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.

  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.

Constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Tangents

Ellipses

Polygons

Non-Euclidean constructions

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