Generating a Lemniscate IV: Rotating a Line
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This Demonstration shows the construction of the lemniscate of Gerono. Take a circle (black with orange interior) with center O and fix one of its tangent lines (blue). Consider a point P (red) on the circle and the perpendicular to the fixed line through P intersecting at a point M. Let Q (yellow) be the intersection of line OM and a vertical line passing through P. The trace of Q as P moves on the circle is the lemniscate.
Contributed by: Jaime Rangel-Mondragon (March 2011)
Open content licensed under CC BY-NC-SA
See Lemniscate of Gerono and Visual Dictionary of Special Plane Curves. This curve is not the same as the lemniscate of Bernoulli (Wolfram MathWorld).
"Generating a Lemniscate IV: Rotating a Line"
Wolfram Demonstrations Project
Published: March 7 2011