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- W214971210 abstract "We show other generalizations of Ceva’s theorem on the triangle to the n dimensional simplex than the theorems given in [2]. They are Theorems 1.1, 1.2, 2.1 and 3.1 below. Let n be any integer>2. Let 0 1 2 P P P Pn denote an arbitrary n dimensional simplex in Euclidean space n R , whose vertices are {P | 0 } j j n . Let denote the standard Euclidean measure (=volume) on n R . Let m denote the standard Euclidean measure on 1 n R . Let T be any point in the interior of 0 1 2 P P P Pn . For each integer j with 0 j n , write {P | 0 , } j x C x n x j . For each integer j with 0 j n , let j H denote the 1 n dimensional hyper-plane containing all the points in j C . For each integer j with 0 j n , let Pj denote the point of the intersection of line P T j and hyper-plane j H . For arbitrary finite points {V |1 } j j k in Euclidean space n R , let {V |1 } j j k denote the minimum closed convex subset, of n R , containing all the points {V |1 } j j k . Section 1. Case of any integer 2. n Recall that 0 1 2 P P P Pn denote an arbitrary n dimensional simplex in Euclidean space n R , whose vertices are {P | 0 } j j n . Let j be any integer with" @default.
- W214971210 created "2016-06-24" @default.
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- W214971210 date "2009-02-01" @default.
- W214971210 modified "2023-09-28" @default.
- W214971210 title "Theorems for the n dimensional simplex which are generalizations of Ceva's theorem on the triangle" @default.
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