What is the connection between hypercubes and graph theory?

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Discussion Overview

The discussion explores the connection between hypercubes and graph theory, initiated by a playful question regarding the mathematical operation of combining shapes, specifically squares and cubes. Participants delve into the geometric representation of numbers and related concepts, referencing various mathematical constructs and theories.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant reflects on a nonsensical question about self-consumption and its implications on mass, suggesting that mass would remain the same.
  • Another participant prompts for a definition of the "+" operation in the context of combining a square and a cube.
  • A later reply humorously suggests that the definition of "+" can be flexible, especially in a lighthearted context.
  • References to geometric constructs like the Menger sponge and Koch triangle are made, with one participant suggesting that the visual representation may imply subtraction rather than addition.
  • Another participant introduces the concept of the "mandelbrunch," implying a relationship between the inside and outside of geometric shapes.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the mathematical operation being discussed, particularly regarding the interpretation of "+" and the implications of geometric representations. The discussion remains unresolved with multiple competing interpretations.

Contextual Notes

Some assumptions about the definitions of mathematical operations and geometric representations are not explicitly stated, leading to ambiguity in the discussion. The exploration of hypercubes and graph theory is not fully developed, indicating potential limitations in the depth of the topic.

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.
 
Last edited by a moderator:


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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