Pythagorean triple
a set of three positive integers that work in the Pythagorean theorem
A Pythagorean triple is a set of three integers a, b, and c, that satisfy the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides:
c² = a² + b²
Therefore, a Pythagorean triple is a set of three integers that can be the lengths of the sides of a right-angled triangle.
Examples of Pythagorean triples include:
– (3, 4, 5)
– (5, 12, 13)
– (8, 15, 17)
– (7, 24, 25)
There are an infinite number of Pythagorean triples, and they can be derived using various methods, including the Euclidean algorithm and the properties of Pythagorean triangles.
Pythagorean triples have applications in geometry, trigonometry, and number theory. For example, they can be used to solve problems involving right-angled triangles, such as finding missing side lengths or angles. They also have connections to other mathematical concepts, such as Diophantine equations and congruences.
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