An isoperimetric problem for tetrahedra |
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Authors: | V A Zalgaller |
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Institution: | (1) Weizmann Institute, Israel |
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Abstract: | It is proved that a regular tetrahedron has the maximal possible surface area among all tetrahedra having surface with unit
geodesic diameter. An independent proof of O’Rourke-Schevon’s theorem about polar points on a convex polyhedron is given.
A. D. Aleksandrov’s general problem on the area of a convex surface with fixed geodesic diameter is discussed. Bibliography:
4 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 28–55. |
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Keywords: | |
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