The word geometry comes from two Greek words meaning earth and to measure. There are three types of geometry used today. The first is called non-Euclidean geometry. There are two types of non-Euclidean Geometry. One type is called Hyperbolic geometry. This specific type deals with parallel lines, planes, and regular lines. Hyperbolic geometry defines lines as a chord of a circle. It defines parallel lines as lines that never intersect. And it defines planes as a set of points that lie in the interior of a circle. Hyperbolic geometry is also sometimes called Lobachevskian geometry, because it was developed in the early 1800’s by the Russian mathematician Nikolai Lobachevsky. The Second type of non-Euclidean geometry is elliptical geometry. Elliptical geometry replaces the parallel axiom with the statement through a point not on a given line, there are no lines that do not intersect the given line. In other words parallel lines do not exist. In elliptical geometry line is defined as a great circle of a sphere. Elliptical geometry is also called Riemannian geometry. It was developed in the mid-1800’s by the German mathematician George Friedrich Bernhard Riemann.
The second type of geometry it Euclidean geometry. Euclidean geometry is based on the axioms developed by Euclid in the Elements and on axioms later derived from Euclid’s axioms. Euclidean geometry can be divided into plane geometry and solid geometry. Plane geometry involves the study of suck two-dimensional figures as lines, angles, triangles, quadrilaterals, and circles. Solid geometry involves the sridy of three-dimensional figures.
And the third type of geometry is Analytic geometry. Analytic geometry is a method of studying the properties of geometric figures by using algebraic techniques. It deals with the same subject as Euclidean geometry, but provides simpler ways of proving many theorems. It has an important role in trigonometry and calculus. We use this form of geometry for a coordinate system and it deals with the same subject matter as Euclidean geometry but it makes it easier to prove many theorems.
Geometry was used back in the bible days by the Egyptians and the Babylonians. Know one really knows where or when geometry was originated but we do know that the Egyptians and the Babylonians used it. However, records of the ancient Egyptians and the Babylonians indicate that they were aware of some geometric principles as ling as 5,000 years ago. The Egyptians also developed geometric ideas that could be used to reestablish land boundaries after the flooding of the Nile River which happened every year. They also used it to build the pyramids, sphinxes, temples and so on. Like the Egyptians, the Babylonians were interested primarily in the practical applications of geometry. They used it for building and surveying. The Babylonians knew about the ideas later expressed in certain geometric theorems, including the Pythagorean Theorems which states that in a right triangle the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
During the 500’s B.C. two Greek philosophers, Thales and Pythagoras influenced the later development of geometry. Thales is known for having created the first deductive proof of a theorem. Pythagoras, often called the father of mathematics, founded a school in which mathematics was studied extensively. He also formulated a theorem called the Pythagorean theorem. The greeks became the first people to study mathematics from a theoretical point of view, and not simply for its practical applications in the 300’s B.C. A Greek philosopher named Plato and the students at his Academy were a great influence in this change of emphasis by the Greek people. Plato’s most lasting contribution to mathematics was his insistence on the use of deductive reasoning in proving geometric theorems. He argued that a person should use reason instead of physical diagrams to prove geometric theorems. Also during the 300’s B.C., the Greek philosopher Aristotle laid out very clearly the foundations for an axiomatic system.

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