Feuerbach's relation and Ptolemy's theorem in R
n |
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Authors: | R J Gregorac |
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Institution: | (1) Iowa State University, 50011 Ames, IA, USA |
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Abstract: | Ptolemy's equality for four points on a circle is related to a Feuerbach-type area relation. This suggested an extension of Ptolemy's inequality to a Feuerbach type volume relation between simplexes formed from n+2 points in R
n
(n 2). Extensions of the Möbius-Neuberg and Pompeiu Theorems in R
2 are given for R
n
. Ptolemy's inequality is also extended to convex n-gons in R
2 yielding an extension of Fuhrmann's hexagon theorem to 2n-gons in R
2 (n 3). |
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Keywords: | 51M16 |
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