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Generating a Lemniscate I: Envelope of Circles
Generating a Lemniscate I: Envelope of Circles
A lemniscate is the generic name given to a figure resembling an infinite symbol or an inverted 8. The most famous is the lemniscate of Bernoulli depicted in red in this Demonstration. This lemniscate can be generated as the envelope of circles with centers on a rectangular hyperbola (its two branches shown crossing the lemniscate) and each circle passing through the center of the hyperbola.