Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hi. Say we want to parametrize the plane R^2.

  1. Jan 20, 2010 #1
    Hi. Say we want to parametrize the plane R^2. This can be done for example using (x,y) cartesian, i.e. a pair of intersecting lines, OR (r,theta) polar coordinates, i.e. a half line intersecting a circle. But it cannot be done using (x,r) coordinates, i.e. a line intersecting a circle, because sometimes the line will not intersect the circle, sometimes it will intersect it once and sometimes it will intersect the circle twice! How can I know whether a parametrization is any good? I.e. on what mathematical grounds can I reject the (x,r) parametrization?
     
    Last edited: Jan 21, 2010
  2. jcsd
  3. Jan 21, 2010 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Re: Parametrization

    You at least need a function from your parameter space (u,v) onto the (x,y) plane. And a function must be single valued. Your example fails because the (x,r) = (1,2) would map to two points: (1,sqrt(3)) and (1,-sqrt(3)).
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook