Mathematical Intentions logo

Quadrivium logo

The characteristic ratio for a parabola

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Facts about the area under a parabolic curve were known to the ancient Greeks; no calculus is necessary to derive these facts.

Take a tangent, a, to the parabola at E, and a line, c, through E, that is parallel to the line of symmetry of the parabola. Pick a second point, G, on the parabola, and form the parallelogram with vertices E and G, and sides determined by the directions of the two lines. Then the parabola cuts the rectangle in the ratio 1:2. That is, The red region is 1/3 the area of the parallelogram.

Susan Addington, Created with GeoGebra


Mathematical Intentions
Measuring the World


Contact us

Last updated January 15, 2010

Copyright 2009 David Dennis and Susan Addington. All rights reserved.