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- Tree_of_primitive_Pythagorean_triples abstract "In mathematics, a Pythagorean triple is a set of three positive integers a, b, and c having the property that they can be respectively the two legs and the hypotenuse of a right triangle, thus satisfying the equation the triple is said to be primitive if and only if a, b, and c share no common divisor. The set of all primitive Pythagorean triples has the structure of a rooted tree, specifically a ternary tree, in a natural way. This was first discovered by B. Berggren in 1934.F. J. M. Barning showed that when any of the three matrices is multiplied on the right by a column vector whose components form a Pythagorean triple, then the result is another column vector whose components are a different Pythagorean triple. If the initial triple is primitive, then so is the one that results. Thus each primitive Pythagorean triple has three "children". All primitive Pythagorean triples are descended in this way from the triple (3 ,4, 5), and no primitive triple appears more than once. The result may be graphically represented as an infinite ternary tree with (3, 4, 5) at the root node (see classic tree at right). This tree also appeared in papers of A. Hall in 1970 and A. R. Kanga in 1990.".
- Tree_of_primitive_Pythagorean_triples thumbnail Pythagorean.tree.svg?width=300.
- Tree_of_primitive_Pythagorean_triples wikiPageExternalLink PT_matrix.html.
- Tree_of_primitive_Pythagorean_triples wikiPageExternalLink EJ992372.pdf.
- Tree_of_primitive_Pythagorean_triples wikiPageID "33358028".
- Tree_of_primitive_Pythagorean_triples wikiPageRevisionID "602611059".
- Tree_of_primitive_Pythagorean_triples hasPhotoCollection Tree_of_primitive_Pythagorean_triples.
- Tree_of_primitive_Pythagorean_triples subject Category:Diophantine_equations.
- Tree_of_primitive_Pythagorean_triples subject Category:Graph_theory.
- Tree_of_primitive_Pythagorean_triples subject Category:Number_theory.
- Tree_of_primitive_Pythagorean_triples type Abstraction100002137.
- Tree_of_primitive_Pythagorean_triples type Communication100033020.
- Tree_of_primitive_Pythagorean_triples type DiophantineEquations.
- Tree_of_primitive_Pythagorean_triples type Equation106669864.
- Tree_of_primitive_Pythagorean_triples type MathematicalStatement106732169.
- Tree_of_primitive_Pythagorean_triples type Message106598915.
- Tree_of_primitive_Pythagorean_triples type Statement106722453.
- Tree_of_primitive_Pythagorean_triples comment "In mathematics, a Pythagorean triple is a set of three positive integers a, b, and c having the property that they can be respectively the two legs and the hypotenuse of a right triangle, thus satisfying the equation the triple is said to be primitive if and only if a, b, and c share no common divisor. The set of all primitive Pythagorean triples has the structure of a rooted tree, specifically a ternary tree, in a natural way. This was first discovered by B. Berggren in 1934.F. J. M.".
- Tree_of_primitive_Pythagorean_triples label "Tree of primitive Pythagorean triples".
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- Tree_of_primitive_Pythagorean_triples sameAs Q7837618.
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- Tree_of_primitive_Pythagorean_triples wasDerivedFrom Tree_of_primitive_Pythagorean_triples?oldid=602611059.
- Tree_of_primitive_Pythagorean_triples depiction Pythagorean.tree.svg.
- Tree_of_primitive_Pythagorean_triples isPrimaryTopicOf Tree_of_primitive_Pythagorean_triples.