Pythagorean Quadruple
978-613-4-45519-0
6134455199
76
2011-02-25
34.00 €
eng
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A Pythagorean quadruple is a tuple of integers a, b, c and d, such that d > 0 and a2 + b2 + c2 = d2, and is often denoted (a,b,c,d). Geometrically, a Pythagorean quadruple (a,b,c,d) defines a cuboid with side lengths |a|, |b|, and |c|, whose space diagonal has integer length d. Pythagorean quadruples are thus also called Pythagorean Boxes. All Pythagorean quadruples (including non-primitives, and with repetition, though a, b and c do not appear in all possible orders) can be generated from two positive integers a, odd, and b, even, as follows: Let p be any factor of a2 + b2, such that p2 < a2 + b2. Then c = (a2 + b2 − p2) / 2 and d = (a2 + b2 + p2) / 2. Note that |p| = sqrt{d - c}. A similar method exists for a,b both even, with the further restriction that 2p must be an even factor of a2 + b2. No such method exists if both a and b are odd.
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