Pythagorean theorem summary

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Below is the article summary. For the full article, see Pythagorean theorem.

Pythagorean theorem, Rule relating the lengths of the sides of a right triangle. It says that the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse (the side opposite the right angle). That is, a² + b² = c², where c is the length of the hypotenuse. Triads of whole numbers that satisfy it (e.g., 3, 4, and 5) are called Pythagorean triples. See also law of cosines; law of sines.

Euclid Summary

Euclid was the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry, the Elements. Of Euclid’s life nothing is known except what the Greek philosopher Proclus (c. 410–485 ce) reports in his “summary” of famous Greek mathematicians. According to him, Euclid