# Transcendenz vone und π

@article{Gordan1893TranscendenzVU,
title={Transcendenz vone und $\pi$},
author={P. Gordan},
journal={Mathematische Annalen},
year={1893},
volume={43},
pages={222-224}
}
• P. Gordan
• Published 1 June 1893
• Mathematics
• Mathematische Annalen
9 Citations

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Transcendence of a number implies the irrationality of powers of a number, but in the case of π there are no separate proofs that powers of π are irrational. We investigate this curiosity.

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We generalize P. Gordan's proof of the transcendence of e ((3); (5), p. 170), and obtain a criterion of irrationality (Theorem 1 below). Using this criterion, we can prove the irrationality of f(z) =

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• Education
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Part 1 is a study about the evolution of the concept of absolute value in the history of mathematics. It shall allow to identify possible obstacles related to the development of this concept in the

### Transcendence of e and π

• Mathematics, Philosophy
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The main purpose of this chapter is to prove that the number π is transcendental, thereby completing the proof of the impossibility of squaring the circle (Problem III of the Introduction). We first