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The Product of a Box

For pairs of numbers, {$m,n$}, the product of the greatest common divisor and the least common multiple is the product, {$mn$} of the two numbers. This will be true for our analogous GCD and LCM, except that we must define product. On the rectangle, the product is the area of the rectangle. On the box, we choose as ``product'' the sum of the areas of the different faces.

Definition: For {$T=\langle a,b,c\rangle\in\mathcal{B}^+$}, PROD{$_{_T}=ab+bc+ac$}.

The product is half the area of the box. It is also one-fourth the sum of the lengths of all the paths from corners and all the loops.

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Page last modified on May 29, 2013, at 01:40 PM