Pythagoraslause

The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental principle in Euclidean geometry. It 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. This relationship can be expressed as an equation: a² + b² = c², where 'a' and 'b' represent the lengths of the two shorter sides (legs) of the triangle, and 'c' represents the length of the hypotenuse.

The theorem is named after the ancient Greek mathematician Pythagoras, although the concept was likely understood in various forms by earlier civilizations. The theorem has numerous applications in mathematics, physics, engineering, and architecture. It is used to calculate distances, determine the lengths of unknown sides in right triangles, and forms the basis for many other mathematical concepts. For example, it is crucial in coordinate geometry when calculating the distance between two points.

There are many different proofs of the Pythagorean theorem, demonstrating its robustness and importance in mathematical understanding. These proofs range from geometric rearrangements to algebraic manipulations. The theorem's enduring relevance highlights its significance as a cornerstone of geometry and a powerful tool for problem-solving across various disciplines. Its simplicity and broad applicability make it one of the most well-known and widely used theorems in mathematics.