On perimeters of sections of convex polytopes |
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| Authors: | V Yaskin |
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| Institution: | Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada |
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| Abstract: | In his book “Geometric Tomography” Richard Gardner asks the following question. Let P and Q be origin-symmetric convex bodies in R3 whose sections by any plane through the origin have equal perimeters. Is it true that P=Q? We show that the answer is “Yes” in the class of origin-symmetric convex polytopes. The problem is treated in the general case of Rn. |
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| Keywords: | Convex bodies Sections of convex bodies Convex polytopes |
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