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Journals ACM SIGAPL APL Quote Quad Volume 34 Issue 4

Integer length integer vectors correspond to solutions of Diophantine equations where a sum of squares is a square. In two dimensions, this equation is a 2 + b 2 = c 2 , and solutions in positive integers correspond to Pythagorean Triples (or integer length integer vectors < a , b > in Z 2 ). In three dimensions, this equation is x 2 + y 2 + z 2 = r 2 , and integer solutions correspond to integer length integer vectors < x , y , z > in Z 3 . We investigate methods of visualizing twodimensional integer length integer vectors with J 5.04 6, and then create three-dimensional generalizations with J and POV-Ray 3.6 7. This work has been motivated in part by the Perfect Cuboid and Perfect Parallelepiped problems, which are open problems regarding integer length integer vectors 3. A discussion of these problems, as well as the parameterizations and algebraic structures of integer length integer vectors in Z 2 and Z 3 is available at 2.

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Visualizing integer length integer vectors with J and POV-Ray

Tirrell, Jordan
ACM SIGAPL APL Quote Quad , Volume 34 (4)
Association for Computing Machinery – Sep 1, 2004

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