Hyperbolic Triangle Centers by A.A. Ungar

Author:A.A. Ungar
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht

(6.68)

Fig. 6.5The Law of Gyrosines. Drawing gyrotriangle gyroaltitudes in Einstein Gyrovector Spaces , and employing a basic gyrotrigonometric formula, shown in Fig. 6.4, we obtain the Law of Gyrosines, (6.44), in full analogy with the derivation of its Euclidean counterpart, the Law of Sines. The orthogonal projection of a on c ′=⊖ B⊕A is c 2 and, similarly, the orthogonal projection of b ′=⊖ A⊕C on c is c 1. Clearly, ‖b ′‖=‖b‖, and ‖c ′‖=‖c‖. It follows from the gyrotriangle equality that ‖c‖=‖c 1‖⊕‖c 2‖

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