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A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
There are an infinite number of Pythagorean triples, and this is quite easy to prove. Consider the triple (3, 4, 5). We can create another triple by multiplying each value by 2:
With a the shorter and b the longer legs of a triangle and c its hypotenuse, the Pythagoras family of triplets is defined by c − b = 1, the Plato family by c − b = 2, and the Fermat family by |a − b| = 1.
Pythagorean triples (a,b,c) are three non-negative integers that satisfy the condition of Pythagoras theorem for a right-angled triangle. Learn the formulas, list, and examples at BYJU’S.
Triangles. When a triangle's sides are a Pythagorean Triple it is a right angled triangle. See Pythagoras' Theorem for more details. Example: The Pythagorean Triple of 3, 4 and 5 makes a Right Angled Triangle: Here are two more Pythagorean Triples: And each triangle has a right angle! List of the First Few.
Constructing Pythagorean Triples. It is easy to construct sets of Pythagorean Triples. When m and n are any two positive integers (m > n): a = m 2 − n 2; b = 2mn; c = m 2 + n 2; Then a, b and c form a Pythagorean Triple. This is known as "Euclid's formula".
24 Οκτ 2024 · A Pythagorean triple is a triple of positive integers , , and such that a right triangle exists with legs and hypotenuse . By the Pythagorean theorem, this is equivalent to finding positive integers , , and satisfying. (1) The smallest and best-known Pythagorean triple is .
