# Area of Circle/Proof 7

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## Theorem

The area $A$ of a circle is given by:

- $A = \pi r^2$

where $r$ is the radius of the circle.

## Proof

By the method of exhaustion:

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## Historical Note

The technique of finding the Area of Circle by means of the method of exhaustion was devised by Archimedes of Syracuse.

## Sources

- 1977: K.G. Binmore:
*Mathematical Analysis: A Straightforward Approach*... (previous) ... (next): $\S 2$: Continuum Property: $\S 2.1$: Achilles and the tortoise