Geometry of the Hyperbolic Plane

The hyperbolic plane is a two-dimensional surface where the rules of geometry differ from those on a flat, Euclidean plane. In hyperbolic geometry, parallel lines diverge, meaning they spread apart as they extend, and the angles of a triangle sum to less than 180 degrees. This creates a space that curves inward, resembling a saddle shape. Such a geometry is used in advanced mathematics and physics to understand complex structures and models, offering insights into concepts like space, curvature, and the universe’s shape.