## Geometry |

**Geometry** (from the *geo-* "earth", *-metron* "measurement") is a branch of ^{[1]} A mathematician who works in the field of geometry is called a

Geometry arose independently in a number of early cultures as a practical way for dealing with ^{[1]} Geometry began to see elements of formal ^{[2]} By the 3rd century BC, geometry was put into an *Elements*^{[3]} Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC.^{[4]} Islamic scientists preserved Greek ideas and expanded on them during the ^{[5]} By the early 17th century, geometry had been put on a solid ^{[6]}

While geometry has evolved significantly throughout the years, there are some general concepts that are fundamental to geometry. These include the concepts of ^{[7]}

Geometry has applications to many fields, including ^{[8]}

- history
- important concepts in geometry
- contemporary geometry
- applications
- see also
- notes
- sources
- further reading
- external links

The earliest recorded beginnings of geometry can be traced to ancient ^{[9]}^{[10]} Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in * Rhind Papyrus* (2000–1800 BC) and

In the 7th century BC, the ^{[2]} Pythagoras established the ^{[15]} though the statement of the theorem has a long history.^{[16]}^{[17]} ^{[18]} as well as a theory of ratios that avoided the problem of * Elements*, widely considered the most successful and influential textbook of all time,

* Satapatha Brahmana* (3rd century BC) contains rules for ritual geometric constructions that are similar to the

*In the Middle Ages, mathematics in medieval Islam contributed to the development of geometry, especially algebraic geometry.*

*In the early 17th century, there were two important developments in geometry. The first was the creation of analytic geometry, or geometry with coordinates and equations, by René Descartes (1596–1650) and Pierre de Fermat (1601–1665).*

*Two developments in geometry in the 19th century changed the way it had been studied previously. ^{[36]} These were the discovery of non-Euclidean geometries by Nikolai Ivanovich Lobachevsky, János Bolyai and Carl Friedrich Gauss and of the formulation of symmetry as the central consideration in the Erlangen Programme of Felix Klein (which generalized the Euclidean and non-Euclidean geometries). Two of the master geometers of the time were Bernhard Riemann (1826–1866), working primarily with tools from mathematical analysis, and introducing the Riemann surface, and Henri Poincaré, the founder of algebraic topology and the geometric theory of dynamical systems. As a consequence of these major changes in the conception of geometry, the concept of "space" became something rich and varied, and the natural background for theories as different as complex analysis and classical mechanics.^{[37]}
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