Number Theory


Counter to Zhou's Criticism of Jones' Proof of the Irrationality of π and π2

Authors: Tim Jones

A geometric proof of the irrationality of π is given. It uses an evaluation of the area given by the product of two symmetric functions, together with bounds on the integral. The symmetric functions embed the assumption of rational π; one function is dependent on n; as the evaluation of the integral exceeds the upper bound for large n for any given rational π, a contradiction is obtained. This proof has been criticized, but here some counters to the criticism are offered.

Comments: 5 pages

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Submission history

[v1] 6 Jan 2011

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