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Pyramid and inequality

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November 19, 2005
geometry3D geometrypyramidinequalitiesgeometry unsolved

Problem Statement

PA1A2...AnPA_1A_2...A_n is a pyramid. The base A1A2...AnA_1A_2...A_n is a regular n-gon. The apex PP is placed so that the lines PAiPA_i all make an angle 60⋅60^{\cdot} with the plane of the base. For which nn is it possible to find BiB_i on PAiPA_i for i=2,3,...,ni = 2, 3, ... , n such that A1B2+B2B3+B3B4+...+Bn−1Bn+BnA1<2A1PA_1B_2 + B_2B_3 + B_3B_4 + ... + B_{n-1}B_n + B_nA_1 < 2A_1P?
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