The Pythagorean theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b, and the hypotenuse c, sometimes called the Pythagorean equation: a^2 + b^2 = c^2. The theorem is named after the Greek philosopher Pythagoras, who was born around 570 BC. The theorem has been proved numerous times by many different methods, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The Pythagorean theorem isnt just for math class; its like a puzzle-solving tool that architects, engineers, and even treasure hunters use. The theorem can be used to calculate distances between points and to find the value of the hypotenuse in a right triangle. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power. The theorem can also be generalized in various ways, such as to higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and to objects that are not triangles at all but n-dimensional solids.