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Drawing geometrical figures

  1. Jan 3, 2006 #1
    If one can draw (or represent) a 3 dimentional figure on a 2 dimensional surface (ie-a cube on a blackboard), is it possible to "draw" (or represent) a 4 dimensional "figure" on a 3 dimensional "surface"?
     
  2. jcsd
  3. Jan 3, 2006 #2
    Yes; however, just as in two-dimensional representations of three-dimensional objects, you can only see one view of the object. Also, because we have no experience with four-dimensional objects and because our eyes are limited to a planar visionscape, it would be much more difficult to intuitively grasp a four-dimensional object's representation than it is that of a three-dimensional one.
     
  4. Jan 3, 2006 #3

    robphy

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    Just as a cube drawn on a blackboard introduces distortions [e.g., some 90-degree angles are not drawn as such, or true lengths are not drawn], a 4-D figure drawn on a 3-D surface will have distortions.

    Have you seen the Necker cube?
    http://www.yorku.ca/eye/necker.htm
    http://dogfeathers.com/java/necker.html

    For some attempts to visualize in 4-D, look for my post in this thread
    https://www.physicsforums.com/showthread.php?t=101720
     
  5. Jan 3, 2006 #4
    Thanks a lot for the replies, they both make quite a bit of sense.

    robphy- I have seen the animated Necker cube before, but had forgotten about it. Thanks for the link, it's really neat.
     
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