Hackers' Pub

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`(` condition `)`	Combines the operators within the parentheses first.	`(#HackersPub OR "Hackers' Pub" OR "Hackers Pub") lang:en`

Brando Barclay @brandon@mathstodon.xyz

3/13/2025, 12:14:30 AM

Public

This particular approach using companion matrices to analyze the trace sequence is especially powerful because it provides a constructive proof of cubic irrationality without having to explicitly compute the roots. The non-periodic nature of the trace sequence (3, 2, 2, 5, 11, ...) confirms the cubic irrational nature in a way that aligns with Hermite's analytical methods.

Here's the paper

https://github.com/bbarclay/hermitesproblem/blob/main/paper/main.pdf

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