Mamikon's Method for the Area under a Parabola

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The area under a parabola is determined without recourse to calculus, using only geometric concepts.

Contributed by: Tomas Garza (February 2020)
Open content licensed under CC BY-NC-SA



In 1959, Mamikon Matsakanian, generally known as Mamikon, devised an original method for solving problems in geometry. This is described in full in [1]. This Demonstration presents an example in which the area under a parabola is obtained using only elementary concepts of geometry.

A result used in the Demonstration is the scaling property, which says that if each tangent segment of a tangent sweep is scaled (expanded or contracted) by the same positive factor , then the area of the tangent sweep is multiplied by [1, p. 19].


[1] T. M. Apostol and M. Matsakanian, New Horizons in Geometry, Washington, DC: The Mathematical Association of America, 2012.

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