Visual calculus

Mamikon collaborated with Tom Apostol on the 2013 book New Horizons in Geometry describing the subject.

Mamikon devised his method in 1959 while an undergraduate, first applying it to a well-known geometry problem: find the area of a ring (annulus), given the length of a chord tangent to the inner circumference.

Perhaps surprisingly, no additional information is needed; the solution does not depend on the ring's inner and outer dimensions.

Now if all the (constant-length) tangents used in constructing the ring are translated so that their points of tangency coincide, the result is a circular disk of known radius (and easily computed area).

Moreover, the two starting curves need not be circular—a finding not easily proven by more traditional geometric methods.

Mamikon's theorem - the area of the tangent clusters are equal. Here the original curve with the tangents drawn from it is a semicircle.
Illustration of Mamikon's method showing that the areas of two annuli with the same chord length are the same regardless of inner and outer radii. [ 2 ]
Finding the area of a cycloid using Mamikon's theorem.