1. Mar 13, 2005

### eljose

let suppose we have an hypercube in R^4 then m y question is how many 3-dimensional cubes could we put inside our hypercube?...

2. Mar 13, 2005

### matt grime

A rhetorical question for you to ponder: how many squares are there in a cube?

3. Mar 13, 2005

### damoclark

If you mean "How many cube faces does a hyper-cube have"?
then 8, possibly

otherwise your question doesn't make sense, as there is no number of 3-dimensional cubes that we could put inside a hypercube.

Last edited: Mar 13, 2005
4. Mar 13, 2005

### eljose

the question is let,s suppose we have a four dimensional space,then could we put inside this four dimensional space our 3-dimensional space?,i think the question has been answered when considering a plane made by an infinite numer of curves or a line made by an infinite numer of points

5. Mar 13, 2005

### Data

Is the statement $$\mathbb{R}^3 \subseteq \mathbb{R}^4$$ true? (Hint: NO!!!!)

6. Mar 13, 2005

### HallsofIvy

Good point. (But there is, of course, a subset of R4 that is diffeomorphic to R3.)

7. Mar 13, 2005

### Data

True. And now that I think about it, my original post isn't anything close to a good answer to the original question at all~

8. Mar 14, 2005

### Aki

there are infinite squares in a cube. so to draw a conclusion: there are infinite cubes in a hypercube.

9. Mar 14, 2005

### Icebreaker

I don't really understand the erm "put inside". What if a squre is bigger than the face of a cube? Wouldn't the cube only be able to contain squares that are smaller than or equal to the size of its faces?

10. Mar 14, 2005

### Alkatran

Only if they weren't on curved surfaces.