VARIOUS MODELS OF THE LOBACHEVSKY PLANE AND THEIR GEOMETRIC INTERPRETATIONS

This article explores the fundamental models of the Lobachevsky plane, a cornerstone of hyperbolic geometry. It focuses on three major representations: the Poincaré disk model, the Beltrami-Klein model, and the upper half-plane model. The models are compared in terms of their geometric features, such as distance, angles, and parallel lines. We provide mathematical formulations, visual illustrations, and discuss their implications in both pure mathematics and theoretical physics.