De La Hire's Construction of an Ellipse

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One of many ways to construct an ellipse using only a ruler and compass is due to de La Hire [1]. Proceed as follows:


1. Draw two circles with radii and , equal to the semimajor and semiminor axes of the ellipse.

2. Draw a radial line from the center, at an angle from the horizontal, that intersects the two circles at points and .

3. Drop a line from to the horizontal axis (shown in blue).

4. Draw a line from the vertical axis through point to intersect this line (shown in green).

5. The intersection represents a point on the ellipse. To trace the ellipse, repeat steps 2 to 4 for different angles .

This construction reproduces the standard parametric trigonometric representation of an ellipse: .


Contributed by: S. M. Blinder (October 2019)
Open content licensed under CC BY-NC-SA



[1] Wikipedia. "Ellipse." (Sep 25, 2019) De la Hire construction taken from K. Strubecker: Vorlesungen über Darstellende Geometrie, Göttingen: Vandenhoeck & Ruprecht, 1967 p. 26.


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