# Pythagorean Numbers

## Pythagorean numbers

[pə‚thag·ə′rē·ən ′nəm·bərz]
(mathematics)
Positive integers x, y, and z which satisfy the equation x 2+ y 2= z 2. Also known as Pythagorean triple.

## 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.

References in periodicals archive ?
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.
On the connection between Pythagorean numbers and Neoplatonism, as a conceptual backdrop to the present study, see, for example, Celenza (and, moreover, in the section "Bibliography," 707, various items by Allen).

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