The Lobachevsky Space

Lobachevsky space, also known as hyperbolic space, is a type of non-Euclidean geometry where, unlike flat or spherical spaces, parallel lines diverge and the angles of triangles sum to less than 180°. Imagine a saddle-shaped surface that extends infinitely, where distances and angles behave differently than on a flat plane. This geometry has applications in advanced physics and cosmology, helping us understand possible shapes of the universe. It provides a mathematically consistent way to explore curved spaces with constant negative curvature, expanding our comprehension of the shapes and structures beyond traditional Euclidean geometry.