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In the left diagram, line segment ... is tangent to the inner circle of an annular ring. Using the "sweep" slider, you can sweep ... through the entire area of the ring. Simultaneously, on the right, that same line segment, ... —now with one end pegged to a single point—sweeps out the same area, but forms a circular disk. Surprisingly, a new proof of the Pythagorean theorem discovered by Mamikon Mnatsakanian in 1959 (first published in 1981) dramatically appears.
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