Geometry began as land measure in Mesopotamia and Egypt
Geometry studies the distance, shape, size and relative position of figures, and alongside arithmetic it is one of mathematics' oldest branches. Its earliest records come from Mesopotamia and Egypt in the second millennium BC, where rules of thumb served surveyors, builders, astronomers and craftsmen.
The oldest known geometry texts are the Egyptian Rhind Papyrus and Moscow Papyrus and Babylonian tablets such as Plimpton 322, all from roughly 2000 to 1800 BC. The Moscow Papyrus gives the volume of a truncated pyramid. Later Babylonian tablets tracked Jupiter with trapezoid methods that anticipated the medieval Oxford Calculators by 14 centuries. In the seventh century BC Thales of Miletus measured pyramids and the distance of ships at sea and is credited with the first deductive geometry. Eudoxus devised the method of exhaustion for curved areas and volumes, and around 300 BC Euclid's Elements set the pattern of definition, axiom, theorem and proof still used today.
India's Śulba Sūtras hold the earliest surviving verbal statement of the Pythagorean theorem, though the Old Babylonians already knew it, along with lists of Pythagorean triples. Aryabhata computed areas and volumes in 499, and in 628 Brahmagupta gave his theorem on the diagonals of a cyclic quadrilateral and a formula for its area. In the Islamic world al-Mahani turned problems like doubling the cube into algebra, and Omar Khayyam solved cubic equations geometrically. Work on quadrilaterals by Ibn al-Haytham, Khayyam and al-Tusi fed a long European inquiry into the parallel postulate that ended in hyperbolic geometry.
The nineteenth century widened the field. Gauss's Theorema Egregium showed a surface's curvature does not depend on how it sits in surrounding space, opening the way to manifolds and Riemannian geometry, and geometries without the parallel postulate proved free of contradiction. General relativity rests on one of them.
Since then geometry has split by method into differential, algebraic, computational and discrete branches, or by what it ignores: projective geometry drops distance and affine geometry drops angle. Algebraic geometry was central to Wiles's proof of Fermat's Last Theorem.
Source: Geometry
