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!

3D object in 2D space

  1. Jan 31, 2016 #1
    I am concerned that this question may instead be a philosophical one although if it it mathematical, any insights would be very appreciated. The question is this; could an object of N dimensions exist entirely in N-1 dimensions? In other words, could an infinitely flat object have 3 degrees of freedom and also be able to fit entirely in 2D space? Thank you and please excuse any naivety
     
  2. jcsd
  3. Jan 31, 2016 #2

    fresh_42

    Staff: Mentor

  4. Jan 31, 2016 #3

    WWGD

    User Avatar
    Science Advisor
    Gold Member

    Maybe , OP, you want to know if an n-dimensional object can be embedded in (n-1)-dimensions? Or are there other types of properties of the object that you want to preserve? I think you can say no for n-spheres (I think a corollary of Borsuk-Ulam theorem) and for ##\mathbb R^n ##, but I don't know of a more general result. But I think the answer ultimately depends on what (types of) intrinsic properties of the object you want to preserve in the lower dimensions: topology, geometry, etc.? Interesting question, though.
    In one sense of dimension, the answer is no: if you see the dimension n of an object as the minimal number of coordinates of a point needed to uniquely identify each point in the space, then the answer would be (is) no.
     
    Last edited: Jan 31, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: 3D object in 2D space
  1. LINE in 3D SPACE (Replies: 2)

  2. 3d surface in 4d space (Replies: 2)

Loading...