Area of a circle

[repugno]

Hello all. Where can I find proof that the area of a circle can be calculated using the formula πr2? Any response will be greatly appreciated, thank you.

[StephenPrivitera]

I believe it can be done using a limit process. Cut the circle into n equal triangles and take the limit as n goes to infinity.

[HallsofIvy]

And, of course, the area of a circle of radius R, with center at the origin of a coordinates system is the integral
∫-RR2√(R2- x2)dx. That gives πR2 as the area.