# From the sacred triangle to the Pythagorean theorem | Science

Long before Pythagoras (or one of his disciples) demonstrated his famous theorem, the Babylonians, the Indians and the Egyptians knew-and used effectively-the properties of the triangle of sides 3, 4 and 5, which was considered sacred. The most remarkable thing about this triangle is that the angle opposite the greater side is straight, and it is not necessary to point out the importance of the right angle in all types of measurements and constructions. In ancient Egypt, the triangle of proportions 3-4-5 most used in architecture and surveying was the one with equal sides at 15, 20 and 25 cubits respectively (about 7.5, 10 and 12.5 meters), called "isiac triangle" in honor to the goddess Isis, which was already used in the construction of the pyramid of Khafre, in the XXVI century a. C. But were the Pythagoreans who, two thousand years later, demonstrated the theorem and gave it its well-known canonical expression:

### From Pythagoras to Fermat

The Pythagorean formula to^{two} + b^{two} = c^{two} invites us to ask ourselves what happens if we generalize it to other exponents and turn it into a^{n} + b^{n} = c^{n}, where n is a whole number. Well, in 1637 Pierre de Fermat he concluded that for n greater than 2 there are not three natural numbers (integers and positives) a, b, c such that this equality is met. Fermat wrote in the margin of a book that he had found an "admirable" proof of this theorem; but such a demonstration was never found, and experts assume that Fermat was wrong … or wanted to play a joke on the mathematical community. In fact, the theorem remained in a state of conjecture for three and a half centuries, until, after numerous attempts, it was demonstrated by Andrew Wiles in 1995.

"I have found a really admirable demonstration, but it does not fit in the meager margin of this book," Fermat wrote. In this, too, time proved him right: Wiles' demonstration would be difficult to fit into the margins of a book, since it occupies about 100 pages.

**Master forms** is a section by Carlo Frabetti dedicated to explaining the main formulas of mathematics and physics, their origin, evolution and precise meaning.

**Carlo Frabetti** He is a writer and mathematician, a member of the New York Academy of Sciences. He has published more than 50 scientific dissemination works for adults, children and young people, among them *Damn physics*, *Damn mathematics* or *The big game*. He was a screenwriter *The Cristal ball.*

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