# What is geometry?

• (noun): The pure mathematics of points and lines and curves and surfaces.

## Geometry

Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metron "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 a 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 mapping the positions of the 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. Both geometry and astronomy were considered in the classical world to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.

### Some articles on geometry:

Dehn Planes - Dehn's Semi-Euclidean Geometry
... values in Ω(t), gives a model of Euclidean geometry ... the plane (points (x,y) with x and y finite), a geometry is obtained in which the parallel postulate fails but the sum of the angles of a triangle is π ... This is Dehn's semi-Euclidean geometry ...
List Of Interactive Geometry Software
... Interactive geometry software (IGS, or dynamic geometry environments, DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry ...
Contemporary Geometry - Algebraic Geometry
... The field of algebraic geometry is the modern incarnation of the Cartesian geometry of co-ordinates ... problems, the Hodge conjecture, is a question in algebraic geometry ... Gröbner basis theory and real algebraic geometry are among more applied subfields of modern algebraic geometry ...
List Of Interactive Geometry Software - 2D Programs - GCLC
... GCLC is a dynamic geometry tool for visualizing and teaching geometry, and for producing mathematical illustrations ... There is a built-in geometry theorem prover (based on the area method) ...
Differential Geometers - Branches of Differential Geometry - CR Geometry
... CR geometry is the study of the intrinsic geometry of boundaries of domains in complex manifolds ...

### Famous quotes containing the word geometry:

I am present at the sowing of the seed of the world. With a geometry of sunbeams, the soul lays the foundations of nature.
Ralph Waldo Emerson (1803–1882)

... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or process pain.
Louise Bourgeois (b. 1911)

The geometry of landscape and situation seems to create its own systems of time, the sense of a dynamic element which is cinematising the events of the canvas, translating a posture or ceremony into dynamic terms. The greatest movie of the 20th century is the Mona Lisa, just as the greatest novel is Gray’s Anatomy.
—J.G. (James Graham)