Pythagorean theorem Pythagorean theorem In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides "a", "b" and "c", often called the "Pythagorean equation": where "c" represents the length of the hypotenuse and "a" and "b" the lengths of the triangle's other two sides. Although it is
Pythagorean theorem the dot product of vectors. The dot product is called the "standard" inner product or the "Euclidean" inner product. However, other inner products are possible. The concept of length is replaced by the concept of the norm ||v|| of a vector v, defined as: In an inner-product space, the Pythagorean theorem states that for any two orthogonal vectors v and w we have Here the vectors v and w are akin to the sides of a right triangle with hypotenuse given by the vector sum v + w. This form of the Pythagorean theorem is a consequence of the properties