Pythagorean theorem Pythagoras personally, [...] one can safely assume that it belongs to the very oldest period of Pythagorean mathematics." Around 400 BC, according to Proclus, Plato gave a method for finding Pythagorean triples that combined algebra and geometry. Around 300 BC, in Euclid's "Elements", the oldest extant axiomatic proof of the theorem is presented. 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
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