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Differential geometry

  • #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)
 

Answers and Replies

  • #2
tiny-tim
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Homework Helper
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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:)
given a cirlce on S^2 of radius p in the spherical metric, show that its area is 2pi(1-cos p)
Divide the circular region into ring-shaped slices of thickness ds, and integrate …

what do you get? :smile:
 
  • #3
I'm not sure I understand what you wrote.
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
249
I'm not sure I understand what you wrote.
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:
 
  • #5
ok I'll give that a try. thanks!
 

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