Pythagorean Triples Flashcards

A set of three positive integers (a, b, c) that satisfy the equation a² + b² = c².

The smallest Pythagorean triple is (3, 4, 5).

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

(5, 12, 13) is a Pythagorean triple because 5² + 12² = 13².

(8, 15, 17) is a Pythagorean triple because 8² + 15² = 17².

You can generate Pythagorean triples using the formula: a = m² - n², b = 2mn, c = m² + n², where m > n > 0.

A Pythagorean triple is primitive if a, b, and c have no common factors other than 1.

A non-primitive Pythagorean triple is a multiple of a primitive triple, e.g., (6, 8, 10) is a multiple of (3, 4, 5).

Pythagorean triples are used in construction and design to create right angles.

To check if (a, b, c) is a Pythagorean triple, verify that a² + b² = c².