Pythagoras' theorem is a fundamental principle in geometry that states that in a right-angled triangle, 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. Mathematically, it can be expressed as ( a^2 + b^2 = c^2 ), where ( c ) represents the length of the hypotenuse, and ( a ) and ( b ) represent the lengths of the other two sides. This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.