# What is the connection between hypercubes and graph theory?

• Samardar
In summary, the conversation is about nonsensical questions and the asker's tendency to find logical answers for them. The latest question is "Square + cube =?" and the asker delves into exploring hypercubes and graph theory to find an answer. They also mention Minkowski space and ask if anyone with a math degree knows about it. The conversation then shifts to discussing the Menger sponge and its similarities to the question. Ultimately, the conversation concludes with the idea that the result of eating oneself would result in the mass of a "mandelbrunch."
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

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.

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

## 1. What is a hypercube?

A hypercube is a geometric shape that is formed by connecting the corners of a square in higher dimensions. In two dimensions, it is a square, in three dimensions, it is a cube, and in higher dimensions, it is called a hypercube.

## 2. What is the significance of hypercubes in graph theory?

Hypercubes are important in graph theory because they represent the highest degree of connectivity that a graph can have. This makes them useful for studying and analyzing complex networks and systems.

## 3. How many dimensions can a hypercube have?

A hypercube can have any number of dimensions, but the most commonly studied ones are up to 5 dimensions. However, mathematically, a hypercube can have an infinite number of dimensions.

## 4. What is the relationship between hypercubes and binary codes?

Hypercubes have a strong connection to binary codes, as each vertex of a hypercube can be represented as a binary string. This makes them useful for coding and error-correction in computer science.

## 5. Can hypercubes be visualized in 3 dimensions?

While hypercubes exist in higher dimensions, they can be projected and visualized in 3 dimensions. However, this visualization may not accurately represent the properties of a hypercube in higher dimensions, as our brains are not equipped to perceive more than 3 dimensions.

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