The History of Geometry

Early geometry goes back to about 3000 BC, as one of the first advancements of geometry. It started in Europe as the Egyptians used it in many ways such as, surveying of land, construction of the pyramids and astronomy. The next advancement came from the Babylonians in 2000-500 BC. Ancient clay tablets showed that the Babylonians knew about the pythagorean relationships.

In 750-250 BC the Greeks, practiced experimental geometry like Egypt and Babylonia had. They created the first formal mathematics of any kind by organizing geometry with rules of logic. The next advancement in geometry game from Euclid. In 300 BC he wrote a text titled "Elements". This stated that ideas could be proven through a small set of statements (postulates).

The five postulates were:

1. A straight line segment can be drawn joining any two points.
2. Given any straight line segment, a circle can be drawn having the segment as a radius and one endpoint as the center.
3. All right angles are congruent.
4. If two lives are drawn which intersect a third line in such a way that the sum of the inner angles, then the two lines inevitably, must intersect each other on the side if extended indefinitely. There was a lot of controversy over the fifth postulate.
5. The fifth postulate states "Given a line and a point not on the line, it is possible to draw exactly one line through the given point parallel to the line." Many mathematicians throughout the next centuries unsuccessfully attempted to prove this postulate.

In 1600 AD, Rene Descartes made one of the greatest advancements in geometry. He connected algebra and geometry. A myth is that he was watching a fly on the ceiling when he conceived of locating points on a plane with a pair of numbers. Fermat also discovered coordinate geometry but Descartes’ version is the one we use today.

In the early 1800’s Bolyai and Lobachevsky the first non-euclidean geometries. Since no one could prove Euclid's fifth postulate, they devised new geometries with "strange" notions of parallelism. In the late 1800’s to early 1900’s, Gauss and Riemann laid the foundation for differential geometry. Differential geometry combines geometry with the techniques of calculus to provide a method for studying geometry on curved surfaces.

Also in the late 1800’s to early 1900’s Mandelbrot and some other researchers researched fractal geometry. Fractals are geometric figures that model many natural structures. The invention of computers has helped with the study of fractals.