Geometry

In common parlance, geometry is a branch of mathematics that studies the relationships between figures such as e.g. points, lines, polygons, solids, vectors, surfaces and others in a space, such as plane, a higher dimensional Euclidean space, a sphere or other non-Euclidean space, or more generally, a manifold.

As a mathematical term, geometry refers to either the spatial (metric) properties of a given space or, more specifically in differential geometry, a given complete locally homogeneous Riemannian manifold.

History of geometry

The ancient Greeks developed the structure of geometry as it is currently known, including the use of mathematical proofs to demonstrate theorems, and distinguishing between axioms, definitions, and theorems. Euclid, a Greek mathematician living in Alexandria about 300 BC wrote a 13-volume book of geometry titled The Elements (Στοιχεῖα), which set forth in a structured way the geometrical knowledge of the Greeks.