Once has been defined as the ratio circumference to diameter, the area of a circle must be .

A proof relies on an infinite, limiting process which paves the way to some calculus-like ideas.

A circle is cut up into 6 sectors which are then rearranged into a near rectangle,

What doesn’t look too close to a rectangle at 6 sectors looks better at 26:

As the number of sectors becomes *very big* the shape becomes indistinguishable from a rectangle and the argument is complete.

I think that Archimedes used such arguments, or, *proof by exhaustion*, in some of his solid geometry work.

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