Well circumference is specifically the full arc length of a circle... The formula you have is for any curve that you can write in the form r=f(theta). Think of anything ever drawn by a spirograph... This formula would let you calculate how long the curve is, that is, how far the pen would have travelled. As always, finding the function can be the hardest part!

If r is constant, dr/dΘ is 0, and the integral evaluates as πr^2 -- the circumference of a circle. This makes sense since the curve would be a circle if r is constant.

If r is not constant, then you have some other shape being described, and C is the length of the curve. You can think of it as the length an ant would walk if it followed the line of the graph of (r, f(Θ)).

Since we evaulate from 0 to 2*pi, that's a complete revolution, right? That's why I'm saying the formula was supposed to describe the circumference of a circular (or circular-like) object. Thanks to everyone who helped me puzzle this out!

sig225oscarlikesbugsyeric_mathgeekIf r is constant, dr/dΘ is 0, and the integral evaluates as πr^2 -- the circumference of a circle. This makes sense since the curve would be a circle if r is constant.

If r is not constant, then you have some other shape being described, and C is the length of the curve. You can think of it as the length an ant would walk if it followed the line of the graph of (r, f(Θ)).

mudcub