Greek Mathematics

Greek Mathematics
pre-Euclidean period

The Greeks not only made significant advancements in geometry, but also changed the way mathematicians think. They preferred abstract concepts. Thales introduced the use of logical proof on deductive reasoning, whilst Euclid used his own ideas of axioms or postulates, assumptions accepted without justification. Other famous Greek mathematicians include Archimedes and Apollonius.

Thales Miletus, who learnt geometry from the Egyptians, discovered many geometric properties. They include, that the angle inscribed in a semicircle is a right angle, the diameter of a circle is a bisector of the circle, base angles of an isosceles triangle are equal, vertically opposite angles are equal, as well as properties of similar and congruent triangles. It is possible, but not established, that he is Pythagoras' teacher.

Pythagoras, who has the famous theorem named after him, was another early Greek mathematician. He founded a school, with aims political, philisophical and religious, almost like a cult. Pupils studied arithmetic, music, geometry and astronomy. Musical octaves and notes were established by Pythagoras. The theory of numbers, as well as the construction of Pythagorean triples, were explored.

Hippocrates of Chios was one of the first to investigate the problem of squaring the circle and doubling the cube. He eventually developed the idea of proportion in similar figures and solids. Plato distinguished between the theoretical and practical geometry, the former being the ideal case whilst the latter being the imperfect shapes drawn by people. He also ventured into the field of solid geometry. Aristotle's contributions were mainly about the logic behind arguments and proofs.