Lobachevsky's Principles of Geometry

Lobachevsky’s Principles of Geometry, also known as hyperbolic geometry, challenge traditional ideas by proposing that through a point not on a line, there are infinite lines parallel to the original. Unlike Euclidean geometry, where only one parallel line exists, hyperbolic geometry allows many. This leads to unique properties, such as the angles of a triangle summing to less than 180 degrees, and demonstrates that the rules of space can vary depending on geometric context. Lobachevsky’s work expanded our understanding of possible geometrical systems beyond everyday, flat Euclidean space.