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- W3216145041 abstract "Barycentric coordinates are commonly used in Euclidean geometry. Following the adaptation of barycentric coordinates for use in hyperbolic geometry in recently published books on analytic hyperbolic geometry, known and novel results concerning triangles and circles in the hyperbolic geometry of Lobachevsky and Bolyai are discovered. Among the novel results are the hyperbolic counterparts of important theorems in Euclidean geometry. These are: (1) the Inscribed Gyroangle Theorem, (ii) the Gyrotangent-Gyrosecant Theorem, (iii) the Intersecting Gyrosecants Theorem, and (iv) the Intersecting Gyrochord Theorem. Here in gyrolanguage, the language of analytic hyperbolic geometry, we prefix a to any term that describes a concept in Euclidean geometry and in associative algebra to mean the analogous concept in hyperbolic geometry and nonassociative algebra. Outstanding examples are {it gyrogroups} and {it gyrovector spaces}, and Einstein addition being both {it gyrocommutative} and {it gyroassociative}. The prefix gyro stems from gyration, which is the mathematical abstraction of the special relativistic effect known as Thomas precession." @default.
- W3216145041 created "2021-12-06" @default.
- W3216145041 creator A5007987799 @default.
- W3216145041 date "2013-05-22" @default.
- W3216145041 modified "2023-09-27" @default.
- W3216145041 title "On the Study of Hyperbolic Triangles and Circles by Hyperbolic Barycentric Coordinates in Relativistic Hyperbolic Geometry" @default.
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