In common parlance, geometry is a branch of mathematics that studies the relationships between figures such as points, lines, polygons, solids, vectors, surfaces and others in a space, such as a 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
Geometry comes from two Greek roots, 'γῆ' ('gê') meaning earth and 'μετρέω' ('metréō') meaning 'measure'. This shows the original use that this subject was put to, the measurement of land. This is evident from the regular layout of Greek cities, dating from ancient times. The "measurement of earth" was taken to its extreme by ancient Greek estimates of the size of the earth.
The ancient Greeks developed the formal structure of geometry, including the use of mathematical proofs to demonstrate claims, and distinguishing between axioms (and postulates), definitions, and theorems. Euclid, a Greek mathematician living in Alexandria about 300 BC wrote a 13-volume book of geometry titled The Elements (Στοιχεῖα – Stoicheía), which set forth in a structured way the geometrical knowledge of the Greeks.