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 is not just for math class; it is a puzzle-solving tool that architects, engineers, and even treasure hunters use. It is useful in geometry, trigonometry, and calculating distances between points.