On Cauchy's Lemma Concerning Convex Polygons
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 1062-1071
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Schoenberg, I. J.; Zaremba, S. K. On Cauchy's Lemma Concerning Convex Polygons. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 1062-1071. doi: 10.4153/CJM-1967-096-4
@article{10_4153_CJM_1967_096_4,
author = {Schoenberg, I. J. and Zaremba, S. K.},
title = {On {Cauchy's} {Lemma} {Concerning} {Convex} {Polygons}},
journal = {Canadian journal of mathematics},
pages = {1062--1071},
year = {1967},
volume = {19},
number = {1},
doi = {10.4153/CJM-1967-096-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-096-4/}
}
TY - JOUR AU - Schoenberg, I. J. AU - Zaremba, S. K. TI - On Cauchy's Lemma Concerning Convex Polygons JO - Canadian journal of mathematics PY - 1967 SP - 1062 EP - 1071 VL - 19 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-096-4/ DO - 10.4153/CJM-1967-096-4 ID - 10_4153_CJM_1967_096_4 ER -
[1] 1. Alexandrow, A. D., Konvexe Polyeder (German translation from Russian; Akademie-Verlag, Berlin, 1958). Google Scholar
[2] 2. Cauchy, A., Sur les polygones et les polyèdres (Second Mémoire, Oeuvres Complètes, IIe Série, vol. 1; Paris, 1905). Google Scholar
[3] 3. Rouché, E. et de Comberousse, Ch., Traité de géométrie (Deuxième Partie, Géométrie de l'espace; Paris, 1883). Google Scholar
[4] 4. Steinitz, E. und Rademacher, H., Vorlesungen über die Theorie der Polyeder (Springer-Verlag, Berlin, 1934). Google Scholar
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