Ellipse

There are mechanical devices, called ellipsographs, based on Definition 4 for drawing ellipses precisely, but lacking such a device, one can use simple equipment and the definitions above to draw ellipses which are accurate enough for most practical purposes.

To draw large ellipses one can use the pin-and-string method based on Definition 1: Stick pins into the drawing board at the two foci and at one end of the minor axis. Tie a loop of string snugly around the three pins. Replace the pin at the end of the minor axis with a pencil and, keeping the loop taut, draw the ellipse. If string is used that does not stretch, the resulting ellipse will be quite accurate.

To draw small and medium sized ellipses a technique based on Definition 4 can be used: Draw two concentric circles whose radii are equal to the semimajor axis and the semiminor axis respectively. Draw a ray from the center, intersecting the inner circle at y and outer circle at x. From y draw a short horizontal line and from x a short vertical line. Where these lines intersect is a point on the ellipse. Continue this procedure with many different rays until points all around the ellipse have been located. Connect these points with a smooth curve. If this is done carefully, using ordinary drafting equipment, the resulting ellipse will be quite accurate.