Mamikon's Method for the Area of the Cycloid

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step
1
2
3
distance traversed
by the rolling circle
0
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.

Details

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.

Permanent Citation

Tomas Garza
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​"Mamikon's Method for the Area of the Cycloid" from the Wolfram Demonstrations Project http://demonstrations.wolfram.com/MamikonsMethodForTheAreaOfTheCycloid/​
​Published: November 5, 2019
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