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Other small Pythagorean triples such as (6, 8, 10) are not listed because they are not primitive; for instance (6, 8, 10) is a multiple of (3, 4, 5). Each of these points (with their multiples) forms a radiating line in the scatter plot to the right. Additionally, these are the remaining primitive Pythagorean triples of numbers up to 300:
If any of the above matrices, say A, is applied to a triple (a, b, c) T having the Pythagorean property a 2 + b 2 = c 2 to obtain a new triple (d, e, f) T = A(a, b, c) T, this new triple is also Pythagorean.
With a the shorter and b the longer legs of a triangle and c its hypotenuse, the Pythagoras family of triplets is defined by c − b = 1, the Plato family by c − b = 2, and the Fermat family by | a − b | = 1. The Stifel sequence produces all primitive triplets of the Pythagoras family, and the Ozanam sequence produces all primitive triples ...
Its three integer sides are known as a Pythagorean triple or Pythagorean triplet or Pythagorean triad. [9] All Pythagorean triples ( a , b , c ) {\displaystyle (a,b,c)} with hypotenuse c {\displaystyle c} which are primitive (the sides having no common factor ) can be generated by
The 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 consist of all red or all blue members.
A Pythagorean quadruple is called primitive if the greatest common divisor of its entries is 1. Every Pythagorean quadruple is an integer multiple of a primitive quadruple. The set of primitive Pythagorean quadruples for which a is odd can be generated by the formulas = +, = (+), = (), = + + +, where m, n, p, q are non-negative integers with greatest common divisor 1 such that m + n + p + q is o
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[9] [10] The Tetractys [also known as the decad] is an equilateral triangle formed from the sequence of the first ten numbers aligned in four rows. It is both a mathematical idea and a metaphysical symbol that embraces within itself—in seedlike form—the principles of the natural world, the harmony of the cosmos, the ascent to the divine ...