A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), a well-known... 81 KB (11,502 words) - 19:20, 12 April 2024 |
formulas for generating Pythagorean triples have been developed. Euclid's, Pythagoras' and Plato's formulas for calculating triples have been described here:... 29 KB (4,748 words) - 05:45, 9 April 2024 |
the Pythagorean theorem, but that "there is no evidence that they used it to construct right angles". The following are all the Pythagorean triple ratios... 20 KB (1,681 words) - 19:37, 20 April 2024 |
In mathematics, a tree of primitive Pythagorean triples is a data tree in which each node branches to three subsequent nodes with the infinite set of... 15 KB (2,370 words) - 20:37, 26 February 2024 |
Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored red and blue so that no Pythagorean triples... 4 KB (534 words) - 07:28, 26 May 2023 |
side of the fifth smallest right triangle that forms a primitive Pythagorean triple (20, 21, 29). It is the third tetrahedral number. In decimal, 20 is... 15 KB (1,696 words) - 04:49, 30 April 2024 |
Pell number (section Pythagorean triples) b, c (necessarily satisfying the Pythagorean theorem a2 + b2 = c2), then (a,b,c) is known as a Pythagorean triple. As Martin (1875) describes, the Pell... 28 KB (3,701 words) - 10:56, 6 January 2024 |
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans... 76 KB (9,712 words) - 05:00, 31 March 2024 |
zero (thus allowing Pythagorean triples to be included) with the only condition being that d > 0. In this setting, a Pythagorean quadruple (a, b, c, d)... 11 KB (1,270 words) - 09:30, 28 March 2024 |
Similar to a Pythagorean triple, an Eisenstein triple (named after Gotthold Eisenstein) is a set of integers which are the lengths of the sides of a triangle... 3 KB (292 words) - 10:38, 27 October 2022 |
In geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem or the upside down Pythagorean theorem) is as follows: Let... 6 KB (776 words) - 17:53, 12 March 2024 |
Quadric (section Pythagorean triples) transforms a Pythagorean triple into another Pythagorean triple, only one of the two cases is sufficient for producing all primitive Pythagorean triples. The... 41 KB (7,405 words) - 22:28, 22 February 2024 |
of the Pythagorean theorem, both in the case of an isosceles right triangle and in the general case, as well as lists of Pythagorean triples. In Baudhayana... 24 KB (3,010 words) - 14:55, 12 April 2023 |
(ed.). "Sequence A103606 (Primitive Pythagorean triples in nondecreasing order of perimeter, with each triple in increasing order, and if perimeters... 97 KB (12,152 words) - 23:09, 24 April 2024 |
vegetarianism before the nineteenth century Pythagorean theorem Pythagorean triple Pythagorean prime Pythagorean trigonometric identity Table of Pythagoras... 1,003 bytes (138 words) - 14:22, 29 May 2023 |
Square root of 2 (redirect from Pythagorean constant) {\displaystyle b^{2}+b^{2}=a^{2}} Here, (b, b, a) is a primitive Pythagorean triple, and from the lemma a is never even. However, this contradicts the... 39 KB (5,485 words) - 11:37, 19 April 2024 |
Fermat's Last Theorem (category Pythagorean theorem) This is now known as the Pythagorean theorem, and a triple of numbers that meets this condition is called a Pythagorean triple; both are named after the... 103 KB (11,488 words) - 20:39, 7 April 2024 |
simple Pythagorean triples, such as: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), and (12, 35, 37), as well as a statement of the Pythagorean theorem... 102 KB (13,440 words) - 06:52, 22 April 2024 |
lengths of the smallest whole number right triangle: 3, 4, 5, a type of Pythagorean triple. The first fullerene to be discovered was buckminsterfullerene C60... 12 KB (1,512 words) - 16:03, 25 April 2024 |
to confirm if an angle is a true right angle. It is based on the Pythagorean triple (3, 4, 5) and the rule of 3-4-5. From the angle in question, running... 7 KB (839 words) - 04:50, 10 April 2024 |
{1}{2}}\alpha }}\end{aligned}}} Using double-angle formulae and the Pythagorean identity 1 + tan 2 α = 1 / cos 2 α {\textstyle 1+\tan ^{2}\alpha... 14 KB (3,045 words) - 02:16, 10 April 2024 |
Power point tracking, a solar energy charging technology Primitive Pythagorean triple, three integers that form a right triangle Probabilistic polynomial-time... 2 KB (324 words) - 09:57, 11 September 2023 |
Pythagorean tree may refer to: Tree of primitive Pythagorean triples Pythagoras tree (fractal) This disambiguation page lists articles associated with... 127 bytes (45 words) - 20:16, 29 December 2019 |
List of trigonometric identities (redirect from Triple angle formulae) t2, 1 + t2) values in the above formulae are proportional to the Pythagorean triple (2pq, q2 − p2, q2 + p2). For example, for n = 3 terms, π 2 = arctan... 82 KB (12,166 words) - 17:44, 25 April 2024 |