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A question about dimension

  1. Mar 13, 2005 #1
    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. jcsd
  3. Mar 13, 2005 #2

    matt grime

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    A rhetorical question for you to ponder: how many squares are there in a cube?
  4. Mar 13, 2005 #3

    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
  5. Mar 13, 2005 #4
    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
  6. Mar 13, 2005 #5
    Is the statement [tex]\mathbb{R}^3 \subseteq \mathbb{R}^4[/tex] true? (Hint: NO!!!!)
  7. Mar 13, 2005 #6


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    Good point. (But there is, of course, a subset of R4 that is diffeomorphic to R3.)
  8. Mar 13, 2005 #7
    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~
  9. Mar 14, 2005 #8


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    there are infinite squares in a cube. so to draw a conclusion: there are infinite cubes in a hypercube.
  10. Mar 14, 2005 #9
    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?
  11. Mar 14, 2005 #10


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    Only if they weren't on curved surfaces.
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