Geometry is the branch of mathematics concerned with the properties, measurement, and relationships of points, lines, angles, surfaces, and solids.
Geometry studies shapes, sizes, positions, and dimensions. It is divided into plane geometry (2D: points, lines, circles, triangles) and solid geometry (3D: spheres, cubes, cylinders). Euclidean geometry is based on axioms and postulates. Key concepts include congruence, similarity, symmetry, transformations, and coordinate geometry. Geometry is essential in architecture, engineering, art, navigation, and computer graphics.
Geometry originated in ancient civilizations for land measurement (Egyptian "geo-metria" means "earth measurement"). Greek mathematician Euclid wrote "Elements" (300 BCE), one of the most influential works in mathematics, organizing geometry into a logical system of axioms and theorems. Non-Euclidean geometries were developed by Gauss, Bolyai, and Lobachevsky in the 19th century, leading to Einstein's theory of general relativity.