Proof that the area of circle equals to pi*r^2

The circle is subdivided into equal pieces, then rearranged. As the number of pieces gets larger, the resulting shape gets closer and closer to a rectangle. It is obvious that the short side of this rectangle has length r, and a little thought will show that the two long sides each have a length half the circumference, or pi*r, giving an area for the rectangle of pi*r^2.
taken from: http://math.stackexchange.com/a/743459

Pythagorean Theorem Proof

in graphical form

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