ISSN : 1226-0657
We give an elementary proof of Descartes' theorem for polyhedra. Since Descartes' theorem is equivalent to Euler's theorem for polyhedra, this also gives an elementary proof of Euler's theorem.
A Survey of Geometry.
Descartes on Polyhedra: A Study of the De Solidorum Elementis.
(1981). Descartes, Euler, Poincare, Polya. Enseign. Math., 27, 327-343.
(1996). The Euler Characteristic and Polya's Dream. Amer. Math. Monthly, 103, 121-131. 10.2307/2975104.
Mathematical Discovery.