Non-Euclidean geometry is a branch of mathematics that explores the properties of geometric objects and spaces that do not adhere to the rules of Euclidean geometry, which is based on the work of the ancient Greek mathematician Euclid.
Some examples of non-Euclidean geometry include hyperbolic geometry, which involves curved spaces, and elliptic geometry, which deals with spherical surfaces. These types of geometry have different principles and measurements than those found in Euclidean geometry.
Non-Euclidean geometry has various applications in fields such as physics, engineering, and computer graphics. It is also essential in understanding the curvature of space-time in Einstein's theory of general relativity.
The main difference between Euclidean and non-Euclidean geometry lies in their fundamental principles and theorems. In Euclidean geometry, the basic axioms are based on the concept of a flat, two-dimensional space, while non-Euclidean geometry considers curved or higher-dimensional spaces.
Some recommended books on non-Euclidean geometry include "The Non-Euclidean Revolution" by Richard J. Trudeau, "Non-Euclidean Geometry: A Critical and Historical Study of Its Development" by Roberto Bonola, and "Non-Euclidean Geometry: A Unified Approach" by Herbert Meschkowski.