Area of a Circle: Find Proof of πr2 Formula

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The discussion centers on finding proof for the area of a circle formula, A = πr². One suggested method involves dividing the circle into n equal triangles and using a limit process as n approaches infinity. Another approach mentioned is using integral calculus, specifically the integral of the function that describes the circle. Both methods ultimately confirm that the area of a circle with radius R is indeed πR². The conversation highlights the mathematical foundations behind this well-known formula.
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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.
 
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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.
 
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.
 

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