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given a cirlce on S^2 of radius p in the spherical metric, show that its area is 2pi(1-cos p)

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- Thread starter halvizo1031
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given a cirlce on S^2 of radius p in the spherical metric, show that its area is 2pi(1-cos p)

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tiny-tim

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Hi halvizo1031! Welcome to PF!

(have a pi: π and a rho: ρ and try using the X

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?

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I'm not sure I understand what you wrote.

- #4

tiny-tim

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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

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ok I'll give that a try. thanks!

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