Greek Geometry

Although the original roots of geometry can be traced to the Egyptians, the Greeks built on most Egyptian theories that we use today. Greek astronomy and Greek geometry were both used in order to answer many difficult questions of the time. Without geometry, the study of astronomy would have been almost impossible, and vice versa. Even though many Greek theorems and principles were later built on by geniuses such as Einstein and Lobachevsky, the basis still remains the same.

The development of Greek geometry is said to be started by Thales of Miletus. Thales came from Egypt with a number of geometric principles that the Greeks were able to use for practical purposes. He lived towards the beginning of the sixth century B.C, and has been credited with many geometric theorems. Some of the most important theorems developed by Thales included:

-If two triangles have two angles and one side is respectively equal, then both triangles are congruent to each other.

-Angles at the base of any isosceles triangle are equal.

-If two straight lines intersect, then the opposite angles formed are equal.

Thales also did much work with the height of pyramids by measuring the height of the pyramid’s shadow only at a specific time of the day. While most of his theorems were proven, some that were not pertained to a ship’s distance from shore and the bisector of a circle. His discoveries led to the formation of many other theorems by later Greeks such as Pythagoras and Plato. These two men (next to Thales) contributed the most to Greek geometry. Pythagoras discovered and proved many different theorems and ideas that contributed greatly to the development of geometry. Some of Pythagoras’s proven discoveries included:

-All of the angles in a triangle add up to the sum of two right angles.

-The development and use of geometrical algebra.

-The theorem of Pythagoras. a^2 + b^2 = c^2

Pythagoras also did many studies with triangles and developing or editing shapes. His most famous discovery was the Pythagorean theorem (listed above). This theorem combined the sides of a right triangle, and this led to the development of irrational numbers by Pythagoras later on. Pythagoras discovered that the square root of 2 was an irrational number.

Plato, another great mind of Greece, did more than just develop theorems for geometry, he stressed that geometry was essential. Plato believed that everyone should be well educated in mathematics as well as geometry. He said that math was the “tool of life”, and his promotion of geometry spread far and inspired many of his followers to pursuit their own studies of geometry. He also built on many of Pythagoras’s teachings, but he is most famous for being the first man to use a hypothesis to solve a problem. He taught that with enough educated guessing, the correct answer will come eventually.

Everyone who uses geometry today draws something from the Greeks. The Egyptians were the first to develop it, but the Greeks kept geometry alive and soon it became part of western society. Today geometry is a worldwide mathematics system, and possibly without the Greeks, geometry would have stayed buried in history, never to be learned.