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rbwang1225
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Homework Statement
By employing spherical polar coordinates show that the circumference C of a circle of radius R inscribed on a sphere [itex]S^{2}[/itex] obeys the inequality C<2[itex]\pi[/itex]R
The Attempt at a Solution
I proved C=2[itex]\pi[/itex]R[itex]\sqrt{1-\frac{R^2}{4r^2}}[/itex]
So if r>R, then the equality is correct.
Am I right? Since the statement of the problem doesn't give me the radius r of the sphere, I doubt my result.