How do you identify a Pythagorean triple?
Determine if the following lengths are Pythagorean Triples. Plug the given numbers into the Pythagorean Theorem. Yes, 7, 24, 25 is a Pythagorean Triple and sides of a right triangle. Plug the given numbers into the Pythagorean Theorem.
So we can make infinitely many triples just using the (3,4,5) triple. Euclid's Proof that there are Infinitely Many Pythagorean Triples.
- The square of the length of the hypotenuse of a right triangle is the sum of the squares of the lengths of the two sides. This is usually expressed as a2+b2 = c2. Integer triples which satisfy this equation are Pythagorean triples. The most well known examples are (3,4,5) and (5,12,13).
- A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime (that is, they have no common divisor larger than 1).
- Pythagoras, (born c. 570 bce, Samos, Ionia [Greece]—died c. 500–490 bce, Metapontum, Lucanium [Italy]), Greek philosopher, mathematician, and founder of the Pythagorean brotherhood that, although religious in nature, formulated principles that influenced the thought of Plato and Aristotle and contributed to the
Updated: 2nd October 2019