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.
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.
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. |