Wings as a math visualization tool...

[Dimitri]

Wings may have an excellent use as a math visualization tool too. Below is one such math problem I did conceive and visualize for putting it in Facebook, so that there may begin a discussion about finding a formula to solve it.

The question is: what is the formula that can give us the way to find how many cubes may be extracted from cubes constructed from whole-smaller cubes. Keep in mind that there are many cubes, inside the total cubes, that interpenetrate each other (as it is illustrated partly in the small image series of the first attached image). To explain it in a more simple way: let say that we have a cube constructed from four smaller cubes (as in the second attached image below), there we have the four small cubes + the one that is constructed from all of them = 5 cubes. So, how many cubes would we have in case of a whole cube which is constructed from 512 whole –undivisible- smaller cubes (as the one in the upper right corner in the first image)?

It is a problem that I did conceive it but I still did not be able to find a solution. So, if anyone has an idea let share it. If not, let be content with the enjoyment of the visuals. : - )

(the rendering is made with Blender's internal renderer)