Author(s)

Weiyu Luo

School of Mathematics and Statistics, Guangxi Normal University, Guilin, China.

In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry.

Lorentz Transformation, Einstein Velocity Addition, Hyperbolic Space

Luo, W. (2024) The Vertical Projection Model of Hyperbolic Space and Geometric Illustration of Special Relativity. Journal of Applied Mathematics and Physics, 12, 72-90. doi: 10.4236/jamp.2024.121008.