What is the connection between hypercubes and graph theory?

[Samardar]

Some background: my friends love to confound me with nonsensical questions, because they know I'm the type of person who cannot let a question go, even if it has no answer, and when I arrive at one, it will be so rigidly logical that no matter how ridiculous it sounds it must be correct. My previous stumper was: if I ate myself, would my mass be multiplied by 2, zero, or remain the same (no, conservation law is not necessarily the answer, see Noether's theorem)?

The latest one is: Square + cube = ?

My latest venture into this question let me into exploration of hypercubes and graph theory http://en.wikipedia.org/wiki/Coxeter-Dynkin_diagram
however, the geometric representation of numbers does not seem to be a vast field in itself. Does anybody with a math degree know anything about this, in particular: http://en.wikipedia.org/wiki/Minkowski_space

 

[tahayassen]

If you eat yourself, your mass would remain the same, right? Hmmm...

 

[DaveC426913]

The latest one is: Square + cube = ?

Define "+" in this equation.

 

[Samardar]

Define "+" in this equation.


In the spirit of the original question, delivered when everybody was not just a little inebriated, you can define it any way you want.

 

[Samardar]

http://en.wikipedia.org/wiki/Menger_sponge

[PLAIN]http://justplainron.com/wp-content/uploads/2010/05/menger.jpg

Something like this I would Imagine

 

[tahayassen]

Totally ignored

 

[Samardar]

?

 

[tahayassen]

If you eat yourself, your mass would remain the same, right? Hmmm...

...

 

[Samardar]

To me the picture looks like it is more like subtraction than addition. The Koch triangle does add stuff to get a triangle with fractile boundaries.

 

[Deveno]

you would have the mass of the "mandelbrunch" whose insides are 1-1 with its outsides.