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Differential geometry

  1. Apr 27, 2009 #1
    I need help with this problem:

    given a cirlce on S^2 of radius p in the spherical metric, show that its area is 2pi(1-cos p)
     
  2. jcsd
  3. Apr 28, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi halvizo1031! Welcome to PF! :smile:

    (have a pi: π and a rho: ρ and try using the X2 tag just above the Reply box :wink:)
    Divide the circular region into ring-shaped slices of thickness ds, and integrate …

    what do you get? :smile:
     
  4. Apr 28, 2009 #3
    I'm not sure I understand what you wrote.
     
  5. Apr 28, 2009 #4

    tiny-tim

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    Divide the circle into rings …

    the area of each ring is its thickness times its length (ie its perimeter) …

    use the metric to find the length of the perimeter of each ring …

    then add up the areas of all the rings :smile:
     
  6. Apr 28, 2009 #5
    ok I'll give that a try. thanks!
     
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