The Saga of Theorems: Pythagoras
Pythagoras is much more than a mathematician, whose theorem, famous since Antiquity, has traversed generations and has sparked, over the centuries, an impressive number of proofs. Whether one speaks with deference of the Pythagorean school or with distrust of the sect of Pythagoreans, one cannot forget that this mysterious figure, about whom almost nothing is known, is at the center of a philosophical framework perpetuated by his disciples that influenced, beyond mathematics and astronomy, music itself.
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Proofs of the Pythagorean theorem through the ages
The Pythagorean theorem began as a result about squares constructed on the sides of a right triangle. Those geometric squares later became arithmetic squares, before the theorem ventured into abstract spaces. Would Pythagoras recognize his theorem if he came back to life today?
Pythagorean triples
In a right triangle, the square of the hypotenuse equals the sum of the squares of the two sides forming the right angle. When three integers satisfy this relation, they are called a Pythagorean triple. What are these numbers, and how can they be characterized?
Pythagoras without words: visual proofs | Tangente
How many students can prove the Pythagorean theorem? Yet there is certainly no shortage of proofs.
What if it were false?
Is Pythagoras' theorem really true? The question may seem strange, but in fact it all depends on the setting in which we wish to apply this geometric result.
The Pythagorean circle
The radius of the circle inscribed in a right triangle whose three sides have integer lengths is itself an integer! This little arithmetical curiosity is very easy to prove.
Pythagoras: much more than a theorem
Pythagoras is more than the name of a famous theorem: he inspired an entire philosophical tradition that would influence not only mathematics and astronomy but music itself. Beyond the sciences, history has not heard the last of the "long-haired Samian"!