@johndcook@mathstodon.xyz

John D. Cook @johndcook@mathstodon.xyz · 5d ago

DNA and Bessel functions

https://www.johndcook.com/blog/2026/08/09/dna-and-bessel-functions/

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John D. Cook @johndcook@mathstodon.xyz · 5d ago

New post: A simple range reduction algorithm

https://www.johndcook.com/blog/2026/08/09/simple-range-reduction/

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John D. Cook @johndcook@mathstodon.xyz · Aug 07, 2026

How not to calculate cosine

https://www.johndcook.com/blog/2026/08/07/how-not-to-calculate-cos/

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John D. Cook @johndcook@mathstodon.xyz · Aug 07, 2026

Why is cos(200!) harder to compute than log(200!)?

https://www.johndcook.com/blog/2026/08/07/cos200/

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John D. Cook @johndcook@mathstodon.xyz · Aug 06, 2026

New post: Calculating log(1000!)

https://www.johndcook.com/blog/2026/08/06/log1000/

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John D. Cook @johndcook@mathstodon.xyz · Aug 05, 2026

Enumerating rooted trees and non-overlapping circles
https://www.johndcook.com/blog/2026/08/05/enumerating-trees-and-circles/

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John D. Cook @johndcook@mathstodon.xyz · Aug 04, 2026

Metallic ratio alchemy: Can you make gold from lead?

https://www.johndcook.com/blog/2026/08/04/metallic-alchemy/

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John D. Cook @johndcook@mathstodon.xyz · Aug 04, 2026

New post: Ratios of metallic ratios

https://www.johndcook.com/blog/2026/08/04/ratio-of-metallic-ratios/

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John D. Cook @johndcook@mathstodon.xyz · Aug 02, 2026

New post: Holonomic functions

https://www.johndcook.com/blog/2026/08/02/holonomic-functions/

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John D. Cook @johndcook@mathstodon.xyz · Aug 02, 2026

New post: Estimating a cumulative sum

https://www.johndcook.com/blog/2026/08/02/estimating-a-cumulative-sum/

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John D. Cook @johndcook@mathstodon.xyz · Aug 01, 2026

Why is one special area of differential equations -- 2nd order linear equations with polynomial coefficients -- so important?

https://www.johndcook.com/blog/2026/08/01/why-polynomial-coefficients/

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John D. Cook @johndcook@mathstodon.xyz · Aug 01, 2026

Counting rooted trees. With a surprising connection to differential equations.

https://www.johndcook.com/blog/2026/08/01/counting-rooted-trees/

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John D. Cook @johndcook@mathstodon.xyz · Jul 31, 2026

Solving the Runge-Kutta design equations

https://www.johndcook.com/blog/2026/07/31/runge-kutta-design/

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John D. Cook @johndcook@mathstodon.xyz · Jul 30, 2026

Comparing forward Euler and symplectic Euler ODE solvers on the preditor-prey equations.

https://www.johndcook.com/blog/2020/09/12/symplectic-euler/

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John D. Cook @johndcook@mathstodon.xyz · Jul 28, 2026

A better algorithm for inverting the gamma function

https://www.johndcook.com/blog/2026/07/28/inverse-factorial-improved/

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John D. Cook @johndcook@mathstodon.xyz · Jul 28, 2026

You can hide a cryptographic key in the order of a deck of cards. How big a deck would you need to store various sizes of keys?

https://www.johndcook.com/blog/2026/07/28/keys-and-cards/

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John D. Cook @johndcook@mathstodon.xyz · Jul 27, 2026

New post: Hiding data in permutations

https://www.johndcook.com/blog/2026/07/27/hiding-data-in-permutations/

John D. Cook | Applied Mathematics Consulting

Hiding data in permutations

The latest issue of Paged Out! has an article by Stephen Hewitt "An off-line backup of your cryptographic key using playing cards." The idea is to use a deck of 52 to store a 128-bit cryptographic key

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John D. Cook @johndcook@mathstodon.xyz · Jul 19, 2026

Fitting a regular expression to a list of words https://www.johndcook.com/blog/2026/07/19/fitting-a-regex/

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John D. Cook @johndcook@mathstodon.xyz · May 03, 2026

Update to my previous post. By changing the parameter k from 1.5 to 1.6 I get the red curve, which fits the gray photographic image quite well.

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John D. Cook @johndcook@mathstodon.xyz · May 03, 2026

Equation for the shape of a guitar pick
https://www.johndcook.com/blog/2026/05/03/guitar-pick/

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John D. Cook @johndcook@mathstodon.xyz · Apr 30, 2026

Replying to @johndcook@mathstodon.xyz

@tpfto@mathstodon.xyz Looks like you can generalize Burmann's theorem by generalizing the series inversion theorem. This article includes the case of phi having a fixed number of zero derivatives at a. https://www.mathematica-journal.com/2014/11/24/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/

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John D. Cook @johndcook@mathstodon.xyz · Apr 30, 2026

Replying to @tpfto@mathstodon.xyz

@tpfto@mathstodon.xyz That's really cool. Hadn't seen that before. Maybe I'm missing something. In the notation of the Mathworld article, a = 0 and phi = cos. But phi'(a) = 0, and so it seems Bürmann's theorem doesn't apply.

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John D. Cook @johndcook@mathstodon.xyz · Apr 28, 2026

Turning a trick into a technique
https://www.johndcook.com/blog/2026/04/28/even-series-trick/

John D. Cook | Applied Mathematics Consulting

Turning a trick into a technique

A technique is a trick that works twice. Finding a new use for the even function series trick.

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John D. Cook @johndcook@mathstodon.xyz · Mar 13, 2026

I asked Grok and ChatGPT to write Lilypond code to reproduce a photo of some sheet music. The results were hilariously bad, and yet they got some things right.

https://www.johndcook.com/blog/2026/03/13/typesetting-sheet-music-with-ai/