Transcendenz vone und π

  title={Transcendenz vone und $\pi$},
  author={P. Gordan},
  journal={Mathematische Annalen},
  • P. Gordan
  • Published 1 June 1893
  • Mathematics
  • Mathematische Annalen

Historical Events in the Background of Hilbert’s Seventh Paris Problem

David Hilbert’s lecture, “Mathematical Problems,” [Hilbert 1900] delivered in Paris in 1900 at the Second International Congress of Mathematicians, has long been recognized as marking a milestone in

The Powers of π are Irrational

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.

Some transcendental functions that yield transcendental values for every algebraic entry

A transcendental function usually yields a transcendental value for an algebraic entry belonging to its domain, the algebraic exceptions forming the so-called \emph{exceptional set}. For instance,

Some transcendental functions with an empty exceptional set

A transcendental function usually returns transcendental values at algebraic points. The (algebraic) exceptions form the so-called \emph{exceptional set}, as for instance the unitary set $\{0\}$ for


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) =

Eine Studie zur historischen Entwicklung und didaktischen Transposition des Begriffs „absoluter Betrag“

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

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

The Ubiquitous π