The envelope of a one-parameter family of curves given implicitly by
|
(1)
|
or in parametric form by ,
is a curve that touches every member of the family tangentially.
For a curve represented by ,
the envelope is found by solving
|
(2)
|
For a curve represented implicitly, the envelope is given by simultaneously solving
See also
Astroid,
Cardioid,
Catacaustic,
Caustic,
Cayleyian Curve,
Dürer's
Conchoid,
Ellipse Envelope,
Envelope
Theorem,
Evolute,
Glissette,
Hedgehog,
Kiepert Parabola,
Lindelof's Theorem,
Negative
Pedal Curve
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References
Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 33-34, 1972.Yates,
R. C. "Envelopes." A
Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards,
pp. 75-80, 1952.Referenced on Wolfram|Alpha
Envelope
Cite this as:
Weisstein, Eric W. "Envelope." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Envelope.html
Subject classifications