Einstein's velocity addition law and its hyperbolic geometry
Einstein's velocity addition law and its hyperbolic geometry
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DOI：
10.1016/j.camwa.2006.05.028
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发表时间：
2007-04
期刊：
影响因子：
--
通讯作者：
A. Ungar
中科院分区：
文献类型：
--
作者：
A. Ungar
在简要回顾爱因斯坦狭义相对论的速度相加定律与波耶伊和罗巴切夫斯基的双曲几何之间联系的历史之后，我们利用爱因斯坦速度相加的二元运算将矢量、角和三角的概念引入双曲几何。与欧几里得几何完全相似，我们在本文中表明，将这些概念引入双曲几何会导致双曲向量空间。后者反过来又构成了双曲几何的基础，就像向量空间构成了欧几里得几何的基础一样。
Following a brief review of the history of the link between Einstein’s velocity addition law of special relativity and the hyperbolic geometry of Bolyai and Lobachevski, we employ the binary operation of Einstein’s velocity addition to introduce into hyperbolic geometry the concepts of vectors, angles and trigonometry. In full analogy with Euclidean geometry, we show in this article that the introduction of these concepts into hyperbolic geometry leads to hyperbolic vector spaces. The latter, in turn, form the setting for hyperbolic geometry just as vector spaces form the setting for Euclidean geometry.