Besides Euclid's formula, many other formulas for generating Pythagorean triples have been developed. these formulas are used variously to generate pythagorian triples.
Read more about Formulas For Generating Pythagorean Triples: Euclid's, Pythagoras', and Plato's Formulas, Some Variations On Euclid's Method, Generating Triples When One Side Is Known, Fibonacci's Method, Progressions of Whole and Fractional Numbers, Dickson's Method, Generating Triples Using A Square, Generating Triples Using Quadratic Equations, Pythagorean Triples By Use of Matrices and Linear Transformations, Area Proportional To Sums of Squares, Height-excess Enumeration Theorem
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