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Draw an ellipse using string and 2 pins
This is not a true Euclidean construction as defined in
Constructions - Tools and Rules but a practical way to draw
an ellipse given its width and height and when mathematical precision is not so important.
It is sometimes called the "Gardener's Ellipse", because
it works well on a large scale, using rope and stakes, to lay out elliptical flower beds in formal gardens.
You can also calculate the positions of the focus points.
See Foci of an Ellipse.
Printable step-by-step instructions
The above animation is available as a
printable step-by-step instruction sheet, which can be used for making handouts
or when a computer is not available.
Proof
The image below is the final drawing above with the some items added.
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Argument |
Reason |
| 1 |
F1, F2 are the
foci of the ellipse |
By construction. See
Constructing the foci of an ellipse for method and proof. |
| 2 |
a + b, the length of the string, is equal to the major axis length PQ of the ellipse. |
The string length was set from P and Q in the construction. |
| 3 |
The figure is an ellipse |
From the definition of an ellipse:
From any point C on the ellipse, the sum of the distances from C to each focus is equal to the major axis length.
The string is kept taut to ensure this condition is met. |
- Q.E.D
Try it yourself
Click here for a printable worksheet containing an ellipse drawing problem.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Other constructions pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
Non-Euclidean constructions
(C) 2011 Copyright Math Open Reference. All rights reserved
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