Mamikon's Method for the Area under a Parabola
The area under a parabola is determined without recourse to calculus, using only geometric concepts.
In 1959, Mamikon Matsakanian, generally known as Mamikon, devised an original method for solving problems in geometry. This is described in full in . 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].
 T. M. Apostol and M. Matsakanian, New Horizons in Geometry, Washington, DC: The Mathematical Association of America, 2012.