Mamikon's Method for the Area of the Cycloid

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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.

Contributed by: Tomas Garza (November 2019)
Open content licensed under CC BY-NC-SA


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.


[1] Wikipedia. "Visual Calculus." (Nov 4, 2019)

[2] U. Rane. Geometry with MicroStation Mamikon's Theorem [Video]. (Nov 4, 2019)


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