Rational Claim:For the rim {$a\times b\times c\ $}, {$\frac ab$} is rational iff {$\frac ac$} and {$\frac bc$} are rational. Proof: This is true for the triangular box, {$c\times d\times (c+d)\ $}. If all ratios in {$c\times d\times e\ $} are rational, the same is true for {$c\times d\times (e+c+d)\ $} and for {$c\times d\times (e-c-d)$}. |