Quadratic sequences in Pythagorean triples

Raymond Calvin Ochieng; Chiteng’a John Chikunji; Vitalis Onyango-Otieno

dc.contributor.author	Raymond Calvin Ochieng
dc.contributor.author	Chiteng’a John Chikunji
dc.contributor.author	Vitalis Onyango-Otieno
dc.date.accessioned	2024-02-27T12:27:35Z
dc.date.available	2024-02-27T12:27:35Z
dc.date.issued	2022
dc.identifier.uri	http://localhost:8080/xmlui/handle/123456789/616
dc.description	"There exist several techniques used to generate Pythagorean triples. The most effective formula for generating Pythagorean triples is the Euclid’s formula. Whereas the Euclid’s formula generate infinitely many Pythagorean triples, it does not generate all of them. For instance, the Euclid’s formula generates the triple (3, 4, 5) but does not generate (4, 3, 5), in which case a transposition is needed. In addition, the triple (9, 12, 15) cannot be generated directly from the Euclid’s formula but rather a multiplier to the triple (3, 4, 5) does so. In this note, we establish a formula which generates all Pythagorean triples, primitive and non-primitive, without using a transformation and without using a multiplier."	en_US
dc.description.abstract	Using the Euclid’s formula, we obtain an alternative formula for generating Pythagorean triples, both primitive and non-primitive. It easy to classify Pythagorean triples using this formula based on the divisibility of the leg of a Pythagorean triple by any positive integer. The differences in lengths between the hypotenuse and the legs of a Pythagorean triple obtained by this alternative formula form Quadratic sequences. These quadratic sequences have applications in various fields such as tiling	en_US
dc.publisher	Constructive Mathematical Analysis	en_US
dc.title	Quadratic sequences in Pythagorean triples	en_US