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On Cauchy's Lemma Concerning Convex Polygons

Published online by Cambridge University Press:  20 November 2018

I. J. Schoenberg  and
S. K. Zaremba
I. J. Schoenberg
Affiliation:
Mathematics Research Center, U.S. Army, University of Wisconsin and University of Wales, Swansea
S. K. Zaremba
Affiliation:
Mathematics Research Center, U.S. Army, University of Wisconsin and University of Wales, Swansea
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One of the authors having just presented Cauchy's theorem on convex polyhedra to a class on “Convexity” at the University of Wisconsin, a discussion on Cauchy's lemma on convex polygons led to an exchange of letters which are here reproduced. The three letters are independently readable. Two new proofs of Cauchy's lemma are given, of which the second (§3) is very short.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1062 - 1071
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Alexandrow, A. D., Konvexe Polyeder (German translation from Russian; Akademie-Verlag, Berlin, 1958).Google Scholar
2. Cauchy, A., Sur les polygones et les polyèdres (Second Mémoire, Oeuvres Complètes, IIe Série, vol. 1; Paris, 1905).Google Scholar
3. Rouché, E. et de Comberousse, Ch., Traité de géométrie (Deuxième Partie, Géométrie de l'espace; Paris, 1883).Google Scholar
4. Steinitz, E. und Rademacher, H., Vorlesungen über die Theorie der Polyeder (Springer-Verlag, Berlin, 1934).Google Scholar