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

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  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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  A better algorithm for inverting the gamma function https://www.johndcook.com/blog/2026/07/28/inverse-factorial-improved/

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  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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  Solving the Runge-Kutta design equations https://www.johndcook.com/blog/2026/07/31/runge-kutta-design/

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

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

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

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  Metallic ratio alchemy: Can you make gold from lead? https://www.johndcook.com/blog/2026/08/04/metallic-alchemy/

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

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  New post: Calculating log(1000!) https://www.johndcook.com/blog/2026/08/06/log1000/

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  Why is cos(200!) harder to compute than log(200!)? https://www.johndcook.com/blog/2026/08/07/cos200/

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

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  New post: A simple range reduction algorithm https://www.johndcook.com/blog/2026/08/09/simple-range-reduction/

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

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

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

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

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  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/

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  https://www.johndcook.com/blog/2026/02/24/a-curious-trig-identity/