John D. Cook
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johndcook.mathstodon.xyz.ap.brid.gy
John D. Cook
@johndcook.mathstodon.xyz.ap.brid.gy
150 followers 0 following 320 posts
Consultant in applied mathematics and data privacy

https://www.johndcook.com

[bridged from https://mathstodon.xyz/@johndcook on the fediverse by https://fed.brid.gy/ ]
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johndcook.mathstodon.xyz.ap.brid.gy
Four generalizations of the Pythagorean theorem

https://www.johndcook.com/blog/2025/11/13/pythagorean-generalizations/
November 13, 2025 at 3:31 PM
johndcook.mathstodon.xyz.ap.brid.gy
The graph below appears to show that the correlation between two stocks peaks about every 50 days. But this is purely an analysis artifact. The two series are in fact independent random walks. Shows how analysis can be misleading.

https://www.johndcook.com/blog/2025/11/09/rolling-correlation/
November 9, 2025 at 7:03 PM
johndcook.mathstodon.xyz.ap.brid.gy
There's talk of building gigawatt data centers. How much is a gigawatt? https://www.johndcook.com/blog/2025/11/07/how-much-is-a-gigawatt/
November 7, 2025 at 2:17 PM
johndcook.mathstodon.xyz.ap.brid.gy
The sum of the inradii in any triangulation of a cyclic polygon is the same for all triangulations.

https://www.johndcook.com/blog/2025/11/05/japanese-polygon-theorem/
Two examples
November 5, 2025 at 12:03 PM
johndcook.mathstodon.xyz.ap.brid.gy
The Pythagorean theorem squares the lengths of the sides in a right triangle. An analogous theorem squares the areas of faces of a right tetrahedron and generalizes to higher dimensions.

https://www.johndcook.com/blog/2025/11/03/de-gua/
November 3, 2025 at 4:44 PM
johndcook.mathstodon.xyz.ap.brid.gy
The anti-Smith chart
https://www.johndcook.com/blog/2025/11/02/anti-smith-chart/
November 2, 2025 at 10:14 PM
johndcook.mathstodon.xyz.ap.brid.gy
Impedance and triangular numbers

https://www.johndcook.com/blog/2025/11/02/impedance-and-trianglular-numbers/
November 2, 2025 at 1:13 PM
johndcook.mathstodon.xyz.ap.brid.gy
Capitalization impacts the size of QR codes

https://www.johndcook.com/blog/2025/10/31/smaller-qr-codes/
October 31, 2025 at 3:55 PM
johndcook.mathstodon.xyz.ap.brid.gy
An ancient generalization of Pythagorean theorem

https://www.johndcook.com/blog/2025/10/30/apollonius-theorem/
October 30, 2025 at 1:11 PM
johndcook.mathstodon.xyz.ap.brid.gy
Comparing physical keys and encryption keys

https://www.johndcook.com/blog/2025/10/29/physical-keys-encryption-keys/
Metal key with 55 cuts
October 29, 2025 at 3:20 PM
johndcook.mathstodon.xyz.ap.brid.gy
Why and how Bitcoin uses Merkle trees

https://www.johndcook.com/blog/2025/10/28/bitcoin-merkle-trees/
October 28, 2025 at 2:09 PM
johndcook.mathstodon.xyz.ap.brid.gy
How blocks are chained in a blockchain, in full detail

https://www.johndcook.com/blog/2025/10/27/blockchain/
October 27, 2025 at 4:00 PM
johndcook.mathstodon.xyz.ap.brid.gy
Follow up to my post on the Smith chart:
How to adjust the spacing of the circles

https://www.johndcook.com/blog/2025/10/25/smith-chart-spacing/
October 25, 2025 at 2:57 PM
johndcook.mathstodon.xyz.ap.brid.gy
New post: The Smith chart

https://www.johndcook.com/blog/2025/10/23/smith-chart/
October 23, 2025 at 2:24 PM
johndcook.mathstodon.xyz.ap.brid.gy
Randomly generating points in Colorado

https://www.johndcook.com/blog/2025/10/22/generating-random-points-in-colorado/
October 22, 2025 at 1:07 PM
johndcook.mathstodon.xyz.ap.brid.gy
Distribution of the correlation coefficient

https://www.johndcook.com/blog/2025/10/20/distribution-of-correlation/
October 20, 2025 at 12:16 PM
johndcook.mathstodon.xyz.ap.brid.gy
Converting between nines and sigmas

https://www.johndcook.com/blog/2025/10/18/quality-metrics/
October 18, 2025 at 7:55 PM
johndcook.mathstodon.xyz.ap.brid.gy
Turning trig identities into Fibonacci identities

https://www.johndcook.com/blog/2025/10/17/trig-fibonacci/
October 17, 2025 at 12:08 PM
johndcook.mathstodon.xyz.ap.brid.gy
Ethereum’s consensus layer elliptic curve: BLS12-381

https://www.johndcook.com/blog/2025/10/13/ethereum-bls12-381/
Ethereum branded hero image
October 13, 2025 at 1:44 PM
johndcook.mathstodon.xyz.ap.brid.gy
A different graphic for introducing my latest blog post.
October 13, 2025 at 10:42 AM
johndcook.mathstodon.xyz.ap.brid.gy
The connection between Möbius transformations and 2 x 2 matrices.

https://www.johndcook.com/blog/2025/10/12/invert-mobius/
October 12, 2025 at 5:48 PM
johndcook.mathstodon.xyz.ap.brid.gy
Differential equation on a donut

https://www.johndcook.com/blog/2025/10/08/diffeq-donut/
October 9, 2025 at 12:50 AM
johndcook.mathstodon.xyz.ap.brid.gy
"Mathematicians love ... [to] take a familiar concept, relax one of its assumptions, and then torture it until it squeals."

https://www.thepsmiths.com/p/briefly-noted-summer-reading
October 6, 2025 at 3:12 PM
johndcook.mathstodon.xyz.ap.brid.gy
The ratio of logs to different bases is constant.

What can you say about the ratio of iterated logs to different bases?

https://www.johndcook.com/blog/2025/09/29/log-log-x/
September 30, 2025 at 1:12 AM
johndcook.mathstodon.xyz.ap.brid.gy
Extrapolating quantum factoring

https://www.johndcook.com/blog/2025/09/28/extrapolating-quantum-factoring/
September 28, 2025 at 7:13 PM