Generating an Ellipse Using Steiner's Method

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This Demonstration shows the construction of an ellipse from the intersections of two pencils of lines drawn from points and .

Contributed by: Tomas Garza (January 2021)
Open content licensed under CC BY-NC-SA



The construction illustrates the Steiner generation of nondegenerate conic sections [1].

In step 1, equally spaced points are taken on the segments from to , to , to and to . A pencil of lines is drawn from point to each of the points on the segments , and . The procedure is repeated starting from to each point on the segments , and . The intersections of the first line of the first pencil with the first line of the second pencil, the second line of the first pencil with the second line of the second pencil, and so on, produce a collection of red points lying on an ellipse.

In step 2, the generating lines are deleted and the red points are joined to show the ellipse, together with its foci and center. Increasing the number of points improves the definition of the curve.

[1] Wikipedia. "Steiner Conic." (Jan 20, 2021)

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