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The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula + =; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples.
Pythagorean triples are sets of three positive integers (a, b, c) that satisfy the equation $$a^2 + b^2 = c^2$$, representing the lengths of the sides of a right triangle. These triples have important implications in various mathematical contexts, including geometry, algebra, and number theory.
A Pythagorean triple is a set of three positive integers $(a, b, c)$ that satisfy the equation $$a^2 + b^2 = c^2$$, where $c$ is the largest number and represents the hypotenuse of a right triangle. These triples are fundamental in the study of geometry and number theory, illustrating the relationship between the sides of right triangles.
Definition. Pythagorean triples are sets of three positive integers, usually denoted as (a, b, c), that satisfy the equation $$a^2 + b^2 = c^2$$. This relationship is derived from the Pythagorean theorem, which connects the sides of a right triangle.
History Of Pythagorean Triples. Geometry, as we know it, has roots stemming from Euclid. Today, we refer to it as Euclidean Geometry. We know from the Plimpton 322, a Babylonian clay tablet, that Geometry and Mathematics have been around at least as long as the Babylonians. This tablet is written in a sexagesimal number system.
Pythagorean triples, in simple words, are the integer solutions to the Pythagoras’ theorem, containing positive integers. Here, “c” is the “hypotenuse” or the longest side of the triangle, and “a” and “b” are the other two sides of the right-angled triangle.
PYTHAGOREAN TRIPLES KEITH CONRAD 1. Introduction A Pythagorean triple is a triple of positive integers (a;b;c) where a2 +b2 = c2. Examples include (3;4;5), (5;12;13), and (8;15;17). Below is an ancient Babylonian tablet listing 15 Pythagorean triples. It is called Plimpton 322 (George Arthur Plimpton donated it to Columbia University).
