De La Hire's Construction of an Ellipse

semimajor axis a

semiminor axis b

1.022

show construction

trace ellipse

θ/2π

0.11

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:

(x,y)=(acosθ,bsinθ)

References

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

External Links

Locus of Points Definition of an Ellipse, Hyperbola, Parabola, and Oval of Cassini

Da Vinci's Construction of an Ellipse

Permanent Citation

S. M. Blinder

"De La Hire's Construction of an Ellipse" from the Wolfram Demonstrations Project http://demonstrations.wolfram.com/DeLaHiresConstructionOfAnEllipse/
Published: October 30, 2019