**Geometry** (from the ; "earth", "measurement") is a branch of

mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a

geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning

lengths,

areas, and

volumes, with elements of formal

mathematical science emerging in the West as early as

Thales (6th century BC). By the 3rd century BC, geometry was put into an

axiomatic form by

Euclid, whose treatment—

Euclidean geometry—set a standard for many centuries to follow.

Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern

integral calculus. The field of

astronomy, especially as it relates to mapping the positions of

stars and

planets on the

celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. In the classical world, both geometry and astronomy were considered to be part of the

Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.