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  2. Pythagorean triple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_triple

    When a triple of numbers a, b and c forms a primitive Pythagorean triple, then (c minus the even leg) and one-half of (c minus the odd leg) are both perfect squares; however this is not a sufficient condition, as the numbers {1, 8, 9} pass the perfect squares test but are not a Pythagorean triple since 1 2 + 8 2 ≠ 9 2. At most one of a, b, c ...

  3. Tree of primitive Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Tree_of_primitive...

    A tree of primitive Pythagorean triples is a mathematical tree in which each node represents a primitive Pythagorean triple and each primitive Pythagorean triple is represented by exactly one node. In two of these trees, Berggren's tree and Price's tree, the root of the tree is the triple (3,4,5), and each node has exactly three children ...

  4. Formulas for generating Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Formulas_for_generating...

    We remember that the Euclid’s formulas do not give all Pythagorean triples that involves a predetermined positive integer x —for example, the triples (12,9,15), (33,180,183), and (33,44,55). Moreover, it can be laborious to find m and n such that x = m 2 − n 2 .

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  8. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    A Pythagorean triple has three positive integers a, b, and c, such that a 2 + b 2 = c 2. In other words, a Pythagorean triple represents the lengths of the sides of a right triangle where all three sides have integer lengths. [1] Such a triple is commonly written (a, b, c). Some well-known examples are (3, 4, 5) and (5, 12, 13).

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