Are there any tools for drawing a mathematically precise ellipse?
Like drawing it by hand and using pre-determined radii.
One way is to use the property that the sum of the distances to the two foci is constant.
A simple way is to put two pins at the foci of the ellipse, put a loop of string over the pins, and use your pencil to stretch it tight and draw the ellipse. However you can't draw an exact size and shape of ellipse that way because you can''t make a loop of string with an accurate length.
You can use the same technique to plot points accurately. Draw two sets of concentric circles around the foci, then use the intersection points where the sum of the radii is constant.
Another way is to draw a circle with radius equal to the major axis. Draw the diameter along the major axis, then draw chords at right angles to this. Then reduce the length of each chord by the same proportion (i.e. the ratio of minor axis / major axis) and draw a curve though the points.
You can also get plastic templates with elliptical shaped holes of various sizes, but they are usually all at the same eccentricity ratio and designed for drawing projections of circles on isometric drawings, not for drawing "arbitrary shaped" ellipses.
Of course the really easy way is use a computer drawing program!
Drawing Tools
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