A fundamental concept in geometry, it describes the relationship between the sides of a right triangle. Specifically, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). This relationship is commonly expressed as a2 + b2 = c2, where ‘c’ represents the length of the hypotenuse, and ‘a’ and ‘b’ represent the lengths of the legs. As an example, in a right triangle with legs of length 3 and 4, the hypotenuse has a length of 5, because 32 + 42 = 52 (9 + 16 = 25).
This theorem is crucial for various applications in mathematics, engineering, and physics. Its importance stems from its ability to determine unknown distances and angles in right triangles, facilitating calculations related to areas, volumes, and other geometric properties. Historically, its conceptual underpinnings were understood and utilized by ancient civilizations, even prior to its formal proof and articulation attributed to Pythagoras.
