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!

Is a (hyper)sphere a (hyper)plane in spherical coordinates?

  1. Sep 6, 2013 #1
    Hi,
    can I say that a sphere is a plane, because in spherical coordinates, I can simply express it as [itex]<(r, \theta, \varphi)^T, (1, 0, 0)^T> = R[/itex]? It does sound too easy to me. I'm asking because I'm thinking about whether it is valid to generalize results from the John-Radon transform (over k-planes in an n-dimensional space) to curvilinear coordinates. In the book I'm reading (Analytic tomography), a k-plane is the set of points x in ℝn with [itex]<x, u> = c[/itex], with c real and u any unit vector in ℝn. Clearly, R is real and [itex](r, \theta, \varphi) = (1, 0, 0)^T[/itex] is a unit vector in ℝn.

    I believe the above is invalid because the dot product is expressed differently in spherical coordinates - is that already the answer?

    Thanks
    bers
     
  2. jcsd
  3. Sep 6, 2013 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    "Sphere" and "plane" are geometric objects and so completely independent of the coordinate system. They are not the same thing no matter what coordinate system you use.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Is a (hyper)sphere a (hyper)plane in spherical coordinates?
  1. Spherical Coordinates (Replies: 3)

  2. Spherical coordinates? (Replies: 4)

Loading...