What is the connection between hypercubes and graph theory?

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SUMMARY

The discussion explores the relationship between hypercubes and graph theory, particularly through the lens of geometric representations of numbers. Participants reference concepts such as Minkowski space and Menger sponges to illustrate their points. The conversation emphasizes the need to define mathematical operations, such as addition, in unconventional ways. The interplay between geometry and abstract mathematical concepts is highlighted as a key area of interest.

PREREQUISITES
  • Understanding of hypercubes and their properties
  • Familiarity with graph theory fundamentals
  • Knowledge of Minkowski space and its applications
  • Basic concepts of fractals, specifically Menger sponges
NEXT STEPS
  • Research the properties and applications of hypercubes in mathematics
  • Study the principles of graph theory and its connections to geometry
  • Explore Minkowski space and its relevance in modern physics
  • Investigate fractals, focusing on the Menger sponge and Koch triangle
USEFUL FOR

Mathematicians, students of geometry and graph theory, and anyone interested in the abstract connections between mathematical concepts and their geometric representations.

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


Samardar said:
The latest one is: Square + cube = ?
Define "+" in this equation.
 


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.
 
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Totally ignored
 

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?
 


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

...
 


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.
 
  • #10


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

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