lim_{x→ 0}(sin x)/(x) and the definition of π

2013/02/03 by Helmut Zeisel, Zeisel, Helmut
Mathematics · #26A09 #39B22 #97D40 #FOS: Mathematics #History and Overview (math.HO) #math.HO #msc:26A09 #msc:39B22 #msc:97D40

paper · pdf · doi:10.48550/arxiv.1302.1167

6 pages

arxiv created 2013/02/03 · arxiv updated 2013/02/06

Abstract

Leopold Vietoris and Guido Hoheisel showed how the existence of lim_{x→ 0}(sin x)/(x) can be derived from the trigonometric addition formulas. In this article two new proofs for this result are given. In addition it is discussed how this limit is related to the definition of π.

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