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...

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...

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

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...

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...

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

Pythagorean triangle 3-4-5 represents the 6th metallic mean. Likewise, the Pythagorean triple 12-35-37 gives the 12th metallic mean, the Pythagorean triple...

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...

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...

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

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

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

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

smallest integer-sided right triangle, making part of the smallest Pythagorean triple (3, 4, 5). 5 is the first safe prime, and the first good prime. 11...

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...

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...

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...

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...

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...

{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...

equation of degree two that has been studied. Its solutions are the Pythagorean triples. This is also the homogeneous equation of the unit circle. In this...

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...

Power point tracking, a solar energy charging technology Primitive Pythagorean triple, three integers that form a right triangle Probabilistic polynomial-time...

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...

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...

{\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...

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...

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