High Quality Content by WIKIPEDIA articles! Visual Calculus by Mamikon Mnatsakanian is an approach to solving a variety of integral calculus problems. Many problems which would otherwise seem quite difficult yield to the method with hardly a line of calculation, what Martin Gardner calls "aha! solutions" or Roger Nelsen a proof without words. The method was devised by Mamikon in 1959 while a young undergraduate. It is based on the old puzzle: what is the area of a ring if the tangent to the inner circle is 6" long? With Mamikon's insight the solution becomes obvious—the area is the same as that swept by a tangent from the inner circle to the outer circle, and the tangents can all be translated parallel to themselves to make a smaller circle the points of tangency at the centre and with same radius as the tangent length. Thus it doesn't really matter that the inner and outer curves are circles, just that the tangent to one side of the inner curve should have a constant length.

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