
Tales of Thales
Thales fascinates! Many historians of science and mathematics have taken an interest in this legendary figure.


Thales fascinates! Many historians of science and mathematics have taken an interest in this legendary figure.


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Who has never heard of Thales's theorem? Yet this extremely famous geometric statement is also one of the theorems whose history is least certain. Let's try to separate history from legend...

Since antiquity, navigators have sought to find their position at sea, first developing instruments and then maps before the practice was standardized in the 19th century. This practical and strategic use of mathematics endured for centuries before other tools superseded it.

Many proofs in elementary geometry rely on proportionality. Almost all of geometry’s classic theorems involve it: Thales, Ptolemy, Menelaus, Ceva, Pappus… Here is a brief tour of these great problems.

In France, Thales' theorem concerns parallel lines and proportionality. Its proof, combining algebra and plane geometry, is remarkably elegant. It also leads naturally to two landmark results in triangle geometry: Menelaus' and Ceva's theorems.
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