1996
DOI: 10.1080/0025570x.1996.11996425
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Proof Without Words: Parametric Representation of Primitive Pythagorean Triples

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“…The integers u and v, or simply (u, v) in the formula (9), are called the generating numbers or generators of the triple (a, b, c). Neugebauer claims that this sufficiency part was known to the Babylonians.…”
Section: Characterizationmentioning
confidence: 99%
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“…The integers u and v, or simply (u, v) in the formula (9), are called the generating numbers or generators of the triple (a, b, c). Neugebauer claims that this sufficiency part was known to the Babylonians.…”
Section: Characterizationmentioning
confidence: 99%
“…The converse, i.e., showing that any Pythagorean triple is necessarily of the form (9), is more difficult. The earliest record for some special cases of the proof of the converse can be found in the solutions of Problems 8 and 9 of Book II of the Arithmetica of Diophantus.…”
Section: Characterizationmentioning
confidence: 99%
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