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Draw an ellipse using string and 2 pins
Click here for a printable ellipse construction worksheet
How to draw an ellipse using string and pins when you are given the major and minor axis (width and height) of the ellipse. We start with four points defining the ends of the two axes. We end up with an ellipse that passes through these points.

Note: This is not a Euclidean construction as defined in Constructions - Tools and Rules but a practical way to draw an ellipse when mathematical precision is not so important.

Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)


This is not an extremely accurate way to draw an ellipse, but if you need one that is reasonably accurate and you are careful, you can get fairly close. It is sometimes called the "Gardner'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.
Step-by-step Instructions
Step 1 With the compass point on the center, set the compass width to half the width (major axis) of the desired ellipse.
Step 2 Move the compass point to one end of the minor axis of the desired ellipse and draw two arcs across the major axis.
Step 3 Where these arcs cross the major axis are the foci of the ellipse. Label them F1, F2.
Step 4 Put a pin in each end of the major axis (they will be moved later), and tie a string to them so that the string between them is taut. The best way to do this is to push the pin through the string itself if possible, rather than tying a knot.
Step 5 Leaving the string attached, move the pins to the focus points F1, F2. Put a pencil point against the string and pull the string taut with the pencil.
Step 6 Keeping the string taut, move the pencil in a large arc. The pencil will draw out the desired ellipse. To avoid the string catching on the pins, you may find it better to draw the upper and lower halves of the ellipse separately.
Step 7 Done. The ellipse will pass through the four initial points defining the ends of the major and minor axes.
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

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions

(C) 2008 Copyright John Page