – johndcook.com
25. 7. 2023A note on Zipf’s law – johndcook.com
24. 7. 2023Natural language processing and unnatural text – johndcook.com
23. 7. 2023How rare is it to encounter a rare word? – johndcook.com
23. 7. 2023How an LLM might leak medical data – johndcook.com
19. 7. 2023V-statistics – johndcook.com
18. 7. 2023Filtering on how words are being used – johndcook.com
18. 7. 2023Forever chemicals and blood donation – johndcook.com
17. 7. 2023Searching for proper nouns – johndcook.com
17. 7. 2023Moments of Tukey’s g-and-h distribution – johndcook.com
16. 7. 2023Symmetric functions and U-statistics – johndcook.com
15. 7. 2023Relating perimeter, inner radius, outer radius, and sides of a triangle – johndcook.com
15. 7. 2023Experiments with Bing chat – johndcook.com
15. 7. 2023Boolean function minimization with AI – johndcook.com
14. 7. 2023Large language models and mnemonics – johndcook.com
14. 7. 2023When does a function have an addition theorem? – johndcook.com
12. 7. 2023How to mark a language in HTML – johndcook.com
11. 7. 2023Russian transliteration hack – johndcook.com
11. 7. 2023Symbols for transforms – johndcook.com
10. 7. 2023Visualizing a determinant identity – johndcook.com
10. 7. 2023How Lewis Carroll computed determinants – johndcook.com
10. 7. 2023Gram matrix – johndcook.com
9. 7. 2023Circular, hyperbolic, and elliptic functions – johndcook.com
8. 7. 2023Mnemonic hexagons – johndcook.com
8. 7. 2023Best line to fit three points – johndcook.com
7. 7. 2023Lehman’s inequality, circuits, and LaTeX – johndcook.com
6. 7. 2023Contraharmonic mean quirk – johndcook.com
6. 7. 2023Technological schadenfreude – johndcook.com
5. 7. 2023Complex differential equations – johndcook.com
5. 7. 2023Convert LaTeX to Microsoft Word – johndcook.com
5. 7. 2023Cosine power approximation to Gaussian density – johndcook.com
4. 7. 2023Buy one, get one free – johndcook.com
4. 7. 2023What good is a DE once you have the solution? – johndcook.com
4. 7. 2023Halley’s variation on Newton’s method – johndcook.com
3. 7. 2023Three advantages of non-AI models – johndcook.com
3. 7. 2023Eccentricity of bivariate normal level sets – johndcook.com
2. 7. 2023Bounds on the incomplete beta function (beta CDF) – johndcook.com
2. 7. 2023Upper and lower bounds on the beta function – johndcook.com
2. 7. 2023nth root of n! – johndcook.com
1. 7. 2023Activation functions and Iverson brackets – johndcook.com
30. 6. 2023Cayley graphs in Mathematica – johndcook.com
30. 6. 2023Permutations and centralizers in Mathematica – johndcook.com
30. 6. 2023Floors and roots – johndcook.com
29. 6. 2023Multiplication via parabola – johndcook.com
28. 6. 2023Beta inequalities and cross ratios – johndcook.com
27. 6. 2023The 10th Dedekind number – johndcook.com
27. 6. 2023Enumerating monotone Boolean functions – johndcook.com
26. 6. 2023Drag equation exponent variation – johndcook.com
24. 6. 2023Numbers don’t typically have many prime factors – johndcook.com
23. 6. 2023Every factorial is a power – johndcook.com
22. 6. 2023Mentally approximating factorials – johndcook.com
22. 6. 2023Leading digits of primes – johndcook.com
21. 6. 2023Matching delimiters and chiastic patterns – johndcook.com
19. 6. 2023Equation of an ellipse or hyperbola through five points – johndcook.com
18. 6. 2023A parabola, a triangle, and a circle – johndcook.com
18. 6. 2023Equation of a circle through three points – johndcook.com
17. 6. 2023Set of orbits with the same average distance to sun – johndcook.com
12. 6. 2023Pushing numerical integration routines to their limits – johndcook.com
12. 6. 2023Plotting a function with a lot of local minima – johndcook.com
10. 6. 2023Collecting a large number of coupons – johndcook.com
6. 6. 2023Trig crossings and root of gold – johndcook.com
6. 6. 2023Beta-binomial with given mean and variance – johndcook.com
5. 6. 2023Babies and the beta-binomial distribution – johndcook.com
5. 6. 2023Similar triangles and complex numbers – johndcook.com
3. 6. 2023Powers of a 2×2 matrix in closed form – johndcook.com
3. 6. 2023Productive productivity – johndcook.com
1. 6. 2023Computing Stirling numbers with limited integers – johndcook.com
30. 5. 2023Data file character frequencies – johndcook.com
30. 5. 2023Reviewing a thousand things – johndcook.com
28. 5. 2023Comparing approximations for ellipse perimeter – johndcook.com
26. 5. 2023Instant classic – johndcook.com
25. 5. 2023Occupancy problem distribution – johndcook.com
23. 5. 2023Hypergeometric distribution symmetry – johndcook.com
23. 5. 2023AM over GM – johndcook.com
22. 5. 2023Category theory without categories – johndcook.com
20. 5. 2023Contraharmonic mean – johndcook.com
17. 5. 2023Bibliography histogram – johndcook.com
16. 5. 2023Cofactors, determinants, and adjugates – johndcook.com
15. 5. 2023Arithmetic-harmonic mean – johndcook.com
14. 5. 2023Circulant matrices commute – johndcook.com
14. 5. 2023Relativity, complex numbers, and gyrovectors – johndcook.com
13. 5. 2023Relativistic multiplication – johndcook.com
12. 5. 2023Circulant matrices, eigenvectors, and the FFT – johndcook.com
11. 5. 2023Packing versus unpacking – johndcook.com
10. 5. 2023How faithful can a map be? – johndcook.com
9. 5. 2023Recognizing three-digit primes – johndcook.com
6. 5. 2023Expected distance between points in a cube – johndcook.com
5. 5. 2023Sine of factorial degrees – johndcook.com
5. 5. 2023LTI operators commute – johndcook.com
2. 5. 2023Approximate monthly loan payments – johndcook.com
1. 5. 2023How to memorize Unicode codepoints – johndcook.com
29. 4. 2023Golden integration – johndcook.com
26. 4. 2023Moving between differential and integral equations – johndcook.com
25. 4. 2023Symbols for angles – johndcook.com
25. 4. 2023Overpowered proof that π is transcendental – johndcook.com
24. 4. 2023Beta approximation to binomial – johndcook.com
24. 4. 2023Query, then deidentify – johndcook.com
23. 4. 2023Can you have confidence in a confidence interval? – johndcook.com
21. 4. 2023The essence of chaos – johndcook.com
18. 4. 2023Luhn checksum algorithm – johndcook.com
18. 4. 2023What can you learn from a credit card number? – johndcook.com
17. 4. 2023Tradeoff between alphabet size and word size – johndcook.com
14. 4. 2023How Albrecht Dürer drew an 11-sided figure – johndcook.com
14. 4. 2023Gold, silver, and bronze ratios – johndcook.com
14. 4. 2023A pentagon, hexagon, and decagon walk into a bar … – johndcook.com
14. 4. 2023A new trig identity – johndcook.com
10. 4. 2023Piranhas and prime factors – johndcook.com
10. 4. 2023Density of safe primes – johndcook.com
9. 4. 2023Redoing images in Midjourney – johndcook.com
8. 4. 2023Bringing regex modifiers into the regex – johndcook.com
6. 4. 2023Double duals of polyhedra – johndcook.com
6. 4. 2023Hints of regular solid duality – johndcook.com
4. 4. 2023How to turn an unkeyed hash into a keyed hash – johndcook.com
2. 4. 2023First names and Bayes’ theorem – johndcook.com
1. 4. 2023Identifiable to man or machine? – johndcook.com
1. 4. 2023Privacy and tomography – johndcook.com
31. 3. 2023Engine coolant temperature symbol – johndcook.com
29. 3. 2023Privacy implications of hashing data – johndcook.com
28. 3. 2023Topological sort – johndcook.com
27. 3. 2023“We won’t sell your personal data, but …” – johndcook.com
26. 3. 2023Connecting the dots differently – johndcook.com
24. 3. 2023Famous constants and the Gumbel distribution – johndcook.com
23. 3. 2023Strengthen Markov’s inequality with conditional probability – johndcook.com
21. 3. 2023There’s a woset in my reposit – johndcook.com
20. 3. 2023Solid angle of a star – johndcook.com
17. 3. 2023Fixed points of the Fourier transform – johndcook.com
17. 3. 2023Hyperbolic secant distribution – johndcook.com
16. 3. 2023Two-letter abbreviations. – johndcook.com
16. 3. 2023Interpolating rotations with SLERP – johndcook.com
14. 3. 2023Shuffle product – johndcook.com
13. 3. 2023Prime numbers and Taylor’s law – johndcook.com
12. 3. 2023The coupon collector problem and π – johndcook.com
11. 3. 2023Adding stars to constellations – johndcook.com
10. 3. 2023Plotting constellations – johndcook.com
9. 3. 2023Alien astronomers and Benford’s law – johndcook.com
8. 3. 2023Dutton’s Navigation and Piloting – johndcook.com
7. 3. 2023The NBA and MLB trees are isomorphic – johndcook.com
6. 3. 2023Numbering minor league baseball teams – johndcook.com
3. 3. 2023John Conway’s mental factoring method and friends – johndcook.com
2. 3. 2023Major League Baseball and number theory – johndcook.com
2. 3. 2023A mathematical look at the NFL – johndcook.com
1. 3. 2023How Mr. Benjamin squares numbers – johndcook.com
28. 2. 2023Bounding derivatives of the sinc function – johndcook.com
27. 2. 2023Another Napoleon-like theorem – johndcook.com
27. 2. 2023Playfair cipher – johndcook.com
27. 2. 2023Simple substitution ciphers over a gargantuan alphabet – johndcook.com
26. 2. 2023How Mr. Bidder calculated logarithms – johndcook.com
25. 2. 2023Sine of integers – johndcook.com
24. 2. 2023Derive or memorize? – johndcook.com
22. 2. 2023Divisibility by base + 1 – johndcook.com
21. 2. 2023How large is a Maidenhead field? – johndcook.com
21. 2. 2023Area of a “rectangle” on a globe – johndcook.com
19. 2. 2023F# and G – johndcook.com
18. 2. 2023How well does a spline fit a function? – johndcook.com
16. 2. 2023The Pearson distributions – johndcook.com
16. 2. 2023The other Burr distributions – johndcook.com
14. 2. 2023Burr distribution – johndcook.com
13. 2. 2023Quasiperiodic functions – johndcook.com
12. 2. 2023Rotating multiples of 37 – johndcook.com
9. 2. 2023Recognizing squares – johndcook.com
8. 2. 2023Hénon’s dynamical system – johndcook.com
7. 2. 2023Mediant approximation trick – johndcook.com
2. 2. 2023Lagrange multiplier setup: Now what? – johndcook.com
31. 1. 2023Avoid having to integrate by parts twice – johndcook.com
30. 1. 2023Good autocomplete – johndcook.com
29. 1. 2023Small-scale automation – johndcook.com
26. 1. 2023Remove algorithmic filters from what you read – johndcook.com
25. 1. 2023Number of bits in a particular integer – johndcook.com
24. 1. 2023Lemniscate of Bernoulli – johndcook.com
23. 1. 2023Van Aubel’s theorem – johndcook.com
23. 1. 2023Pythagorean triangles with side 2023 – johndcook.com
22. 1. 2023Heat equation and the normal distribution – johndcook.com
21. 1. 2023Airfoils – johndcook.com
20. 1. 2023Oval orbits? – johndcook.com
20. 1. 2023Cassini ovals – johndcook.com
20. 1. 2023Bounds on power series coefficients – johndcook.com
19. 1. 2023Probability problem with Pratt prime proofs – johndcook.com
19. 1. 2023Factoring b^n + 1 – johndcook.com
19. 1. 2023Factoring b^n – 1 – johndcook.com
18. 1. 2023Converting between barycentric and trilinear coordinates – johndcook.com
17. 1. 2023Special primality proofs – johndcook.com
16. 1. 2023Zeta sum vs zeta product – johndcook.com
16. 1. 2023Approximating pi with Bernoulli numbers – johndcook.com
15. 1. 2023Reverse engineering options – johndcook.com
14. 1. 2023Foreshadowing Page Rank – johndcook.com
13. 1. 2023Third order ordinary differential equations – johndcook.com
13. 1. 2023Proof of optimization – johndcook.com
13. 1. 2023Elliptic curve primality certificates – johndcook.com
12. 1. 2023Primes with two non-zero bits – johndcook.com
12. 1. 2023Certified sonnet primes – johndcook.com
11. 1. 2023Self-documenting software – johndcook.com
10. 1. 2023Approximating 1/Γ(x) – johndcook.com
9. 1. 2023Euler line – johndcook.com
9. 1. 2023Relating circumcenter and orthocenter – johndcook.com
9. 1. 2023Computing inscribed radius and circumscribed radius – johndcook.com
7. 1. 2023Maxwell-Boltzmann and Gamma – johndcook.com
7. 1. 2023Visualizing convergence of an infinite product – johndcook.com
6. 1. 2023Rational Trigonometry – johndcook.com
6. 1. 2023Hidden messages in music – johndcook.com
6. 1. 2023Law of cotangents – johndcook.com
6. 1. 2023Law of tangents – johndcook.com
3. 1. 2023Pratt Primality Certificates – johndcook.com
2. 1. 2023Quadratic reciprocity algorithm – johndcook.com
31. 12. 2022Groups of order 2023 – johndcook.com
29. 12. 2022Sinc approximation to Bessel function – johndcook.com
28. 12. 2022A dozen magic square posts – johndcook.com
27. 12. 2022Airport abbreviation origins – johndcook.com
27. 12. 2022Visually symmetric words – johndcook.com
26. 12. 2022Pascal’s triangle mod row number – johndcook.com
26. 12. 2022Chebyshev series for sine – johndcook.com
26. 12. 2022Solar Day vs Sidereal Day – johndcook.com
22. 12. 2022Coding theory posts – johndcook.com
20. 12. 2022Top posts of 2022 – johndcook.com
19. 12. 2022Polynomial approximations to sine – johndcook.com
18. 12. 2022Euler product for sine – johndcook.com
16. 12. 2022Surprisingly not that surprising – johndcook.com
15. 12. 2022Sphere of infuence – johndcook.com
15. 12. 2022Lagrange’s quintic and Descartes’ rule – johndcook.com
14. 12. 2022Poisson distribution tail bounds – johndcook.com
14. 12. 2022Mentally calculating the day of the week in 2023 – johndcook.com
13. 12. 2022Jacobi functions with complex parameter – johndcook.com
12. 12. 2022Conformal map from rectangles to half plane – johndcook.com
12. 12. 2022Solve for Jacobi sn parameter to have given period(s) – johndcook.com
11. 12. 2022Why determinants with columns of ones? – johndcook.com
9. 12. 2022Conformal map of rectangle to ellipse – johndcook.com
7. 12. 2022Sine of a circle – johndcook.com
7. 12. 2022Test whether three complex numbers lie on an equilateral triangle – johndcook.com
6. 12. 2022Arbitrary precision math in gawk – johndcook.com
5. 12. 2022Unicode arrows: math versus emoji – johndcook.com
5. 12. 2022The Orange Book – johndcook.com
4. 12. 2022What does rotating a matrix do to its determinant? – johndcook.com
4. 12. 2022Area of a triangle in the complex plane – johndcook.com
3. 12. 2022Finding a vector potential whose curl is given – johndcook.com
3. 12. 2022Conservative vector fields – johndcook.com
3. 12. 2022{div, grad, curl} of a {div, grad, curl} – johndcook.com
2. 12. 2022Arabic numerals and numerals that are Arabic – johndcook.com
1. 12. 2022Telescopes, awk, and learning – johndcook.com
1. 12. 2022The messy version of Napoleon’s theorem – johndcook.com
30. 11. 2022Napoleon’s theorem – johndcook.com
30. 11. 2022Trilinear coordinates – johndcook.com
30. 11. 2022Unexpected symmetry – johndcook.com
30. 11. 2022Elliptic functions of a complex argument in Python – johndcook.com
28. 11. 2022Conformal map between square and disk – johndcook.com
28. 11. 2022Conformal map of ellipse interior to a disk – johndcook.com
26. 11. 2022Big correlations and big interactions – johndcook.com
26. 11. 2022Incircle and excircles – johndcook.com
26. 11. 2022Double final consonants – johndcook.com
25. 11. 2022Artemis lunar orbit – johndcook.com
25. 11. 2022Feuerbach’s nine-point circle theorem – johndcook.com
23. 11. 2022The Möbius Inverse Monoid – johndcook.com
23. 11. 2022Locally invertible floating point functions – johndcook.com
23. 11. 2022Solving Laplace’s equation in the upper half plane – johndcook.com
22. 11. 2022Solving Laplace’s equation on a disk – johndcook.com
21. 11. 2022Posts on ellipses and elliptic integrals – johndcook.com
21. 11. 2022Design of experiments and design theory – johndcook.com
21. 11. 2022Repunits: primes and passwords – johndcook.com
20. 11. 2022Recent posts on solving equations – johndcook.com
20. 11. 2022Expert witness experiences – johndcook.com
19. 11. 2022Eliminating terms from higher-order differential equations – johndcook.com
19. 11. 2022How to depress a general polynomial – johndcook.com
19. 11. 2022How to solve a cubic equation – johndcook.com
19. 11. 2022How to depress a cubic – johndcook.com
18. 11. 2022New SI prefixes and their etymology – johndcook.com
18. 11. 2022Calculating sine to an absurd number of digits – johndcook.com
18. 11. 2022Simple example of Kleisli composition – johndcook.com
17. 11. 2022Getting pulled back in – johndcook.com
16. 11. 2022Exploring bad passwords – johndcook.com
16. 11. 2022When a cubic or quartic has a double root – johndcook.com
15. 11. 2022Entropy of a Student t distribution – johndcook.com
14. 11. 2022Solving quadratic trig equations – johndcook.com
14. 11. 2022Simultaneous root-finding – johndcook.com
14. 11. 2022Mercator and polar projections – johndcook.com
10. 11. 2022Straight on a map or straight on a globe? – johndcook.com
9. 11. 2022Elliptic coordinates and Laplace’s equation – johndcook.com
9. 11. 2022Computing arccos – johndcook.com
9. 11. 2022Three diagrams – johndcook.com
7. 11. 2022Carlson’s elliptic integrals – johndcook.com
7. 11. 2022Kinds of elliptic integrals – johndcook.com
6. 11. 2022Three interesting curves – johndcook.com
6. 11. 2022What is a Pentanomial GFSR random number generator? – johndcook.com
5. 11. 2022Systematically solving trigonometric equations – johndcook.com
4. 11. 2022Nephroids and evolutes – johndcook.com
4. 11. 2022Evolute of an ellipse – johndcook.com
3. 11. 2022Newton’s method: The Good, The Bad, and The Ugly – johndcook.com
2. 11. 2022Uniform sampling from an ellipse – johndcook.com
2. 11. 2022How to calculate length of an elliptic arc – johndcook.com
2. 11. 2022Python code to solve Kepler’s equation – johndcook.com
1. 11. 2022Solving Kepler’s equation with Newton’s method – johndcook.com
1. 11. 2022The world is lumpy – johndcook.com
31. 10. 2022Another problem with A/B testing: interaction effects – johndcook.com
31. 10. 2022A/B testing and a voting paradox – johndcook.com
30. 10. 2022Smoothly extending arctan(k tan(t)) – johndcook.com
29. 10. 2022Random illustrations of Pascal’s theorem – johndcook.com
28. 10. 2022Finding where two quadratic curves intersect – johndcook.com
27. 10. 2022A more convenient squircle equation – johndcook.com
26. 10. 2022Determining a conic by points and tangents – johndcook.com
26. 10. 2022Four views of multisets – johndcook.com
26. 10. 2022Lambert’s theorem – johndcook.com
25. 10. 2022Gibbs’ method of determining an orbit – johndcook.com
25. 10. 2022ASQ/ANSI Z1.4 sampling procedures – johndcook.com
25. 10. 2022Five points determine a conic section – johndcook.com
24. 10. 2022Sharing data without letting it go – johndcook.com
24. 10. 2022Robustness of mean range – johndcook.com
24. 10. 2022Average digit sum – johndcook.com
24. 10. 2022Using mean range method to measure variability – johndcook.com
22. 10. 2022Elliptical orbit example: Mars Orbiter Mission – johndcook.com
22. 10. 2022Military Standard 105 – johndcook.com
22. 10. 2022Mean anomaly, true anomaly, and eccentric anomaly – johndcook.com
21. 10. 2022Cryptography, hydrodynamics, and celestial mechanics – johndcook.com
21. 10. 2022Repeat shell command replacing a word – johndcook.com
20. 10. 2022How eccentricity matters – johndcook.com
20. 10. 2022Directrix of a conic – johndcook.com
20. 10. 2022Latus rectum of an ellipse – johndcook.com
20. 10. 2022Inequalities for inequality: Gini coefficient lower bounds – johndcook.com
19. 10. 2022Trading generalized derivatives for classical ones – johndcook.com
18. 10. 2022The view from a Galilean moon – johndcook.com
18. 10. 2022What if Copernicus had been a Martian? – johndcook.com
17. 10. 2022How the orbit of one planet appears from another – johndcook.com
15. 10. 2022Using Python as a statistical calculator – johndcook.com
14. 10. 2022Eccentricity, Flattening, and Aspect Ratio – johndcook.com
13. 10. 2022Planetary orbits are very nearly circular – johndcook.com
13. 10. 2022Saving money on big queries – johndcook.com
13. 10. 2022The Pluto-Charon orbit – johndcook.com
13. 10. 2022Shape of moon orbit around sun – johndcook.com
12. 10. 2022A more direct approach to series solutions – johndcook.com
12. 10. 2022Operator calculus – johndcook.com
11. 10. 2022Writing math with Unicode – johndcook.com
11. 10. 2022Cicadas and Chicken Nuggets – johndcook.com
10. 10. 2022The Chicken McNugget Monoid – johndcook.com
10. 10. 2022Efficiently testing a black box – johndcook.com
8. 10. 2022Which one is subharmonic? – johndcook.com
7. 10. 2022Ideograph numerals – johndcook.com
7. 10. 2022Unicode numbers – johndcook.com
6. 10. 2022Regex to match ICD-11 code – johndcook.com
6. 10. 2022The Very Model of a Professor Statistical – johndcook.com
5. 10. 2022Sum of squares mod n uniformly distributed – johndcook.com
5. 10. 2022Quirks in Mathematica’s administrative division data for Mexico – johndcook.com
4. 10. 2022Visualizing Swedish vowels – johndcook.com
4. 10. 2022A traveling salesman tour of Canada – johndcook.com
3. 10. 2022Ligatures for Logic – johndcook.com
2. 10. 2022Making flags in Unicode – johndcook.com
1. 10. 2022Visualizing English and Japanese vowels – johndcook.com
30. 9. 2022Preventing characters from displaying as emoji – johndcook.com
29. 9. 2022Day of the year – johndcook.com
28. 9. 2022The original Room square – johndcook.com
27. 9. 2022Visualizing correlations with graphs – johndcook.com
25. 9. 2022Katakana, Hiragana, and Unicode – johndcook.com
24. 9. 2022Room squares and Tournaments – johndcook.com
23. 9. 2022HCPCS (“hick pics”) codes – johndcook.com
22. 9. 2022Dominoes in Unicode – johndcook.com
21. 9. 2022Raging against the machine – johndcook.com
21. 9. 2022Field of order 9 – johndcook.com
20. 9. 2022Costas arrays in Mathematica – johndcook.com
19. 9. 2022Two-letter vs Three-letter Country Abbreviations – johndcook.com
19. 9. 2022Finding similar world flags with Mathematica – johndcook.com
18. 9. 2022Costas arrays – johndcook.com
17. 9. 2022Balanced tournament designs – johndcook.com
12. 9. 2022Graphing Japanese Prefectures – johndcook.com
12. 9. 2022Classroom exercise with networks – johndcook.com
12. 9. 2022Adjacency networks – johndcook.com
9. 9. 2022Shortest tours of Eurasia and Oceania – johndcook.com
9. 9. 2022Three tours of the Americas – johndcook.com
9. 9. 2022A traveling salesman tour of Africa – johndcook.com
8. 9. 2022Trig in hyperbolic geometry – johndcook.com
6. 9. 2022Eliminating a Bessel function branch cut – johndcook.com
6. 9. 2022Branch cuts for elementary functions – johndcook.com
6. 9. 2022Series for inverse cosine at 1 – johndcook.com
6. 9. 2022Literate programming to reduce errors – johndcook.com
4. 9. 2022Computing VIN checksums – johndcook.com
2. 9. 2022Square root mnemonics – johndcook.com
1. 9. 2022Runs of letters and digits in passwords – johndcook.com
30. 8. 2022Modal logic posts – johndcook.com
28. 8. 2022Radius, circumference, and area in non-Euclidean geometry – johndcook.com
27. 8. 2022Unified Pythagorean Theorem – johndcook.com
26. 8. 2022Can Brownian motion do work? – johndcook.com
24. 8. 2022Direction between two cities – johndcook.com
24. 8. 2022Law of cosines on a sphere – johndcook.com
23. 8. 2022Pythagoras on a sphere – johndcook.com
23. 8. 2022Chimera and sine of 60° – johndcook.com
17. 8. 2022Cross platform muscle memory – johndcook.com
17. 8. 2022More on near-integer decibels – johndcook.com
16. 8. 2022Dump a pickle file to a readable text file – johndcook.com
16. 8. 2022Duodecibels – johndcook.com
15. 8. 2022Keeping data and code together with org-mode – johndcook.com
15. 8. 2022YYZ and Morse code – johndcook.com
9. 8. 2022Twitter follower distribution – johndcook.com
9. 8. 2022Mahler’s inequality – johndcook.com
8. 8. 2022Code katas taken more literally – johndcook.com
8. 8. 2022Seconds to hours – johndcook.com
6. 8. 2022Memorizing Planck’s constant with DALL-E – johndcook.com
6. 8. 2022DALL-E 2 and mnemonic images – johndcook.com
5. 8. 2022Naming probability functions – johndcook.com
5. 8. 2022Floating point inverses and stability – johndcook.com
3. 8. 2022Inline computed content in org-mode – johndcook.com
2. 8. 2022Org-mode as a lightweight notebook – johndcook.com
31. 7. 2022Not so fast – johndcook.com
30. 7. 2022Complex AGM – johndcook.com
28. 7. 2022Galois theory without fields – johndcook.com
25. 7. 2022Galois connections and Galois theory – johndcook.com
21. 7. 2022Helmholtz resonator revisited – johndcook.com
21. 7. 2022Ratio test counterexample – johndcook.com
20. 7. 2022Whittaker and Watson – johndcook.com
19. 7. 2022Keyhole contour integrals – johndcook.com
18. 7. 2022Galois diagram – johndcook.com
18. 7. 2022Book cover posts – johndcook.com
17. 7. 2022Aristeia – johndcook.com
15. 7. 2022Gaussian elimination – johndcook.com
12. 7. 2022Conway’s factoring trick – johndcook.com
10. 7. 2022Adding a tiny trap to stop chaos – johndcook.com
10. 7. 2022Ducci sequences – johndcook.com
7. 7. 2022Dijkstra extends Pythagoras – johndcook.com
1. 7. 2022Phi Phi – johndcook.com
30. 6. 2022Speculation on new SI prefixes – johndcook.com
27. 6. 2022NASA and conformal maps – johndcook.com
26. 6. 2022Transformations of Olympic rings – johndcook.com
26. 6. 2022Circles and lines under a Möbius transformation – johndcook.com
25. 6. 2022Reciprocal of a circle – johndcook.com
24. 6. 2022Computing zeta at even numbers – johndcook.com
24. 6. 2022Constructive Picard – johndcook.com
24. 6. 2022No analytic bump – johndcook.com
24. 6. 2022Bump functions – johndcook.com
23. 6. 2022The quality of an RNG depends on the application – johndcook.com
22. 6. 2022Numerically evaluating a theta function – johndcook.com
19. 6. 2022Illegible work – johndcook.com
18. 6. 2022Length of periods in the (infinite) periodic table – johndcook.com
18. 6. 2022Doubly periodic but not analytic – johndcook.com
16. 6. 2022Letter-like Unicode symbols – johndcook.com
16. 6. 2022Periodic table of abbreviations – johndcook.com
15. 6. 2022Continued fractions as matrix products – johndcook.com
13. 6. 2022Greek letter paradox – johndcook.com
13. 6. 2022Double roots and ODEs – johndcook.com
12. 6. 2022Difference equations and differential equations – johndcook.com
11. 6. 2022Generating functions for polynomial sequences – johndcook.com
11. 6. 2022Generating noble gases – johndcook.com
8. 6. 2022Infinite periodic table – johndcook.com
6. 6. 2022A footnote to year share – johndcook.com
4. 6. 2022Inverse tetrahedral numbers – johndcook.com
4. 6. 2022General tetrahedral numbers – johndcook.com
3. 6. 2022Visualizing C operator precedence – johndcook.com
1. 6. 2022My interview in SIAM News – johndcook.com
1. 6. 2022Numeric distance vs geographic distance in zip codes – johndcook.com
1. 6. 2022Zip codes, geocodes, and Hilbert curves – johndcook.com
30. 5. 2022Conspicuously missing data – johndcook.com
28. 5. 2022How to memorize the ASCII table – johndcook.com
25. 5. 2022Harmonic e – johndcook.com
23. 5. 2022Voiced and unvoiced consonants and digits – johndcook.com
23. 5. 2022Year share – johndcook.com
21. 5. 2022Decoding a grid square – johndcook.com
21. 5. 2022Exponential of a line – johndcook.com
21. 5. 2022Discrete derivatives – johndcook.com
17. 5. 2022Chemical element abbreviation patterns – johndcook.com
16. 5. 2022Mental hash function – johndcook.com
14. 5. 2022Sampling with replacement until you’ve seen everything – johndcook.com
12. 5. 2022Tool recursion – johndcook.com
11. 5. 2022New Twitter account: ElementFact – johndcook.com
10. 5. 2022Approximating a golden spiral with circular arcs – johndcook.com
9. 5. 2022Logarithmic spiral – johndcook.com
9. 5. 2022Iterated golden rectangles in detail – johndcook.com
7. 5. 2022Mentally calculating the day of the week – johndcook.com
5. 5. 2022John Conway and mental exercise rituals – johndcook.com
3. 5. 2022Quartal melody: Star Trek fanfare – johndcook.com
2. 5. 2022Why target ads at pregnant women – johndcook.com
2. 5. 2022Curiously simple approximations – johndcook.com
27. 4. 2022Calculating where projective lines intersect – johndcook.com
26. 4. 2022Random Blaschke products and Mathematica binding – johndcook.com
25. 4. 2022Projective duality – johndcook.com
25. 4. 2022Finite projective planes – johndcook.com
21. 4. 2022Fixed points of bilinear transformations – johndcook.com
21. 4. 2022Partitioning complexity – johndcook.com
20. 4. 2022French palindromes and Morse code – johndcook.com
20. 4. 2022Blaschke factors – johndcook.com
19. 4. 2022Inversion in a circle – johndcook.com
14. 4. 2022How flat is a normal mixture on top? – johndcook.com
13. 4. 2022Hilbert transform and Fourier series – johndcook.com
13. 4. 2022Logarithms yearning to be free – johndcook.com
11. 4. 2022Circular slide rule – johndcook.com
10. 4. 2022Why a slide rule works – johndcook.com
8. 4. 2022Hilbert transform and Mathematica – johndcook.com
8. 4. 2022Visual integration – johndcook.com
7. 4. 2022Regular expressions and successive approximation – johndcook.com
6. 4. 2022Sum the zeros of an analytic function without finding them first – johndcook.com
5. 4. 2022Bounding zeros of an analytic function – johndcook.com
5. 4. 2022Numerically finding roots of a cubic – johndcook.com
5. 4. 2022Mathematics and piano tuning – johndcook.com
4. 4. 2022Computing functions of roots without computing roots – johndcook.com
4. 4. 2022FWHM for a quadratic – johndcook.com
4. 4. 2022Number slang and numbered lists – johndcook.com
2. 4. 2022Oscillations in RLC circuits – johndcook.com
30. 3. 2022How is portable AM radio possible? – johndcook.com
30. 3. 2022Applications of continued fractions – johndcook.com
29. 3. 2022Smoothed step function – johndcook.com
29. 3. 2022Partitions of unity, smooth ramps, and CW clicks – johndcook.com
28. 3. 2022Looking for the next prime – johndcook.com
28. 3. 2022Seed vault, but for code – johndcook.com
24. 3. 2022Series for π – johndcook.com
23. 3. 2022Morse code numbers and abbreviations – johndcook.com
22. 3. 2022Multiple Frequency Shift Keying – johndcook.com
22. 3. 2022Dial tone and busy signal – johndcook.com
21. 3. 2022Solar declination – johndcook.com
20. 3. 2022Reverse engineering Fourier conventions – johndcook.com
16. 3. 2022Dividing an octave into 14 pieces – johndcook.com
14. 3. 2022Phone tones in musical notation – johndcook.com
13. 3. 2022Frequency shift keying (FSK) spectrum – johndcook.com
10. 3. 2022Approximating the range of normal samples – johndcook.com
10. 3. 2022Order statistics for normal distributions – johndcook.com
9. 3. 2022Range trick for larger sample sizes – johndcook.com
7. 3. 2022Estimating standard deviation from range – johndcook.com
2. 3. 2022Varicode – johndcook.com
1. 3. 2022Catenary kiln – johndcook.com
28. 2. 2022Connecting powers of two and decibels – johndcook.com
27. 2. 2022100 digits worth memorizing – johndcook.com
26. 2. 2022Morse code in musical notation – johndcook.com
25. 2. 2022Find log normal parameters for given mean and variance – johndcook.com
21. 2. 2022Q codes in Seveneves – johndcook.com
18. 2. 2022Algorithms at Work – johndcook.com
17. 2. 2022What use is mental math in 2022? – johndcook.com
17. 2. 2022Missing Morse codes – johndcook.com
16. 2. 2022Almost periodic functions – johndcook.com
16. 2. 20222s, 5s, and decibels – johndcook.com
12. 2. 2022A Bayesian approach to pricing – johndcook.com
9. 2. 2022Chaos in the frequency domain – johndcook.com
9. 2. 2022The tent map – johndcook.com
9. 2. 2022Aliasing in a nutshell – johndcook.com
8. 2. 2022Lyapunov exponents – johndcook.com
7. 2. 2022Self-orthogonal vectors and coding – johndcook.com
7. 2. 2022Ternary Golay code in Python – johndcook.com
4. 2. 2022A closer look at zero spacing – johndcook.com
1. 2. 2022Associahedron – johndcook.com
1. 2. 2022Non-associative multiplication – johndcook.com
30. 1. 2022Slowing oscillations – johndcook.com
28. 1. 2022Mental math trick and deeper issues – johndcook.com
27. 1. 2022Information in a discretized normal – johndcook.com
26. 1. 2022A general theory of sub-things – johndcook.com
26. 1. 2022How to subscribe – johndcook.com
26. 1. 2022Non-equivalent floating point numbers – johndcook.com
26. 1. 2022Temporal and polymodal logics – johndcook.com
25. 1. 2022Permutations at the command line – johndcook.com
24. 1. 2022Look up HTML entity or Unicode – johndcook.com
24. 1. 2022Complex analysis calendar – johndcook.com
24. 1. 2022Dual axioms in modal logic – johndcook.com
24. 1. 2022Word problems, logic, and regular expressions – johndcook.com
22. 1. 2022Modal axioms and rules for interplanetary travel – johndcook.com
21. 1. 2022Modal Logic and Science Fiction – johndcook.com
20. 1. 2022Reading plots of a complex function – johndcook.com
20. 1. 2022Glasser’s function – johndcook.com
19. 1. 2022Upper bound on wait time for general queues – johndcook.com
15. 1. 2022Multiserver queues with general probability distributions – johndcook.com
15. 1. 2022Queueing and Economies of Scale – johndcook.com
15. 1. 2022Linear logic arithmetic – johndcook.com
13. 1. 2022Self-Orthogonal Latin Squares – johndcook.com
13. 1. 2022Better parts, worse system – johndcook.com
12. 1. 2022Queueing theory equations – johndcook.com
12. 1. 2022Swanson’s rule of thumb – johndcook.com
11. 1. 2022Random sampling to save money – johndcook.com
11. 1. 2022Greco-Latin squares and magic squares – johndcook.com
11. 1. 2022Latin squares and 3D chess – johndcook.com
11. 1. 2022New R book – johndcook.com
10. 1. 2022Computational asceticism – johndcook.com
9. 1. 2022Beatty’s theorem – johndcook.com
9. 1. 2022Corner quotes in Unicode – johndcook.com
8. 1. 2022Three paths converge – johndcook.com
6. 1. 2022One diagram, two completely different meanings – johndcook.com
5. 1. 2022Memorable techniques – johndcook.com
1. 1. 2022Architecture and Math – johndcook.com
1. 1. 2022Turning the Golay problem sideways – johndcook.com
31. 12. 2021Update on the Golay problem – johndcook.com
30. 12. 2021Names and numbers for modal logic axioms – johndcook.com
30. 12. 2021When do two-body systems have stable Lagrange points? – johndcook.com
28. 12. 2021Finding Lagrange points L1 and L2 – johndcook.com
28. 12. 2021Most popular posts of 2021 – johndcook.com
27. 12. 2021The exception case is normal – johndcook.com
27. 12. 2021Binomial sums and powers of 2 – johndcook.com
24. 12. 2021O Come, O Come, Emmanuel: condensing seven hymns into one – johndcook.com
20. 12. 2021Error correcting code from octonions – johndcook.com
20. 12. 2021Conjugate theorem for octonions – johndcook.com
20. 12. 2021How to multiply octonions – johndcook.com
18. 12. 2021Complex Conjugates versus Quaternion Conjugates – johndcook.com
18. 12. 2021The center may not hold – johndcook.com
17. 12. 2021The congruent number problem – johndcook.com
14. 12. 2021Aesthetic uses of Latin squares – johndcook.com
13. 12. 2021Know the rules to break the rules – johndcook.com
13. 12. 2021How many Latin squares are there? – johndcook.com
12. 12. 2021Yule statistics Y and Q – johndcook.com
12. 12. 2021Deleting reproducible files in Emacs dired – johndcook.com
11. 12. 2021Fraud, Sloppiness, and Statistics – johndcook.com
11. 12. 2021Comparing three discrete power laws – johndcook.com
10. 12. 2021The zeta distribution – johndcook.com
10. 12. 2021Yule-Simon distribution – johndcook.com
10. 12. 2021Mahalanobis distance and Henry V – johndcook.com
9. 12. 2021Probability of a magical permutation – johndcook.com
9. 12. 2021Degree of magic – johndcook.com
8. 12. 2021Universal properties – johndcook.com
7. 12. 2021The ring of entire functions – johndcook.com
7. 12. 2021The awkward middle child of algebra – johndcook.com
6. 12. 2021Partial functions and total functions – johndcook.com
4. 12. 2021Exact sequences – johndcook.com
3. 12. 2021Data swamps – johndcook.com
3. 12. 2021Numerical footnote – johndcook.com
2. 12. 2021Four, five, and nine lemmas – johndcook.com
1. 12. 2021T test with unequal variances – johndcook.com
1. 12. 20213D Go with identities – johndcook.com
30. 11. 2021Area of spherical triangle directly from vertices – johndcook.com
28. 11. 2021Triangles on a pseudosphere – johndcook.com
26. 11. 2021A tale of three cities – johndcook.com
26. 11. 2021Great circle through two points on a sphere – johndcook.com
24. 11. 2021Wire gauge and user perspective – johndcook.com
22. 11. 2021New twitter account: tensor_fact – johndcook.com
18. 11. 2021How to put a series in hypergeometric form – johndcook.com
18. 11. 2021Quintic trinomial root – johndcook.com
17. 11. 2021Theory, practice, and integration – johndcook.com
16. 11. 2021Information loss and entropy – johndcook.com
16. 11. 2021Partition symmetry – johndcook.com
15. 11. 2021Numbering the branches of the Lambert W function – johndcook.com
14. 11. 2021Solving equations with Lambert’s W function – johndcook.com
14. 11. 2021Estimating the number of integer partitions – johndcook.com
12. 11. 2021Vector spaces and subspaces over finite fields – johndcook.com
12. 11. 2021Mathematical plot twist: q-binomial coefficients – johndcook.com
11. 11. 2021Another pentagonal number theorem – johndcook.com
11. 11. 2021Odd parts and distinct parts – johndcook.com
10. 11. 2021Partitions and Pentagons – johndcook.com
9. 11. 2021Rising and falling powers – johndcook.com
9. 11. 2021Three kinds of confluence – johndcook.com
8. 11. 2021Three error function series – johndcook.com
7. 11. 2021A more powerful alternating series theorem – johndcook.com
7. 11. 2021Gamma distribution tail probability approximation – johndcook.com
6. 11. 2021The 1/e heuristic – johndcook.com
5. 11. 2021Simple normal distribution tail estimate – johndcook.com
5. 11. 2021Marden’s amazing theorem – johndcook.com
5. 11. 2021Convex hull of zeros – johndcook.com
3. 11. 2021Escaping the unit disk – johndcook.com
3. 11. 2021Raabe’s convergence test – johndcook.com
3. 11. 2021Hypergeometric equation – johndcook.com
3. 11. 2021It seemed like a good idea at the time – johndcook.com
2. 11. 2021Fractions in Unicode – johndcook.com
1. 11. 2021Number sets in HTML and Unicode – johndcook.com
1. 11. 2021Unicode superscripts and subscripts – johndcook.com
31. 10. 2021Connections – johndcook.com
29. 10. 2021Foreshadowing hypergeometric functions – johndcook.com
28. 10. 2021Hidden double factorial example – johndcook.com
28. 10. 2021Euler polynomials – johndcook.com
27. 10. 2021Logistic counterexamples – johndcook.com
27. 10. 2021Dirichlet series generating functions – johndcook.com
26. 10. 2021Unintended programming languages – johndcook.com
24. 10. 2021An interesting recursion – johndcook.com
24. 10. 2021Dirichlet convolution – johndcook.com
23. 10. 2021Nota bene – johndcook.com
21. 10. 2021What’s “differential” about differential privacy? – johndcook.com
19. 10. 2021Everywhere chaotic map on the sphere – johndcook.com
18. 10. 2021Quadruple factorials and Legendre functions – johndcook.com
18. 10. 2021Triple factorials and Airy functions – johndcook.com
18. 10. 2021Gauss’s constant – johndcook.com
14. 10. 2021Gamma of integer plus one over integer – johndcook.com
14. 10. 2021Multifactorial – johndcook.com
14. 10. 2021Discrete sum analog of Gaussian integral – johndcook.com
14. 10. 2021The Calculus of Finite Differences – johndcook.com
11. 10. 2021Multiple angle identify for cotangent – johndcook.com
11. 10. 2021Multiplication theorem rabbit hole – johndcook.com
7. 10. 2021Gamma and the Pi function – johndcook.com
7. 10. 2021Why is it defined that way? – johndcook.com
7. 10. 2021Sawtooth and replicative functions – johndcook.com
6. 10. 2021Aquinas on epicycles – johndcook.com
5. 10. 2021Estimating normal tail extreme probabilities – johndcook.com
4. 10. 202150 sigma events for t distributions – johndcook.com
4. 10. 2021Guide to the recent flurry of posts – johndcook.com
4. 10. 2021Trailing zeros of factorials, revisited – johndcook.com
3. 10. 2021Filling in gaps in a trig table – johndcook.com
2. 10. 2021Tables and interpolation – johndcook.com
2. 10. 2021Calculating without electricity – johndcook.com
2. 10. 2021Floor exercises – johndcook.com
2. 10. 2021Factorial random number generator – johndcook.com
1. 10. 2021Power law principles are not about power laws – johndcook.com
30. 9. 2021Much ado about NaN – johndcook.com
30. 9. 2021Nonlinear ODEs with stable limit cycles – johndcook.com
29. 9. 2021Linear ODEs with periodic solutions – johndcook.com
28. 9. 2021Reciprocals of prime powers – johndcook.com
26. 9. 2021Monads and Macros – johndcook.com
21. 9. 2021Combinators and Catalan numbers – johndcook.com
18. 9. 2021Planetary code golf – johndcook.com
16. 9. 2021Beta inequalities with integer parameters – johndcook.com
16. 9. 2021Unix via etymology – johndcook.com
15. 9. 2021Carbon nanotube-like plots – johndcook.com
14. 9. 2021Why is the word problem hard? – johndcook.com
11. 9. 2021Much less than, Much greater than – johndcook.com
11. 9. 2021Integer sines – johndcook.com
9. 9. 2021Double, triple, quadruple, … – johndcook.com
9. 9. 2021Functions in bc – johndcook.com
9. 9. 2021Planning a world record calculation – johndcook.com
8. 9. 2021Dunbar’s number and C. S. Lewis – johndcook.com
8. 9. 2021kn choose n – johndcook.com
8. 9. 2021Calculating ζ(3) faster – johndcook.com
7. 9. 2021When derivative equals inverse – johndcook.com
6. 9. 2021Parallel versus sequential binding – johndcook.com
4. 9. 2021Morse code palindromes – johndcook.com
2. 9. 2021Spreading out points on a sphere – johndcook.com
2. 9. 2021Quasi-Monte Carlo integration: periodic and nonperiodic – johndcook.com
31. 8. 2021Differential Equations and Department Stores – johndcook.com
28. 8. 2021Empirical formula for the shape of an egg – johndcook.com
28. 8. 2021Computing ζ(3) – johndcook.com
25. 8. 2021How small can a multiplicative group be? – johndcook.com
25. 8. 2021Encryption in groups of unknown order – johndcook.com
25. 8. 2021Logic in moral terminology – johndcook.com
24. 8. 2021Missing data – johndcook.com
24. 8. 2021Also a crypto library – johndcook.com
23. 8. 2021Naive compression of genetic data – johndcook.com
22. 8. 2021FM signal approximation – johndcook.com
21. 8. 2021Black Swan Gratification – johndcook.com
19. 8. 2021Using cryptography broken 50 years ago – johndcook.com
18. 8. 2021Unicode and Emoji, or The Giant Pawn Mystery – johndcook.com
18. 8. 2021Queens on a donut – johndcook.com
18. 8. 2021How to make a chessboard in Excel – johndcook.com
16. 8. 2021Initial letter frequency – johndcook.com
16. 8. 2021Lake Wobegon Dice – johndcook.com
14. 8. 2021Index of coincidence – johndcook.com
14. 8. 2021S and C functions – johndcook.com
12. 8. 2021Offline documentation – johndcook.com
11. 8. 2021Engineering attitude – johndcook.com
10. 8. 2021Searching for pseudoprimes – johndcook.com
10. 8. 2021Finding computer algebra algorithms with computer algebra – johndcook.com
8. 8. 2021Approximate minimal bounding sphere – johndcook.com
3. 8. 2021Complex floor and a surprising pattern – johndcook.com
2. 8. 2021Plotting the Gauss map – johndcook.com
2. 8. 2021Collatz analog in C – johndcook.com
1. 8. 20213D bifurcation diagram – johndcook.com
31. 7. 2021Where has all the productivity gone? – johndcook.com
30. 7. 2021Alt tags on tweet images – johndcook.com
30. 7. 2021Nonlinear phase portrait – johndcook.com
28. 7. 2021Polynomial analog of the Collatz conjecture – johndcook.com
26. 7. 2021Major memory system telephone keypad – johndcook.com
25. 7. 2021Approximation error over unit disk – johndcook.com
25. 7. 2021Simple derivation of exponential approximation – johndcook.com
23. 7. 2021Upper case, lower case, title case – johndcook.com
22. 7. 2021Continued fraction from entropy source testing – johndcook.com
19. 7. 2021Removing Unicode formatting – johndcook.com
19. 7. 2021How to format text in Twitter – johndcook.com
14. 7. 2021Predator-Prey period – johndcook.com
14. 7. 2021Error estimates for splines with more boundary conditions – johndcook.com
13. 7. 2021Random Fourier series – johndcook.com
12. 7. 2021Rate of natural cubic spline convergence – johndcook.com
11. 7. 2021The fractal nature of Brownian motion – johndcook.com
10. 7. 2021Monotonic interpolation – johndcook.com
10. 7. 2021Interpolating Brownian motion – johndcook.com
9. 7. 2021Anything that starts with an integral sign – johndcook.com
8. 7. 2021Technological boundary layer – johndcook.com
7. 7. 2021Mentally compute cosine – johndcook.com
1. 7. 2021Oscillatory differential equations – johndcook.com
30. 6. 2021Extending AGM to three variables – johndcook.com
29. 6. 2021Average distance to the middle – johndcook.com
29. 6. 2021Average lp distance in a disk – johndcook.com
26. 6. 2021Complexity below the surface – johndcook.com
23. 6. 2021Hebrew letters spotted in applied math – johndcook.com
23. 6. 2021Sum of independent but differently distributed variables – johndcook.com
22. 6. 2021HAKMEM, AGM, and Pi – johndcook.com
22. 6. 2021Computing logs with the AGM – johndcook.com
22. 6. 2021The magic AGM box – johndcook.com
22. 6. 2021Reversed Cauchy-Schwarz inequality – johndcook.com
20. 6. 2021My densest books – johndcook.com
19. 6. 2021Quaternion product as a matrix product – johndcook.com
19. 6. 2021Inner product from norm – johndcook.com
18. 6. 2021Email subscription switchover – johndcook.com
16. 6. 2021Quaternion products with fewer real products – johndcook.com
16. 6. 2021Faster quaternion product rotations – johndcook.com
15. 6. 2021Three kinds of tensor – johndcook.com
14. 6. 2021Laplacian in various coordinate systems – johndcook.com
14. 6. 2021Gauss algorithm for complex multiplication – johndcook.com
12. 6. 2021Vibrating circular membranes – johndcook.com
12. 6. 2021Justifying separation of variables – johndcook.com
11. 6. 2021Visual geometry – johndcook.com
10. 6. 2021Volunteer-generated errata pages – johndcook.com
10. 6. 2021Random drug screening – johndcook.com
8. 6. 2021Blog email subscription – johndcook.com
8. 6. 2021Recommending division – johndcook.com
7. 6. 2021Fourier, Gauss, and Heisenberg – johndcook.com
7. 6. 2021More readable lambda calculus – johndcook.com
5. 6. 2021What does RIPEMD stand for? – johndcook.com
5. 6. 2021Time dilation in SF and GPS – johndcook.com
3. 6. 2021A gentle introduction to QMC and discrepancy – johndcook.com
2. 6. 2021Perfect fifths, octaves, and an ergodic map – johndcook.com
1. 6. 2021Zareba, asterism, and dinkus – johndcook.com
1. 6. 2021A unique property of sine – johndcook.com
30. 5. 2021Information theory and coordinates – johndcook.com
30. 5. 2021Maidenhead geocode system – johndcook.com
27. 5. 2021Plastic number feels plastic – johndcook.com
26. 5. 2021Coin distribution – johndcook.com
26. 5. 2021Why exponential sums are interesting – johndcook.com
24. 5. 2021LaTeX and Lawyers – johndcook.com
22. 5. 2021A Pattern Language – johndcook.com
19. 5. 2021Email subscription changing – johndcook.com
18. 5. 2021The base with the largest decibel – johndcook.com
18. 5. 2021Relating Rényi entropy and q-log entropy – johndcook.com
17. 5. 2021Generalizing Shannon entropy – johndcook.com
17. 5. 2021Stumbling on an abandoned uranium mine – johndcook.com
17. 5. 2021Decibel to log in new base – johndcook.com
12. 5. 2021Most popular posts this year – johndcook.com
10. 5. 2021Cyclic permutations and trace – johndcook.com
8. 5. 2021Trick for 2×2 eigenvalues – johndcook.com
7. 5. 2021Universal confidence interval – johndcook.com
7. 5. 2021What is a polynomial? – johndcook.com
6. 5. 2021Confidence interval widths – johndcook.com
4. 5. 2021Multicolor reproducing cellular automata – johndcook.com
3. 5. 2021Self-reproducing cellular automata – johndcook.com
2. 5. 2021Humming St. Christopher – johndcook.com
1. 5. 2021Aliquot ratio distribution – johndcook.com
1. 5. 2021The iterated aliquot problem – johndcook.com
30. 4. 2021Cologarithms and Entropy – johndcook.com
30. 4. 2021Corollary of a well-known fact – johndcook.com
30. 4. 2021Repeating decimals in any base – johndcook.com
30. 4. 2021Chaotic image out of regular slices – johndcook.com
29. 4. 2021Evolution of random number generators – johndcook.com
29. 4. 2021Powers of 3 in binary – johndcook.com
28. 4. 2021Factors of orders of sporadic groups – johndcook.com
27. 4. 2021Excessive, deficient, and perfect numbers – johndcook.com
26. 4. 2021Is fast grep faster? – johndcook.com
24. 4. 2021Tower of powers and convergence – johndcook.com
24. 4. 2021Lambert W strikes again – johndcook.com
22. 4. 2021Comparing files with very long lines – johndcook.com
20. 4. 2021New ICD-10 diagnosis code weirdness – johndcook.com
20. 4. 2021Magic square of squares – johndcook.com
20. 4. 2021Martian gravity – johndcook.com
19. 4. 2021Hashing phone numbers – johndcook.com
18. 4. 2021Duodecimal vs Hexadecimal – johndcook.com
15. 4. 2021Floor, ceiling, bracket – johndcook.com
15. 4. 2021Box in ball in box in high dimension – johndcook.com
13. 4. 2021More on why simple approximations work – johndcook.com
13. 4. 2021Mathematical stability vs numerical stability – johndcook.com
12. 4. 2021Spaceship operator in Python – johndcook.com
11. 4. 2021Real radical roots – johndcook.com
10. 4. 2021Does chaos imply period 3? – johndcook.com
10. 4. 2021Sarkovsky’s theorem – johndcook.com
10. 4. 2021Period three implies chaos – johndcook.com
8. 4. 2021Better approximation for ln, still doable by hand – johndcook.com
7. 4. 2021Beta distribution with given mean and variance – johndcook.com
6. 4. 2021Close but no cigar – johndcook.com
5. 4. 2021Arithmetic-geometric mean – johndcook.com
3. 4. 2021Higher roots and r-means – johndcook.com
3. 4. 2021Calculating square roots – johndcook.com
1. 4. 2021Efficiently solving Kepler’s equation – johndcook.com
1. 4. 2021Unusually round exponential sum – johndcook.com
1. 4. 2021Hypotenuse approximation – johndcook.com
31. 3. 2021Coulomb’s constant – johndcook.com
30. 3. 2021Within one percent – johndcook.com
30. 3. 2021Recursive grep – johndcook.com
29. 3. 2021Calculating dogleg severity – johndcook.com
28. 3. 2021Solving for Möbius transformation coefficients – johndcook.com
27. 3. 2021Smallest denominator for given accuracy – johndcook.com
26. 3. 2021Simple approximation for Gamma function – johndcook.com
26. 3. 2021Mentally computing e^x – johndcook.com
24. 3. 2021What makes the log10 trick work? – johndcook.com
24. 3. 2021Simple approximation for surface area of an ellipsoid – johndcook.com
24. 3. 2021Simple approximation for perimeter of an ellipse – johndcook.com
23. 3. 2021Books and revealed preferences – johndcook.com
23. 3. 2021Mentally calculating 10^x – johndcook.com
22. 3. 2021Mentally calculating logarithms – johndcook.com
21. 3. 2021Simple trig function approximations – johndcook.com
20. 3. 2021Computing Fourier series coefficients with the FFT – johndcook.com
18. 3. 2021Support of a signal and its FFT – johndcook.com
17. 3. 2021Fourier uncertainty principle – johndcook.com
17. 3. 2021Fourier transforms in Mathematica – johndcook.com
16. 3. 2021Bessel determinants – johndcook.com
15. 3. 2021Computing normal probabilities with a simple calculator – johndcook.com
14. 3. 2021Illustrating Gershgorn disks with NumPy – johndcook.com
14. 3. 2021Calculating π with factorials – johndcook.com
11. 3. 2021Pareto and Pandas – johndcook.com
11. 3. 2021i^i^i … – johndcook.com
10. 3. 2021Broadcasting and functors – johndcook.com
10. 3. 2021Moving between vectors and diagonal matrices – johndcook.com
7. 3. 2021Adding tubes to knots – johndcook.com
4. 3. 2021A stiffening spring – johndcook.com
3. 3. 2021tcgrep: grep rewritten in Perl – johndcook.com
3. 3. 2021Scaled Beta2 distribution – johndcook.com
26. 2. 2021Applications of (1-z)/(1+z) – johndcook.com
26. 2. 2021Saxophone ranges – johndcook.com
25. 2. 2021Fraction comparison trick – johndcook.com
25. 2. 2021Normal probability fixed point – johndcook.com
24. 2. 2021The time-traveling professor – johndcook.com
23. 2. 2021The debauch of indices – johndcook.com
22. 2. 2021Not-to-do list – johndcook.com
19. 2. 2021Herd immunity countdown – johndcook.com
17. 2. 2021Martin’s doileys – johndcook.com
17. 2. 2021Divisibility by any prime – johndcook.com
12. 2. 2021Finding pi in pi with Perl – johndcook.com
12. 2. 2021Solving for neck length – johndcook.com
11. 2. 2021Trig functions across programming languages – johndcook.com
10. 2. 2021Da Vinci on wave propagation – johndcook.com
8. 2. 2021Pitch of a big wine bottle – johndcook.com
5. 2. 2021More images from an oddball coordinate system – johndcook.com
3. 2. 2021Fibonacci numbers and hyperbolic sine – johndcook.com
2. 2. 2021Herd immunity on the back of an envelope – johndcook.com
1. 2. 2021Pythagorean chaos – johndcook.com
30. 1. 2021Python triple quote strings and regular expressions – johndcook.com
28. 1. 2021Mentally computing 3rd and 5th roots – johndcook.com
27. 1. 2021How it started, how it’s going – johndcook.com
23. 1. 2021Newton’s method spirals – johndcook.com
23. 1. 2021Sums of consecutive reciprocals – johndcook.com
18. 1. 2021Peaks of Sinc – johndcook.com
18. 1. 2021Gell-Mann amnesia and its opposite – johndcook.com
18. 1. 2021Rate of convergence for Newton’s method – johndcook.com
18. 1. 2021Reverse iteration root-finding – johndcook.com
15. 1. 2021Low-tech transparency – johndcook.com
15. 1. 2021Zeros of trigonometric polynomials – johndcook.com
13. 1. 2021Just-in-case revisited – johndcook.com
12. 1. 2021Data pathology – johndcook.com
11. 1. 2021More stability, less stress – johndcook.com
6. 1. 2021Quaternion square roots – johndcook.com
5. 1. 2021Bootstrapping a minimal math library – johndcook.com
4. 1. 2021Average sum of digits – johndcook.com
2. 1. 2021Random polynomials revisited – johndcook.com
31. 12. 2020One infinity or two? – johndcook.com
31. 12. 2020Radio Frequency Bands – johndcook.com
29. 12. 2020Most popular posts of 2020 – johndcook.com
29. 12. 2020Relativistic addition – johndcook.com
28. 12. 2020Galileo’s polygon theorem – johndcook.com
28. 12. 2020Visualizing real roots of a high degree polynomial – johndcook.com
27. 12. 2020Expected number of roots – johndcook.com
24. 12. 2020Large matrices rarely have saddlepoints – johndcook.com
21. 12. 2020A generalization of sine and cosine – johndcook.com
20. 12. 2020A connected topology for the integers – johndcook.com
19. 12. 2020Accessing characters by name – johndcook.com
16. 12. 2020Pythagorean dates – johndcook.com
14. 12. 2020Shells, quoting, and one-liners – johndcook.com
12. 12. 2020Factors of consecutive products – johndcook.com
10. 12. 2020Four meanings of ^ – johndcook.com
9. 12. 2020The Crown and The Planets – johndcook.com
8. 12. 2020Predictive probability for large populations – johndcook.com
8. 12. 2020Asymptotic series for gamma function ratios – johndcook.com
5. 12. 2020Redundant Residue Number Systems – johndcook.com
4. 12. 2020Ruling out gaps in the list of Mersenne primes – johndcook.com
3. 12. 2020When are formal proofs worth the effort? – johndcook.com
2. 12. 2020A cross product in 7 dimensions – johndcook.com
1. 12. 2020Density of square-free numbers, cube-free numbers, etc. – johndcook.com
30. 11. 2020Digitally delicate primes – johndcook.com
29. 11. 2020Cubic calendars – johndcook.com
26. 11. 2020Drawing commutative diagrams with Quiver – johndcook.com
23. 11. 2020Refinements to the prime number theorem – johndcook.com
23. 11. 2020Minimizing random Boolean expressions – johndcook.com
19. 11. 2020How much can Boolean expressions be simplified? – johndcook.com
19. 11. 2020Minimizing boolean expressions – johndcook.com
18. 11. 2020Rotating symbols in LaTeX – johndcook.com
18. 11. 2020The smallest number with a given number of divisors – johndcook.com
16. 11. 2020Good news from Pfizer and Moderna – johndcook.com
16. 11. 2020I think I’ll pass – johndcook.com
12. 11. 2020Probability of commuting – johndcook.com
10. 11. 2020Test for divisibility by 13 – johndcook.com
10. 11. 2020Some mathematical art – johndcook.com
8. 11. 2020Counting triangles with integer sides – johndcook.com
6. 11. 2020Ripples and hyperbolas – johndcook.com
4. 11. 2020Informative stopping – johndcook.com
4. 11. 2020Expert determination for CCPA – johndcook.com
2. 11. 2020Category theory for programmers made easier – johndcook.com
31. 10. 2020Is every number a random Fibonacci number? – johndcook.com
31. 10. 2020Random Fibonacci numbers – johndcook.com
30. 10. 2020Edsger Dijkstra, blogger – johndcook.com
29. 10. 2020Gruntled vs disgruntled – johndcook.com
27. 10. 2020Doing well – johndcook.com
22. 10. 2020More fun with quatrefoils – johndcook.com
20. 10. 2020The word problem – johndcook.com
19. 10. 2020Real-time analytics – johndcook.com
19. 10. 2020Naive modeling – johndcook.com
17. 10. 2020Opening Windows files from bash and eshell – johndcook.com
16. 10. 2020Generating all primitive Pythagorean triples with linear algebra – johndcook.com
14. 10. 2020Playing around with a rational rose – johndcook.com
14. 10. 2020Quatrefoils – johndcook.com
12. 10. 2020Kronecker sum – johndcook.com
10. 10. 2020Nonlinear mod 5 – johndcook.com
9. 10. 2020Perfectly nonlinear functions – johndcook.com
7. 10. 2020Python one-liner to print Roman numerals – johndcook.com
6. 10. 2020Bidirectional text – johndcook.com
5. 10. 2020Understanding statistical error – johndcook.com
4. 10. 2020Why a little knowledge is a dangerous thing – johndcook.com
3. 10. 2020Expected value of X and 1/X – johndcook.com
2. 10. 2020The baseball inequality – johndcook.com
28. 9. 2020Solving for the catenary scale parameter – johndcook.com
27. 9. 2020Alphabets and Unicode – johndcook.com
26. 9. 2020How much does it matter if the measuring tape sags? – johndcook.com
26. 9. 2020From tape measures to tensors – johndcook.com
26. 9. 2020It doesn’t matter much if the tape is straight – johndcook.com
25. 9. 2020At the next prime, turn left – johndcook.com
25. 9. 2020Simple equations whose plot looks like field grass – johndcook.com
24. 9. 2020Constructing bilinear transformations – johndcook.com
23. 9. 2020Circles to Circles – johndcook.com
23. 9. 2020Simultaneous projects – johndcook.com
22. 9. 2020Schwarzian derivative – johndcook.com
20. 9. 2020Searching Greek and Hebrew with regular expressions – johndcook.com
20. 9. 2020Descartes and Toolz – johndcook.com
19. 9. 2020Driving vibrations with sawtooth waves – johndcook.com
19. 9. 2020Driving oscillations with square waves – johndcook.com
17. 9. 2020There’s more going on here – johndcook.com
15. 9. 2020Superfactorial – johndcook.com
13. 9. 2020Symplectic Euler – johndcook.com
11. 9. 2020Identifying someone from their heart beat – johndcook.com
9. 9. 2020Overestimating the number of idiots – johndcook.com
9. 9. 2020Inverse Gray code – johndcook.com
8. 9. 2020Gray code – johndcook.com
7. 9. 2020Memorizing numbers and enumerating possibilities – johndcook.com
6. 9. 2020Looking at the bits of a Unicode (UTF-8) text file – johndcook.com
3. 9. 2020How much do you really use? – johndcook.com
1. 9. 2020Make boring work harder – johndcook.com
31. 8. 2020Sum of divisor powers – johndcook.com
30. 8. 2020An almost integer pattern in many bases – johndcook.com
28. 8. 2020Org entities – johndcook.com
27. 8. 2020How big is the monster? – johndcook.com
26. 8. 2020Square waves and cobwebs – johndcook.com
25. 8. 2020Unexpected square wave – johndcook.com
24. 8. 2020Not quite going in circles – johndcook.com
23. 8. 2020Transliterating Hebrew – johndcook.com
23. 8. 2020Permutable polynomials – johndcook.com
22. 8. 2020Including a little Hebrew in an English LaTeX document – johndcook.com
20. 8. 2020All English vowel sounds in one sentence – johndcook.com
18. 8. 2020Three notations by Iverson – johndcook.com
18. 8. 2020Entering symbols in Emacs – johndcook.com
17. 8. 2020Adding phase-shifted sine waves – johndcook.com
15. 8. 2020A different kind of computational survival – johndcook.com
14. 8. 2020Multiply, divide, and floor – johndcook.com
14. 8. 2020Continued fractions with period 1 – johndcook.com
14. 8. 2020A bevy of ones – johndcook.com
13. 8. 2020Symbol pronunciation – johndcook.com
11. 8. 2020Is there a zip code that equals its population? – johndcook.com
10. 8. 2020Fibonacci numbers and ingrown bark – johndcook.com
9. 8. 2020Concentric circle images go wild – johndcook.com
6. 8. 2020Accelerating an alternating series – johndcook.com
6. 8. 2020Compact form of the Lagrange inversion formula – johndcook.com
4. 8. 2020Continued fractions of square roots – johndcook.com
3. 8. 2020Conceptual vs Numerical – johndcook.com
1. 8. 2020Time spent on the moon – johndcook.com
30. 7. 2020Monthly blog highlights – johndcook.com
28. 7. 2020Hexadecimal floating point – johndcook.com
26. 7. 2020Cesàro summation – johndcook.com
26. 7. 2020The worst tool for the job – johndcook.com
24. 7. 2020Not even close – johndcook.com
23. 7. 2020Overview of NIST post-quantum encryption finalists – johndcook.com
22. 7. 2020Banned math book – johndcook.com
22. 7. 2020Hadamard’s upper bound on determinant – johndcook.com
21. 7. 2020Cosine power approximation to normal – johndcook.com
20. 7. 2020Expressiveness – johndcook.com
20. 7. 2020From shell to system – johndcook.com
16. 7. 2020A warped perspective on math history – johndcook.com
15. 7. 2020Decomposing functions of many variables to functions of one variable – johndcook.com
14. 7. 2020Eliminating polynomial terms – johndcook.com
13. 7. 2020Leapfrog integrator – johndcook.com
11. 7. 2020Counterexample to Dirichlet principle – johndcook.com
9. 7. 2020Software analysis and synthesis – johndcook.com
8. 7. 2020COVID19 mortality per capita by state – johndcook.com
7. 7. 2020Morse code golf – johndcook.com
6. 7. 2020Squircle corner radius – johndcook.com
2. 7. 2020Triple words – johndcook.com
2. 7. 2020Kissing circle – johndcook.com
30. 6. 2020Double words – johndcook.com
29. 6. 2020Approximating rapidly divergent integrals – johndcook.com
29. 6. 2020Best approximation of a catenary by a parabola – johndcook.com
28. 6. 2020Five places the Sierpiński triangle shows up – johndcook.com
26. 6. 2020Evolute of an egg – johndcook.com
25. 6. 2020Sample size calculation – johndcook.com
24. 6. 2020Binomial coefficients mod primes – johndcook.com
21. 6. 2020Surface of revolution with minimum area – johndcook.com
20. 6. 2020Chemical element frequency in writing – johndcook.com
18. 6. 2020Convex function of diagonals and eigenvalues – johndcook.com
18. 6. 2020Bit flipping to primes – johndcook.com
17. 6. 2020The shape of beams and bulkheads – johndcook.com
17. 6. 2020NASA’s favorite ODE solver – johndcook.com
15. 6. 2020Hohmann transfer orbit – johndcook.com
14. 6. 2020Change of basis and Stirling numbers – johndcook.com
13. 6. 2020ODE solver landscape – johndcook.com
12. 6. 2020New math for going to the moon – johndcook.com
11. 6. 2020The bucket that can’t hold enough paint to paint itself – johndcook.com
10. 6. 2020Where does the seven come from? – johndcook.com
10. 6. 2020Gibbs phenomenon – johndcook.com
10. 6. 2020Novel and extended floating point – johndcook.com
9. 6. 2020Square roots of Gaussian integers – johndcook.com
9. 6. 2020How to compute the square root of a complex number – johndcook.com
8. 6. 2020Randomization audit – johndcook.com
7. 6. 2020Opposite of the Peter Principle – johndcook.com
4. 6. 2020How probable is a probable prime? – johndcook.com
4. 6. 2020Negative space graph – johndcook.com
3. 6. 2020Relatively prime determinants – johndcook.com
2. 6. 2020Sinc approximation – johndcook.com
31. 5. 2020Accurately computing a 2×2 determinant – johndcook.com
31. 5. 2020Ratio of area to perimeter – johndcook.com
30. 5. 2020Curse of dimensionality and integration – johndcook.com
29. 5. 2020Nuclear Tornadoes – johndcook.com
28. 5. 2020Fundamental Theorem of Arithmetic – johndcook.com
27. 5. 2020The Fundamental Theorem of Algebra – johndcook.com
23. 5. 2020Fundamental theorem of calculus generalized – johndcook.com
23. 5. 2020Square wave, triangle wave, and rate of convergence – johndcook.com
20. 5. 2020Clipped sine waves – johndcook.com
18. 5. 2020Inverse optimization – johndcook.com
18. 5. 2020Accessible math posts – johndcook.com
17. 5. 2020Sum and mean inequalities move in opposite directions – johndcook.com
15. 5. 2020Pretending OOP never happened – johndcook.com
14. 5. 2020Elementary approximation to “impossible” integral – johndcook.com
13. 5. 2020To integrate the impossible integral – johndcook.com
10. 5. 2020Extracting independent random bits from dependent sources – johndcook.com
10. 5. 2020Convert PostScript to PDF locally – johndcook.com
8. 5. 2020Chebyshev’s other polynomials – johndcook.com
8. 5. 2020More juice in the lemon – johndcook.com
7. 5. 2020CRM consulting gig – johndcook.com
7. 5. 2020Manipulating sums – johndcook.com
6. 5. 2020Building high frequencies out of low frequencies – johndcook.com
4. 5. 2020Prime plus power of 2 – johndcook.com
1. 5. 2020Analogy between Fibonacci and Chebyshev – johndcook.com
28. 4. 2020On using your computer as more than a terminal – johndcook.com
26. 4. 2020A spring, a rubber band, and chaos – johndcook.com
25. 4. 2020Hypocycloids – johndcook.com
24. 4. 2020Envelopes of epicycloids (pretty pictures!) – johndcook.com
24. 4. 2020Short essays on programming languages – johndcook.com
24. 4. 2020Probability that a cubic has two turning points – johndcook.com
21. 4. 2020Truncated distributions vs clipped distributions – johndcook.com
21. 4. 2020The truncated Cauchy paradox – johndcook.com
19. 4. 2020LaTeX command frequencies – johndcook.com
19. 4. 2020A shell one-liner to search directories – johndcook.com
18. 4. 2020Expected length of longest common DNA substrings – johndcook.com
14. 4. 2020Powers that don’t change the last digit – johndcook.com
13. 4. 2020An application of Kronecker products – johndcook.com
11. 4. 2020A wrinkle in Clojure – johndcook.com
9. 4. 2020Exponential growth vs logistic growth – johndcook.com
8. 4. 2020Sine series for a sine – johndcook.com
7. 4. 2020Two meanings of QR code – johndcook.com
5. 4. 2020Center of mass and vectorization – johndcook.com
4. 4. 2020Making an invertible function out of non-invertible parts – johndcook.com
1. 4. 2020Underestimating risk – johndcook.com
30. 3. 2020Reasoning under uncertainty – johndcook.com
29. 3. 2020Lee distance: codes and music – johndcook.com
27. 3. 2020Conditional independence notation – johndcook.com
25. 3. 2020Three composition theorems for differential privacy – johndcook.com
24. 3. 2020Minimizing worst case error – johndcook.com
24. 3. 2020Pecunia non olet – johndcook.com
23. 3. 2020Simple clinical trial of four COVID-19 treatments – johndcook.com
23. 3. 2020Product of copulas – johndcook.com
21. 3. 2020How to Set Num Lock on permanently – johndcook.com
21. 3. 2020New Asymptotic function in Mathematica 12.1 – johndcook.com
18. 3. 2020Extended floating point precision in R and C – johndcook.com
17. 3. 2020When is round-trip floating point radix conversion exact? – johndcook.com
16. 3. 2020Group symmetry of copula operations – johndcook.com
15. 3. 2020Product of Chebyshev polynomials – johndcook.com
14. 3. 2020The Brothers Markov – johndcook.com
14. 3. 2020Finding coffee in Pi – johndcook.com
11. 3. 2020Chebyshev approximation – johndcook.com
10. 3. 2020Remez algorithm and best polynomial approximation – johndcook.com
7. 3. 2020MDS codes – johndcook.com
4. 3. 2020Automatic data reweighting – johndcook.com
2. 3. 2020Maximum gap between binomial coefficients – johndcook.com
2. 3. 2020Formatting in comments – johndcook.com
28. 2. 2020Sum of squared digits – johndcook.com
27. 2. 2020Computing the area of a thin triangle – johndcook.com
27. 2. 2020A tale of two iterations – johndcook.com
26. 2. 2020Perfect codes – johndcook.com
24. 2. 2020Computing parity of a binary word – johndcook.com
24. 2. 2020A gentle introduction to Hamming codes – johndcook.com
23. 2. 2020ADFGVX cipher and Morse code separation – johndcook.com
23. 2. 2020ChaCha RNG with fewer rounds – johndcook.com
21. 2. 2020Popcount: counting 1’s in a bit stream – johndcook.com
20. 2. 2020A brief comment on hysteresis – johndcook.com
20. 2. 2020Safe Harbor ain’t gonna cut it – johndcook.com
19. 2. 2020Inverse congruence RNG – johndcook.com
19. 2. 2020A better adaptive Runge-Kutta method – johndcook.com
19. 2. 2020How to estimate ODE solver error – johndcook.com
18. 2. 2020Trapezoid rule and Romberg integration – johndcook.com
18. 2. 2020Python and the Tell-Tale Heart – johndcook.com
17. 2. 2020Why HIPAA matters even if you’re not a “covered entity” – johndcook.com
16. 2. 2020Scaling and memoization – johndcook.com
16. 2. 2020Lobatto integration – johndcook.com
13. 2. 2020Runge-Kutta methods and Butcher tableau – johndcook.com
12. 2. 2020Plotting complex functions – johndcook.com
8. 2. 2020The orbit that put men on the moon – johndcook.com
8. 2. 2020Behold! The Brusselator! – johndcook.com
6. 2. 2020TestU01 small crush test suite – johndcook.com
6. 2. 2020DIEHARDER test suite – johndcook.com
6. 2. 2020Using PractRand to test an RNG – johndcook.com
5. 2. 2020Leap seconds – johndcook.com
4. 2. 2020Testing entropy extractor with NIST STS – johndcook.com
4. 2. 2020Odd numbers in Pascal’s triangle – johndcook.com
2. 2. 2020Stiff differential equations – johndcook.com
31. 1. 2020Mittag-Leffler transform – johndcook.com
29. 1. 2020Updated pitch calculator – johndcook.com
28. 1. 2020Generalization of power polynomials – johndcook.com
26. 1. 2020A different view of the Lorenz system – johndcook.com
23. 1. 2020ODE bifurcation example – johndcook.com
21. 1. 2020Software metric outliers – johndcook.com
20. 1. 2020Scaling up and down – johndcook.com
19. 1. 2020Cobweb plots – johndcook.com
18. 1. 2020CCPA and expert determination – johndcook.com
18. 1. 2020Variation on cosine fixed point – johndcook.com
17. 1. 2020Stable and unstable recurrence relations – johndcook.com
17. 1. 2020Recurrence relations and Python – johndcook.com
16. 1. 2020Reminder of complexity – johndcook.com
16. 1. 2020Logistic trajectories – johndcook.com
15. 1. 2020Analogies between Weierstrass functions and trig functions – johndcook.com
15. 1. 2020More efficient way to sum a list comprehension – johndcook.com
14. 1. 2020On this day – johndcook.com
8. 1. 2020Various kinds of pseudoprimes – johndcook.com
8. 1. 2020Finding large pseudoprimes – johndcook.com
7. 1. 2020Technology à la carte – johndcook.com
6. 1. 2020Estimating the proportion of smooth numbers – johndcook.com
4. 1. 2020Sufficient statistic paradox – johndcook.com
4. 1. 2020Number of forms of a finite field – johndcook.com
31. 12. 2019Area of sinc and jinc function lobes – johndcook.com
31. 12. 2019Doing a database join with CSV files – johndcook.com
30. 12. 2019Exporting Excel files to CSV with in2csv – johndcook.com
30. 12. 2019Minimizing context switching between shell and Python – johndcook.com
28. 12. 2019A new take on the birthday problem – johndcook.com
26. 12. 2019Driven Van der Pol oscillators – johndcook.com
26. 12. 2019Calculating the period of Van der Pol oscillators – johndcook.com
24. 12. 2019Master / Apprentice relationship graph in Star Wars – johndcook.com
23. 12. 2019Top math posts of 2019 – johndcook.com
23. 12. 2019Solving Van der Pol equation with ivp_solve – johndcook.com
20. 12. 2019Exponential Christmas wreath – johndcook.com
17. 12. 2019Convergence rate of random walk on integers mod p – johndcook.com
16. 12. 2019Top privacy-related posts of 2019 – johndcook.com
15. 12. 2019Stability criteria in a nutshell – johndcook.com
13. 12. 2019Random sample overlap – johndcook.com
11. 12. 2019Advantages of redundant coordinates – johndcook.com
10. 12. 2019Determining fundamental frequency – johndcook.com
10. 12. 2019Top command line posts of 2019 – johndcook.com
9. 12. 2019Illustrating Cayley-Hamilton with Python – johndcook.com
7. 12. 2019Why can’t grep find negative numbers? – johndcook.com
5. 12. 2019Why doesn’t grep work? – johndcook.com
4. 12. 2019Top cryptography posts of 2019 – johndcook.com
4. 12. 2019New RSA factoring challenge solved – johndcook.com
3. 12. 2019Distracted by the hard part – johndcook.com
1. 12. 2019Data Science and Star Science – johndcook.com
29. 11. 2019Near zeros of zeta – johndcook.com
26. 11. 2019Fractal via bit twiddling – johndcook.com
25. 11. 2019Stochastic rounding and privacy – johndcook.com
24. 11. 2019Set theory at the command line – johndcook.com
21. 11. 2019Quantum mechanics via quantum computing – johndcook.com
19. 11. 2019Crinkle Crankle Calculus – johndcook.com
19. 11. 2019Rook graphs and Paley graphs – johndcook.com
19. 11. 2019NP vs small P – johndcook.com
18. 11. 2019Inverse trig function implementations – johndcook.com
18. 11. 2019arctan( k tan(x) ) – johndcook.com
17. 11. 2019Orbital resonance in Neptune’s moons – johndcook.com
17. 11. 2019The hardest logarithm to compute – johndcook.com
13. 11. 2019Hand-drawn Graphviz diagrams – johndcook.com
13. 11. 2019Permutation distance – johndcook.com
13. 11. 2019Anagram frequency – johndcook.com
12. 11. 2019A note to new readers – johndcook.com
12. 11. 2019Just evaluating a polynomial: how hard could it be? – johndcook.com
12. 11. 2019Floating point oddity – johndcook.com
11. 11. 2019Mathematical killer apps – johndcook.com
7. 11. 2019Optimization, Dominoes, and Frankenstein – johndcook.com
5. 11. 2019More on attacking combination locks – johndcook.com
5. 11. 2019Summing an array of floating point numbers – johndcook.com
2. 11. 2019Any number can start a factorial – johndcook.com
1. 11. 2019Arbitrary precision is not a panacea – johndcook.com
1. 11. 2019Computed IDs and privacy implications – johndcook.com
31. 10. 2019Generating Python code from SymPy – johndcook.com
31. 10. 2019A simple unsolved problem – johndcook.com
30. 10. 2019Higher order Newton-like methods for root finding – johndcook.com
30. 10. 2019Formatting numbers at the command line – johndcook.com
29. 10. 2019Computing pi with bc – johndcook.com
28. 10. 2019Linear feedback shift registers – johndcook.com
28. 10. 2019Generating De Bruijn cycles with primitive polynomials – johndcook.com
24. 10. 2019Quantum supremacy and post-quantum crypto – johndcook.com
24. 10. 2019Splitting lines and numbering the pieces – johndcook.com
23. 10. 2019Self-curvature – johndcook.com
22. 10. 2019Hacking pass codes with De Bruijn sequences – johndcook.com
22. 10. 2019Drawing with Unicode block characters – johndcook.com
19. 10. 2019Binary surprise – johndcook.com
19. 10. 2019Exact values of sine and cosine – johndcook.com
18. 10. 2019Golay codes – johndcook.com
18. 10. 2019Chinese character frequency and entropy – johndcook.com
17. 10. 2019The science of snow – johndcook.com
17. 10. 2019Greek letter frequency and entropy – johndcook.com
16. 10. 2019File character counts – johndcook.com
15. 10. 2019Survivalist vi – johndcook.com
14. 10. 2019What is a privacy budget? – johndcook.com
14. 10. 2019Queueing theory and regular expressions – johndcook.com
12. 10. 2019Hyperexponential and hypoexponential distributions – johndcook.com
10. 10. 2019Primes that don’t look like primes – johndcook.com
9. 10. 2019Computational survivalist – johndcook.com
9. 10. 2019What exactly is a day? – johndcook.com
8. 10. 2019Harmonographs – johndcook.com
8. 10. 2019Lissajous curves and knots – johndcook.com
8. 10. 2019Curvature of an ellipsoid – johndcook.com
4. 10. 2019Fixed points – johndcook.com
2. 10. 2019Number of real roots in an interval – johndcook.com
2. 10. 2019Total curvature of a knot – johndcook.com
29. 9. 2019A sort of mathematical quine – johndcook.com
28. 9. 2019Control characters – johndcook.com
27. 9. 2019Fat tails and the t test – johndcook.com
25. 9. 2019Amendment to CCPA regarding personal information – johndcook.com
25. 9. 2019Right to be forgotten in the news – johndcook.com
25. 9. 2019Exception Driven Development – johndcook.com
21. 9. 2019One of these days I’m going to figure this out – johndcook.com
20. 9. 2019Typesetting zodiac symbols in LaTeX – johndcook.com
20. 9. 2019Airline flight number parity – johndcook.com
18. 9. 2019Testing Rupert Miller’s suspicion – johndcook.com
17. 9. 2019Why would anyone do that? – johndcook.com
17. 9. 2019Predicted distribution of Mersenne primes – johndcook.com
16. 9. 2019Short video introducing differential privacy – johndcook.com
16. 9. 2019Collatz conjecture skepticism – johndcook.com
13. 9. 2019String interpolation in Python and R – johndcook.com
10. 9. 2019Progress on the Collatz conjecture – johndcook.com
9. 9. 2019How UTF-8 works – johndcook.com
8. 9. 2019Excel, R, and Unicode – johndcook.com
6. 9. 2019How fast were dead languages spoken? – johndcook.com
4. 9. 2019Quiet mode – johndcook.com
4. 9. 2019More bc weirdness – johndcook.com
4. 9. 2019Asimov’s question about π – johndcook.com
3. 9. 2019National Drug Code (NDC) – johndcook.com
3. 9. 2019Prefix code examples – johndcook.com
2. 9. 2019How many possible Unicode characters there are and why – johndcook.com
2. 9. 2019Growth of Unicode over time – johndcook.com
1. 9. 2019The hopeless task of the Unicode Consortium – johndcook.com
31. 8. 2019Regular expressions and special characters – johndcook.com
30. 8. 2019Munging CSV files with standard Unix tools – johndcook.com
30. 8. 2019Three-digit zip codes and data privacy – johndcook.com
28. 8. 2019Working with wide text files at the command line – johndcook.com
27. 8. 2019Estimating vocabulary size with Heaps’ law – johndcook.com
23. 8. 2019Mickey Mouse, Batman, and conformal mapping – johndcook.com
22. 8. 2019Star-crossed lovers – johndcook.com
22. 8. 2019Contributing to open source projects – johndcook.com
22. 8. 2019Stone-Weierstrass on a disk – johndcook.com
21. 8. 2019Distribution of zip code population – johndcook.com
20. 8. 2019Landau kernel – johndcook.com
20. 8. 2019Lebesgue’s proof of Weierstrass’ theorem – johndcook.com
14. 8. 2019Proving that a choice was made in good faith – johndcook.com
12. 8. 2019Detecting a short period in an RNG – johndcook.com
11. 8. 2019Testing Cliff RNG with DIEHARDER – johndcook.com
11. 8. 2019Fixed points of the Cliff random number generator – johndcook.com
10. 8. 2019Ease of learning vs relearning – johndcook.com
9. 8. 2019Uniform approximation paradox – johndcook.com
6. 8. 2019Nearly parallel is nearly transitive – johndcook.com
5. 8. 2019Angles in the spiral of Theodorus – johndcook.com
5. 8. 2019How to plot the spiral of Theodorus – johndcook.com
3. 8. 2019Encryption as secure as factoring – johndcook.com
2. 8. 2019Accelerating convergence with Aitken’s method – johndcook.com
2. 8. 2019Accelerating an alternating series – johndcook.com
31. 7. 2019Data breach trends – johndcook.com
30. 7. 2019Beating the odds on the Diffie-Hellman decision problem – johndcook.com
27. 7. 2019Magic square links and errata – johndcook.com
24. 7. 2019Quaternion reference in the Vulgate – johndcook.com
24. 7. 2019Fame, difficulty, and usefulness – johndcook.com
23. 7. 2019Twisted elliptic curves – johndcook.com
20. 7. 2019Hashing names does not protect privacy – johndcook.com
18. 7. 2019May the best technology win – johndcook.com
17. 7. 2019Integral approximation trick – johndcook.com
16. 7. 2019Number of feet in a mile – johndcook.com
14. 7. 2019Discriminant of a cubic – johndcook.com
12. 7. 2019Distribution of quadratic residues – johndcook.com
12. 7. 2019What does CCPA say about de-identified data? – johndcook.com
11. 7. 2019Serious applications of a party trick – johndcook.com
10. 7. 2019Channel quantity and quality – johndcook.com
9. 7. 2019Symmetry in exponential sums – johndcook.com
6. 7. 2019Proto-calculus – johndcook.com
4. 7. 2019Homomorphic encryption – johndcook.com
3. 7. 2019Journalistic stunt with Emacs – johndcook.com
1. 7. 2019Notes on computing hash functions – johndcook.com
28. 6. 2019Translating poetry – johndcook.com
26. 6. 2019Category theory for data science: cautious optimism – johndcook.com
25. 6. 2019Software to factor integers – johndcook.com
22. 6. 2019Making public keys factorable with Rowhammer – johndcook.com
21. 6. 2019Bounds on the nth prime – johndcook.com
20. 6. 2019Converting between nines and sigmas – johndcook.com
19. 6. 2019Maybe it’s just hard – johndcook.com
19. 6. 2019Why are regular expressions difficult? – johndcook.com
19. 6. 2019Feller-Tornier constant – johndcook.com
18. 6. 2019Translating Robert Burns – johndcook.com
17. 6. 2019Protecting privacy while keeping detailed date information – johndcook.com
14. 6. 2019Per stirpes and random walks – johndcook.com
12. 6. 2019SQRL: Secure Quick Reliable Login – johndcook.com
10. 6. 2019The cost of no costs – johndcook.com
8. 6. 2019Trott’s constant – johndcook.com
5. 6. 2019Using one RNG to sample another – johndcook.com
4. 6. 2019Rock, paper, scissors, algebra – johndcook.com
3. 6. 2019Liminal and subliminal – johndcook.com
2. 6. 2019Cop with a mop – johndcook.com
31. 5. 2019R with Conda – johndcook.com
30. 5. 2019On this day – johndcook.com
27. 5. 2019Sum of all Spheres – johndcook.com
25. 5. 2019Inside the AES S-box – johndcook.com
23. 5. 2019Random sampling from a file – johndcook.com
23. 5. 2019Between now and quantum – johndcook.com
13. 5. 2019Golden ratio primes – johndcook.com
13. 5. 2019Goldilocks and the three multiplications – johndcook.com
12. 5. 2019Tricks for arithmetic modulo NIST primes – johndcook.com
11. 5. 2019Elliptic curve P-384 – johndcook.com
9. 5. 2019Bessel function crossings – johndcook.com
8. 5. 2019Orthogonal graphs – johndcook.com
8. 5. 2019Fascination burnout – johndcook.com
6. 5. 2019Area and volume of Menger sponge – johndcook.com
5. 5. 2019Regular expression for ICD-9 and ICD-10 codes – johndcook.com
30. 4. 2019A misunderstanding of complexity – johndcook.com
30. 4. 2019Improving on the sieve of Eratosthenes – johndcook.com
29. 4. 2019How category theory is applied – johndcook.com
28. 4. 2019Rare and strange ICD-10 codes – johndcook.com
25. 4. 2019State privacy laws to watch – johndcook.com
24. 4. 2019Quantum leaps – johndcook.com
23. 4. 2019Professional, amateur, and something else – johndcook.com
22. 4. 2019Easter and exponential sums – johndcook.com
22. 4. 2019Groups in categories – johndcook.com
21. 4. 2019What is an isogeny? – johndcook.com
20. 4. 2019Isogeny-based encryption – johndcook.com
19. 4. 2019Calling Python from Mathematica – johndcook.com
16. 4. 2019Random projection – johndcook.com
15. 4. 2019A truly horrible random number generator – johndcook.com
11. 4. 2019Maybe you should’t script it after all – johndcook.com
11. 4. 2019Squircle perimeter and the isoparametric problem – johndcook.com
9. 4. 2019Taking the derivative of a muscle car – johndcook.com
8. 4. 2019Safe Harbor and the calendar rollover problem – johndcook.com
8. 4. 2019Data privacy Twitter account – johndcook.com
7. 4. 2019Ratio of Lebesgue norm ball volumes – johndcook.com
4. 4. 2019Higher dimensional squircles – johndcook.com
3. 4. 2019History of the “Squircle” – johndcook.com
2. 4. 2019Covered entities: TMPRA extends HIPAA – johndcook.com
1. 4. 2019Inferring religion from fitness data – johndcook.com
29. 3. 2019Putting topological data analysis in context – johndcook.com
27. 3. 2019Assumed technologies – johndcook.com
26. 3. 2019Elementary solutions to differential equations – johndcook.com
25. 3. 2019Finite rings – johndcook.com
24. 3. 2019Monads and generalized elements – johndcook.com
23. 3. 2019Mixing error-correcting codes and cryptography – johndcook.com
21. 3. 2019US Army applying new areas of math – johndcook.com
19. 3. 2019Riffing on mistakes – johndcook.com
19. 3. 2019A genius can admit finding things difficult – johndcook.com
19. 3. 2019Thermocouple polynomials and other sundries – johndcook.com
18. 3. 2019Digital signatures with oil and vinegar – johndcook.com
14. 3. 2019Counting irreducible polynomials over finite fields – johndcook.com
14. 3. 2019Scaling up differential privacy: lessons from the US Census – johndcook.com
13. 3. 2019Average distance between planets – johndcook.com
11. 3. 2019All elliptic curves over fields of order 2 and 3 – johndcook.com
10. 3. 2019US Census Bureau embraces differential privacy – johndcook.com
9. 3. 2019Efficient modular arithmetic technique for Curve25519 – johndcook.com
7. 3. 2019Why isn’t CPU time more valuable? – johndcook.com
7. 3. 2019Chaos + Chaos = Order – johndcook.com
6. 3. 2019An attack on RSA with exponent 3 – johndcook.com
6. 3. 2019Public key encryption based on squares and non squares – johndcook.com
5. 3. 2019An infinite product challenge – johndcook.com
5. 3. 2019Base85 encoding – johndcook.com
4. 3. 2019Base 58 encoding and Bitcoin addresses – johndcook.com
4. 3. 2019Implementing the ChaCha RNG in Python – johndcook.com
2. 3. 2019Google Adiantum and the ChaCha RNG – johndcook.com
2. 3. 2019Congress and the Equifax data breach – johndcook.com
1. 3. 2019Sharing secrets with polynomials – johndcook.com
27. 2. 2019Miscellaneous – johndcook.com
26. 2. 2019What sticks in your head – johndcook.com
25. 2. 2019Testing for primes less than a quintillion – johndcook.com
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