Pythagorean Triples

Pythagorean Triple - Spinors and The Modular Group
... Pythagorean triples can likewise be encoded into a matrix of the form A matrix of this form is symmetric ... of X is which is zero precisely when (a,b,c) is a Pythagorean triple ... If X corresponds to a Pythagorean triple, then as a matrix it must have rank 1 ...

Pell Number - Pythagorean Triples
... side lengths a, b, c (necessarily satisfying the Pythagorean theorem a2+b2=c2), then (a,b,c) is known as a Pythagorean triple ... (1875) describes, the Pell numbers can be used to form Pythagorean triples in which a and b are one unit apart, corresponding to right triangles that are nearly isosceles ... Each such triple has the form The sequence of Pythagorean triples formed in this way is (4,3,5), (20,21,29), (120,119,169), (696,697,985).. ...

Examples of Ternary Trees
... search tree Ternary heap An infinite ternary tree containing all primitive Pythagorean triples is described in Tree of primitive Pythagorean triples and in Formulas for generating Pythagorean triples ... The root node contains triple ...

Formulas For Generating Pythagorean Triples - Some Variations On Euclid's Method
... sequence that generates some but not all possible triples is based on the positive integers starting with a = 3 ... b = a2/4 − 1 and c = b + 2 Note that a = 3 and a = 4 produce the same primitive triple and that when a = 4n + 2 for integer n (thus a is even), then the triple ... More formally given a positive integer n, the triple can be generated by the following two procedures (see http//www.mcs.surrey.ac.uk/Personal/R.Knott/Pythag/pythag.html ) Example ...

Indian Mathematics - Vedic Period - Śulba Sūtras
... the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians." They contain lists of Pythagorean ... Sulba Sutra, the best-known Sulba Sutra, which contains examples of simple Pythagorean triples, such as, , and as well as a statement of the Pythagorean theorem for the sides of a square "The rope which is. 1850 BCE "contains fifteen Pythagorean triples with quite large entries, including (13500, 12709, 18541) which is a primitive triple, indicating, in particular, that there was ...