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Euler's Identity, Leibniz Tables, and the Irrationality of Pi

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Abstract:

Using techniques that show that e and π are transcendental, we give a short, elementary proof that π is irrational based on Euler's identity. The proof involves evaluations of a polynomial using repeated applications of Leibniz formula as organized in a Leibniz table.

Document Type: Research Article

DOI: http://dx.doi.org/10.4169/college.math.j.43.5.361

Publication date: November 1, 2012

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