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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.19 No.1

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TOTAL ANGULAR DEFECT AND EULER'S THEOREM FOR POLYHEDRA

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2012, v.19 no.1, pp.37-42
https://doi.org/10.7468/jksmeb.2012.19.1.37
Kim, Dong-Soo
Kim, Young-Ho
Kim,, D. , & Kim,, Y. (2012). TOTAL ANGULAR DEFECT AND EULER'S THEOREM FOR POLYHEDRA. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 19(1), 37-42, https://doi.org/10.7468/jksmeb.2012.19.1.37

Abstract

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.

keywords
polygon, polyhedron, exterior angle theorem, Euler's theorem, Descartes' theorem

Reference

1.

A Survey of Geometry.

2.

Descartes on Polyhedra: A Study of the De Solidorum Elementis.

3.

(1981). Descartes, Euler, Poincare, Polya. Enseign. Math., 27, 327-343.

4.

(1996). The Euler Characteristic and Polya's Dream. Amer. Math. Monthly, 103, 121-131. 10.2307/2975104.

5.

Mathematical Discovery.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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