Equation for the shape of a guitar pick
https://www.johndcook.com/blog/2026/05/03/guitar-pick/
Remote
John D. Cook
@johndcook@mathstodon.xyz
mastodon 4.7.2Consultant in applied mathematics and data privacy
1184 Followers
29 Following
25 Posts
Joined November 21, 2022
How not to calculate cosine
https://www.johndcook.com/blog/2026/08/07/how-not-to-calculate-cos/
Enumerating rooted trees and non-overlapping circles
https://www.johndcook.com/blog/2026/08/05/enumerating-trees-and-circles/
New post: Hiding data in permutations
https://www.johndcook.com/blog/2026/07/27/hiding-data-in-permutations/
Solving the Runge-Kutta design equations
https://www.johndcook.com/blog/2026/07/31/runge-kutta-design/
New post: Calculating log(1000!)
New post: Ratios of metallic ratios
https://www.johndcook.com/blog/2026/08/04/ratio-of-metallic-ratios/
New post: Estimating a cumulative sum
https://www.johndcook.com/blog/2026/08/02/estimating-a-cumulative-sum/
Counting rooted trees. With a surprising connection to differential equations.
https://www.johndcook.com/blog/2026/08/01/counting-rooted-trees/
DNA and Bessel functions
https://www.johndcook.com/blog/2026/08/09/dna-and-bessel-functions/
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.
Why is cos(200!) harder to compute than log(200!)?
Metallic ratio alchemy: Can you make gold from lead?
New post: Holonomic functions
https://www.johndcook.com/blog/2026/08/02/holonomic-functions/
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/
Comparing forward Euler and symplectic Euler ODE solvers on the preditor-prey equations.
New post: A simple range reduction algorithm
https://www.johndcook.com/blog/2026/08/09/simple-range-reduction/
A better algorithm for inverting the gamma function
https://www.johndcook.com/blog/2026/07/28/inverse-factorial-improved/
Turning a trick into a technique
https://www.johndcook.com/blog/2026/04/28/even-series-trick/
Fitting a regular expression to a list of words
https://www.johndcook.com/blog/2026/07/19/fitting-a-regex/
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/
Replying to
@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/
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?
Replying to
@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.