A Precise Method for Drawing an Ellipse
An excellent and common technique for how to draw an ellipse is to use two push pins, a string, and a pencil. Trial and error is often recommended as the way to adjust the location of the push pins and the length of the string. These two things can be calculated very easily to give the exact ellipse that you want.
First, determine the length and height of the desired ellipse. The total distance between the push pins will be given by this formula: Distance = the square root of (L2 – H2), where L equals total length and H equals total height.
After placing the push pins the correct distance apart on the major axis, cut a piece of string several inches longer than the total length of the ellipse, and form a big loop using a slip knot. Tension the loop with the pencil, and slip the knot in or out so that the looped string reaches exactly half the total length of the ellipse plus half the distance between the pins. Then, tie off the knot so it can no longer slip.
Use a low-stretch string for the job, and when drawing, keep the tension on the pencil the same all the way around. A tiny grommet on the pencil point will help the string slide. They are readily available from hobby stores and electronic stores like Radio Shack.
From Fine Woodworking #121
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Comments
These instructions are not the clearest. The description for the length of string are very vague. I finally wrapped a loose string around the pins down to the minor axis height, tied it off and that got me close enough.
I believe that the formula for the ellipse is in error, with the correct formula being c^2 = a^2 – b^2 where c is _half_ the distance between the push pin foci, a is _half_ the major axis, and b = _half_ the minor axis. In this article, this would read "Half the distance = the square root of L^2 – H^2), where L equals _one half_ total length and H equals _one half_ the total height. Cf https://www.mathwarehouse.com/ellipse/focus-of-ellipse.php
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