Geometry began with land measurement in ancient Egypt and Babylon. The word means "earth measurement." Greek mathematicians, especially Euclid, turned it into a deductive system. His Elements organized geometry into axioms, definitions, and proofs that influenced mathematics for over two thousand years.

Today geometry covers much more. Euclidean geometry studies flat surfaces and solid figures. Non-Euclidean geometries describe curved spaces. Analytic geometry uses coordinates and algebra. Differential geometry studies curves and surfaces with calculus. Topology extends the study of shape to properties preserved under deformation.

Geometry is visual and logical at the same time. It trains spatial reasoning and proof skills. Architects, engineers, artists, and physicists all rely on geometric thinking. Whether measuring a triangle or describing the curvature of spacetime, geometry provides the language.

• Study of shapes, sizes, and space
• Euclid's Elements systematized the subject
• Includes Euclidean, analytic, and differential geometry
• Essential in architecture, engineering, and physics