Pythagorean Numbers

Pythagorean numbers

[pə‚thag·ə′rē·ən ′nəm·bərz]
Positive integers x, y, and z which satisfy the equation x 2+ y 2= z 2. Also known as Pythagorean triple.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Pythagorean Numbers


triples of natural numbers such that if the lengths of the sides of a triangle are proportional or equal to the numbers of such a triple, the triangle is a right triangle. By the converse to the Pythagorean theorem, it is sufficient if the numbers satisfy the Diophantine equation x2 + y2 = z2. An example of such a triple is x = 3, y = 4, and z = 5. All triples of relatively prime Pythagorean numbers can be obtained from the formulas

x = m2 – n2 y = 2mn z = m2 + n2

where m and n are integers and m > n > 0.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Note: Before we get the cosine or sine, the Pythagorean numbers x, y, r and X, Y, and R need to be reduced to x/r for the cosine and y/r for the sine, becoming rational numbers.
Fourier's decomposition of temperature into harmonic sine waves reaffirms the occidental epistemology of a world ordered by Pythagorean numbers, but results in an overemphasized separation of sound from noise.
Unlike Pythagorean numbers, envisaged as principles of existent entities, these modern numbers stand alone, in stark isolation from anything higher than their own empty notations, representing nothing but quantities devoid of qualities.