Geometry is a branch of mathematics that studies the shapes and properties of patterns. The word "geometry" originally meant surveying (in Greek, geo = earth, metre'in = measure). In ancient Babylonia and Egypt, geometrical data was applied to practical actions. The Egyptians utilized geometry when they built the pyramids. However, geometry only developed into an actual science some decades later in Ancient Greece. The Greeks found that geometry could be utilized in construction, urban zoning, sailing and astronomy. They found that there were laws between the sides and corners of the triangle.

One of the oldest known results related to geometry is the Pythagorean theorem. It is named after the Greek mathematician Pythagoras (ca. 500 BC). However, Pythagoras was more of a mystic than a mathematician. He was the first person to call himself a philosopher, a lover of knowledge. Pythagoras founded a religious secret society, the Union of Pythagoras, whose members were called the Pythagoreans. They explored the harmony of balanced opposites such as odd and even, male and female, and good and evil. The fundamental opposites were the finite, which had a definite form, and the infinite, which was made of chaos. The Pythagoreans believed in the limited influence of the infinite and productive mystical One, which was revered as the source of all the figures. They considered numbers to be the essence of reality. The symbol of the secret society was a pentagonal star or pentagram. 

One of the most significant achievements of Greek science was the presentation of the foundations of geometry compiled by Euclid (ca. 300 BC). In his famous work, Elementa (The Elements), he gathered the knowledge of mathematics of the time. Because of its consistency and clarity, Elementa has influenced the development of mathematics more than any other work.