What is Pythagorean theorem?
[[File:Pythagorean.svg|thumb|260px|'''Pythagorean theorem'''<br/>The sum of the areas of the two squares on the legs (''a'' and ''b'') equals the area of the square on the hypotenuse (''c'').]] In [[mathematics]], the ''' Pythagorean theorem''' or [https://www.bloglovin.com/@justtutors5/pythagoras-theorem-with-proof-formula-example Pythagoras's theorem]{{Dead link|date=March 2024 |bot=InternetArchiveBot |fix-attempted=yes }} is a statement about the [[side]]s of a right [[triangle]]. One of the [[angle]]s of a [[right triangle]] is always equal to 90 [[degree (geometry)|degrees]]. This angle is the [[right angle]]. The two sides next to the right angle are called the legs and the other side is called the [[hypotenuse]]. The hypotenuse is the side opposite to the right angle, and it is always the longest side. ==Claim of the theory== The Pythagorean theorem says that the [[area]] of a [[square (geometry)|square]] on the hypotenuse is equal to the [[sum]] of the areas of the squares on the legs. In this picture, the area of the blue square added to the area of the red square makes the area of the purple square. It was named after the [[Ancient Greece|Greek]] mathematician [[Pythagoras]]: If the lengths of the legs are ''a'' and ''b'', and the length of the hypotenuse is ''c'', then, <math>a^2+b^2=c^2</math>. ==Types of proofs== There are many different proofs of this theorem. They fall into four categories: # Those based on linear relations: the algebraic proofs. # Those based upon comparison of areas: the geometric proofs. # Those based upon the vector operation. # Those based on mass and velocity: the dynamic proofs.<ref>Loomis, Elisha S. 1927. ''The Pythagorean proposition: its proofs analysed and classified and bibliography of sources''. Cleveland, Ohio.</ref> == Proof == [[Image:Pyth_eudoxus.jpg|300px|right]] One [[Mathematical proof|proof]] of the Pythagorean theorem was found by a Greek mathematician, [[Eudoxus of Cnidus]]. The proof uses three [[lemma (mathematics)|lemmas]]: #[[Triangle]]s with the s