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  2. Pythagorean triple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_triple

    A primitive Pythagorean triple is one in which a, b and c are coprime (that is, they have no common divisor larger than 1). [1] For example, (3, 4, 5) is a primitive Pythagorean triple whereas (6, 8, 10) is not. Every Pythagorean triple can be scaled to a unique primitive Pythagorean triple by dividing (a, b, c) by their greatest common divisor ...

  3. Formulas for generating Pythagorean triples - Wikipedia

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

    Wade and Wade [17] first introduced the categorization of Pythagorean triples by their height, defined as c − b, linking 3,4,5 to 5,12,13 and 7,24,25 and so on. McCullough and Wade [18] extended this approach, which produces all Pythagorean triples when k > h √ 2 /d: Write a positive integer h as pq 2 with p square-free and q positive.

  4. 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).

  5. Project Mathematics! - Wikipedia

    en.wikipedia.org/wiki/Project_Mathematics!

    Pythagorean triples occur when all three sides of a right triangle are integers such as a = 3, b = 4 and c = 5. A clay tablet shows that the Babylonians knew of Pythagorean triples 1200 years before Pythagoras, but nobody knows if they knew the more-general Pythagorean theorem.

  6. 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 ...

  7. Pell number - Wikipedia

    en.wikipedia.org/wiki/Pell_number

    If a right triangle has integer side lengths a, b, c (necessarily satisfying the Pythagorean theorem a 2 + b 2 = c 2), then (a,b,c) is known as a Pythagorean triple. As Martin (1875) describes, the Pell numbers can be used to form Pythagorean triples in which a and b are one unit apart, corresponding to right triangles that are nearly isosceles ...

  8. Pythagoreanism - Wikipedia

    en.wikipedia.org/wiki/Pythagoreanism

    The Plimpton 322 tablet records Pythagorean triples from Babylonian times. [1] Animation demonstrating the simplest Pythagorean triple, 3 2 + 4 2 = 5 2. Bust of Pythagoras, Musei Capitolini, Rome. Pythagoras was already well known in ancient times for his supposed mathematical achievement of the Pythagorean theorem. [2]

  9. Integer triangle - Wikipedia

    en.wikipedia.org/wiki/Integer_triangle

    Its three integer sides are known as a Pythagorean triple or Pythagorean triplet or Pythagorean triad. [9] All Pythagorean triples ( a , b , c ) {\displaystyle (a,b,c)} with hypotenuse c {\displaystyle c} which are primitive (the sides having no common factor ) can be generated by