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...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

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...

formulas for generating Pythagorean triples have been developed. Euclid's, Pythagoras' and Plato's formulas for calculating triples have been described here:...

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...

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...

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...

smallest integer-sided right triangle, making part of the smallest Pythagorean triple (3, 4, 5). In geometry, the regular five-sided pentagon is the first...

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)...

side of the fifth smallest right triangle that forms a primitive Pythagorean triple (20, 21, 29). It is the third tetrahedral number. In combinatorics...

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...

Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans...

transforms a Pythagorean triple into another Pythagorean triple, only one of the two cases is sufficient for producing all primitive Pythagorean triples. The...

integers, the triangle is called a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple. The relations between the sides...

In geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem or the upside down Pythagorean theorem) is as follows: Let...

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...

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...

vegetarianism before the nineteenth century Pythagorean theorem Pythagorean triple Pythagorean prime Pythagorean trigonometric identity Table of Pythagoras...

called Pythagorean triples, i.e., integers a, b, and c satisfying a2 + b2 = c2. From a modern perspective, a method for constructing such triples is a significant...

{\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...

squares, counted by the sum of squares function; for instance, every Pythagorean triple a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} gives a second representation...

expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians." They make use of Pythagorean triples, which are...

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...

Pythagorean tree may refer to: Tree of primitive Pythagorean triples Pythagoras tree (fractal) This disambiguation page lists articles associated with...

value stated. Also, if m and x are rational, so are d, a, b and c. A Pythagorean triple can therefore be obtained from a, b and c by multiplying each of them...

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...

triangle with integer sides, or in other words, the largest number in a Pythagorean triple, obtained from the formula ( F n F n + 3 ) 2 + ( 2 F n + 1 F n + 2...

Pythagorean Triangles is a book on right triangles, the Pythagorean theorem, and Pythagorean triples. It was originally written in the Polish language...

set of such points turns out to be closely related to primitive Pythagorean triples. Consider a primitive right triangle, that is, with integer side...

{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...