二维时空几何中的双曲三角
Hyperbolic trigonometry in two-dimensional space-time geometry
摘要：
通过与复数类比，可以以相同的方式引入双曲数系统：z=x+h*y，其中h*h=1，x，y是实数。正如复数与欧几里德几何相联系一样，这个数字系统也与伪欧几里德平面几何（时空几何）相联系。在本文中，我们将展示如何这个系统的数字允许，通过笛卡尔表示，双曲函数的操作定义使用的不变性方面的狭义相对论洛伦兹群。从这个定义，通过使用初等数学和欧几里德方法，可以直接在笛卡尔平面上形式化伪欧几里德三角学，并具有与欧几里德三角学相同的连贯性。
英文摘要：
By analogy with complex numbers, a system of hyperbolic numbers can be introduced in the same way: z=x+h*y with h*h=1 and x,y real numbers. As complex numbers are linked to the Euclidean geometry, so this system of numbers is linked to the pseudo-Euclidean plane geometry (space-time geometry). In this paper we will show how this system of numbers allows, by means of a Cartesian representation, an operative definition of hyperbolic functions using the invariance respect to special relativity Lorentz group. From this definition, by using elementary mathematics and an Euclidean approach, it is straightforward to formalize the pseudo-Euclidean trigonometry in the Cartesian plane with the same coherence as the Euclidean trigonometry.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
