Overview

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 ae' 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.

Full Product Details

9786134455190

Table of Contents

Reviews

Author Information

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available