Euclidean and Hyperbolic Barycentric Coordinates
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.
KeywordsEuclidean Geometry Hyperbolic Geometry Line Parameter Coordinate Representation Opposing Side
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