Thales of Miletus

Thales of Miletus, a man of Greek ancestry, is one of the first individuals that we know of who contributed towards the
evolution of and discoveries in mathematics. What we know of the subject before Thales is largely anonymous.
Thales was born in Miletus, a trading post on the west coast of Asia Minor in about 624 BC.

Sometimes referred to as one of the ‘seven wise men’ of antiquity, Thales was a genius who won a reputation as a
statesman and businessman as well as being a philosopher, mathematician and astronomer. Thales spent his early
life as a trader and became quite rich. In his travels he undoubtedly visited the centres of learning at the time in
Egypt, where he became interested in geometry, and Babylon, where he learned astronomy.

The latter part of his life was spent studying and travelling, including spending some time in Egypt where he
calculated the height of a pyramid. According to Hieronymus, a pupil of Aristotle, Thales calculated the height of the
pyramid using shadows. Thales noted the moment when the length of the shadow of the pyramid was the same as the
length of his own shadow. According to Plutarch, Thales calculated the height of the pyramid using similar triangles.

Thales’ contributions to mathematics were mainly to geometry. Among other things, he is reputed to have proposed
that vertically opposite angles are equal, the theorem that the angle in a semicircle is a right angle and also studied
congruent triangles. He is also accredited with predicting the solar eclipse of 585 BC. His philosophy is summed up in
the words attributed to him: ‘Know thyself.’

Thales died in about 548 BC.

A contribution of Thales to mathematics

P is any point on the circumference of a circle, centre O and AB is a diameter of the circle.

Thales showed that angle APB = 90⁰, or a right angle. It doesn’t matter where P lies on the circumference, the result
is always true.
Although this result was known to the Babylonians, Thales is accredited with some kind of proof of the theorem,
sometimes called ‘The Theorem of Thales’.
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