1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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

    Aki

    User Avatar

    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

    Alkatran

    User Avatar
    Science Advisor
    Homework Helper

    Only if they weren't on curved surfaces.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A question about dimension
  1. Dimension Question. (Replies: 1)

Loading...