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**We explain what the Pythagorean theorem is, how it is formulated and explained. Also, what are its characteristics, uses, and examples?**

The Pythagorean Theorem is **a mathematical postulate made by the Greek philosopher and mathematician Pythagoras of Psalms** (c. 569 - c. 475 BC), a student of the laws of mathematics whose contributions to arithmetic and geometry persist to this day in day. This postulate says that the sum of the square of the legs of a right triangle is always equal to the square of its hypotenuse.

This proposition is, without a doubt, **one of the best known in the history of mathematics**, and the one that has the greatest number of proofs over time, through different methods and elaborated by various philosophers and mathematicians.

According to some authors**, up to a thousand different proofs can be found**, although 367 have been formally cataloged. This is because the proof of the theorem was a requirement during the Middle Ages to achieve the title of *Magister Matheseos* (“Mathematician Teacher”) in the academy.

Although the authorship of the theorem is attributed to the Greek Pythagoras, since his proof **was**** of capital importance for the Pythagorean philosophers** (disciples formed in an almost religious cult of mathematics), the truth is that the origin of this theorem is much earlier.

There is **evidence of its use in Babylonian tablets and papyri from Ancient Egypt**, but no document exposing their relationship is preserved to this day. It is known that the study of triangles was central to many of the ancient cultures.

To begin with the Pythagorean theorem, it must be understood that the *legs*** of a right triangle** that form the right angle (90 °) **are called the legs, and the** remaining and longest side is called the

The Pythagorean theorem **is formulated as follows: a ^{2} + b ^{2} = c ^{2}** where

**a = ? c**(^{2}- b^{2}*a*is equal to the square root of*c*squared minus*b*squared)**b = ?b**(^{2}- a^{2}*b*equals the square root of*c*squared minus*a*squared)**c = ?a**(^{2}+ b^{2}*c*is equal to the square root of*a*squared plus*b*squared)

The logic of the Pythagorean theorem is quite simple and self-evident. Given a triangle with sides a, b, and c, in which a and b form a right angle (that is, 90 °), it is possible to **calculate the length of the hypotenuse by adding the squares of the legs,** or, any of the sides of the triangle.

A simple example of applying the theorem is as follows:

- Given a right triangle whose legs a and b measure 3 and 4 cm respectively, we can calculate its hypotenuse c by substituting the values in the formula, as follows: