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TOTAL ANGULAR DEFECT AND EULER'S THEOREM FOR POLYHEDRA
TOTAL ANGULAR DEFECT AND EULER'S THEOREM FOR POLYHEDRA
한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2012, v.19 no.1, pp.37-42
https://doi.org/10.7468/jksmeb.2012.19.1.37
Kim, Dong-Soo
(Department of Mathematics, Chonnam National University)
Kim, Young-Ho (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
Kim, Young-Ho (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
Kim, Dong-Soo,
&
Kim, Young-Ho.
(2012). TOTAL ANGULAR DEFECT AND EULER'S THEOREM FOR POLYHEDRA. , 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
참고문헌
1.
A Survey of Geometry.
2.
Descartes on Polyhedra: A Study of the De Solidorum Elementis.
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(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.