> Is there a way of drawing an ellipse with a compass?

Not directly, you have to draw a cylinder viewed from each axis first (with 
a compass and ruler), then draw an intersecting shape (eg a titled plane), 
then by projecting a series of intersection points from each view you can 
construct the curve where the two shapes intersect, which if you choose the 
shape type and position correctly will be an ellipse in one of the 
projections.  Yay mechanical drawing is fun :-)

Or if you want to draw one directly, just use a piece of string:

http://www.ellipse.com.au/idea_art_ellipse.html

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