Mamikon's Method for the Area of the Cycloid

The area under the curve traced by a point at the end of the diameter of a circle with radius 1—a cycloid—is determined using only geometric concepts.

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In 1959, Mamikon Mnatsakanian, usually known as Mamikon, devised an original method for solving problems in geometry. His method is described in [1].
In this Demonstration, an example is presented based on work by Ujjwal Rane [2], where the area of the cycloid is obtained without recourse to the methods of calculus.
References
[1] Wikipedia. "Visual Calculus." (Nov 4, 2019) en.wikipedia.org/wiki/Visual_calculus.
[2] U. Rane. Geometry with MicroStation Mamikon's Theorem [Video]. (Nov 4, 2019) www.youtube.com/watch?v=sjqKfuuDZqA.
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