Geometry -- Cultural View

Geometry deals with space and figures in space, properties of figures, such as size and shape. Geometry as a disipline was first documented by Euclid. Euclid was an African who established the School of Mathematics in Alexandria, Egypt around 300 B.C. Euclidean geometry was the heart of nearly all mathematics prior to the seventeenth century A.D. Because of its clear, concise and accurate depiction of the real world, Euclidean geometry stood for almost two thoursand years without being changed or enhanced.

There are several types of Geometry in use today. For example:

	Euclidean Geometry	based on Euclid's axioms
	Plane Geometry	2 dimensional figures
	Solid Geometry	3 dimensional figures
	Spherical Geometry	figures on surface of spheres
	Non-Euclidean Geometry	based on alteration of Euclid's theorems Analytic - algebra and geometry
	Analytic Geometry	The geometry that deals with the relationship between algebra and geometry, using graphs and equations of lines, curves and surfaces to develop and prove relationships.

Any formal gometry is based on assumptions, as set of undefined terms and a set of statements about them that are called postulates, or axioms. From these assumption, you define new terms and prove other statements by the logical process of deduction. The statements that are proved from the postulates by deduction are called theorems or propositions.

Therefore, any formal geometry is a collection of postulates and the theorems that may be deduced from them. Euclid thought it important to make his set of axioms and postulates as small as possible. Another important idea in the study of Euclidean geometry is that of geometric construction. Since the time of Euclid, formal geometric construction allows only two tools: a straightedge and a compass.