Euclidean and Hyperbolic Barycentric Coordinates

Part of the Fundamental Theories of Physics book series (FTPH, volume 166)

Abstract

In Chap. 3, we have seen two important theorems in mechanics. These are Theorem 3.3, p. 69, about the mass and the center of momentum velocity of a particle system in classical mechanics, and Theorem 3.2, p. 64, about the mass and the center of momentum velocity of a particle system in relativistic mechanics. Theorem 3.3 naturally suggests the introduction of the concept of barycentric coordinates into Euclidean geometry. Guided by analogies, we will see in this chapter how Theorem 3.2 naturally suggests the introduction of the concept of barycentric coordinates into hyperbolic geometry, where they are called gyrobarycentric coordinates.

Keywords

Euclidean Geometry Hyperbolic Geometry Line Parameter Coordinate Representation Opposing Side 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Dept. Mathematics 2750North Dakota State UniversityFargoUSA

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