The Lobachevsky plane

The Lobachevsky plane, also known as hyperbolic geometry, is a type of non-Euclidean geometry where the usual rules of flat geometry don't apply. Unlike a flat surface, this space curves inward like a saddle. Parallel lines in this geometry can diverge, meaning they can start out parallel but then spread apart infinitely. It's used to describe spaces with constant negative curvature, often in complex mathematics and physics. Imagine walking on a surface where the rules of straight lines and angles are different from a flat sheet—this is the essence of the Lobachevsky plane.