How to prove the area of a circle is πr²

[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
∫_-R^R2√(R²- x²)dx. That gives πR² as the area.