Some examples of the use of distances as coordinates for Euclidean geometry

Authors:
Timothy F. Havel
Affiliations:
Harvard Medical School, 24O Longwood Ave., Boston, MA 02115, U.S.A.
Venue:
Journal of Symbolic Computation
Year:
1991

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Abstract

Distance geometry provides us with an implicit characterization of the Euclidean metric in terms of a system of polynomial equations and inequalities. With the aid of computer algebra programs, these equations and inequalities in turn provide us with a coordinate-free approach to proving theorems in Euclidean geometry analytically. This paper contains a brief summary of the mathematical results on which this approach is based, together with some examples showing how it is applied. In particular, we show how it can be used to derive the topological structure of a simple linkage mechanism.