Rational Distance Problem

Author

Eric W. Weisstein
December 17, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/ComputationalGeometry/RationalDistaneProblem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/RationalDistaneProblem.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Euler Brick

FindInstance[(Sqrt[a^2+b^2])∈Integers&&(Sqrt[b^2+c^2])∈Integers&&(Sqrt[c^2+a^2])∈Integers&&0<c<b<a,{a,b,c},Integers]

Square distances to 3 edges

FindInstance[(Sqrt[(x^2)+(y^2)])∈Rationals&&(Sqrt[(((1-x))^2)+(y^2)])∈Rationals&&(Sqrt[(x^2)+(((1-y))^2)])∈Integers&&0<x<1&&0<y<1,{x,y},Rationals]