The Sum of Squares Law
Julio Kovacs, Fang Fang, Garrett Sadler, and Klee Irwin
TL;DR
This paper proves a mathematical law relating the sum of squared edge lengths of an edge-transitive polytope in N dimensions to its projection in M dimensions, establishing a ratio of N to M.
Contribution
It introduces the Sum of Squares Law, providing a precise ratio for the sum of squared edge lengths under orthogonal projection of edge-transitive polytopes.
Findings
Sum of squared edges scales with the ratio N/M
Provides a formula for edge length projections
Applicable to N-dimensional edge-transitive polytopes
Abstract
We show that when projecting an edge-transitive N-dimensional polytope onto anM-dimensional subspace of R^N, the sums of the squares of the original and projected edges are in the ratio N=M.
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Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems · Computational Geometry and Mesh Generation