The Pythagorean theorem is a fundamental principle in geometry that relates the sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In algebraic terms, this is represented as a² + b² = c², where 'a' and 'b' are the lengths of the legs of the triangle, and 'c' is the length of the hypotenuse. While the theorem is named after the ancient Greek mathematician and philosopher Pythagoras, who lived around 570–500/490 BCE, evidence suggests that knowledge of the theorem predates him. Remarkably, Babylonian tablets dating back to circa 1900–1600 BCE demonstrate an understanding of this geometric principle. These tablets include precise calculations for the square root of 2, which is the hypotenuse of an isosceles right triangle with legs of length 1, and they also present lists of integer triples known as Pythagorean triples. These triples are sets of three positive integers that fit the theorem's equation, such as the well-known (3, 4, 5) where 3² + 4² = 5², or 9 + 16 = 25. In addition to the Babylonian records, the Pythagorean theorem was mentioned in an ancient Indian text, the Baudhayana Sulba-sutra, written between 800 and 400 BCE. But despite these earlier references, the theorem is most commonly associated with Pythagoras himself. This theorem is fundamental to many areas of mathematics and science. It is also prominently featured in Greek mathematics, including being the 47th proposition in Book I of Euclid’s "Elements," which is one of the most influential works in the history of mathematics. The Pythagorean theorem continues to be an essential tool in modern mathematics, education, and fields that involve spatial relationships, such as physics, engineering, architecture, and various applied sciences.