Geometric Applications of The Grassmann-Cayley Algebra

Authored by: Neil L. White

Discrete and Computational Geometry

Print publication date:  April  2004
Online publication date:  April  2004

Print ISBN: 9781584883012
eBook ISBN: 9781420035315
Adobe ISBN:

10.1201/9781420035315.ch59

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Abstract

Grassmann-Cayley algebra is first and foremost a means of translating synthetic projective geometric statements into invariant algebraic statements in the bracket ring, which is the ring of projective invariants. A general philosophical principle of invariant theory, sometimes referred to as Gram’s theorem , says that any projectively invariant geometric statement has an equivalent expression in the bracket ring; thus we are providing here the practical means to carry this out. We give an introduction to the basic concepts, and illustrate the method with several examples from projective geometry, rigidity theory, and robotics.

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