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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 ...
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.
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).
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 ...
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 ...
The Pythagorean triple (4,3,5) is associated to the rational point (4/5,3/5) on the unit circle. In mathematics, the rational points on the unit circle are those points (x, y) such that both x and y are rational numbers ("fractions") and satisfy x 2 + y 2 = 1. The set of such points turns out to be closely related to primitive Pythagorean triples.
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