Tracing Out An Ellipes
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here.
This animation shows how to use the definition of ellipse to trace out
such a curve.
(See notes below.)
The horizontal line segment shown below the curve consists
of a copy of the blue segment that connects the left-hand focus with the moving
point on the ellipse and a copy of the red segment that connects the right-hand
focus with the moving point; as the moving point traces out the curve,
the sum of the two lengths
remains constant.
A similar figure, colored differently, lies in the plane
that appears in the
Quetelet/Dandelin argument, Another Proof of Quetelet & Dandelin,
for the ellipse.
(12/01/07)