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![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
envelope
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(Definition)
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Two plane curves are said to touch each other or have a tangency at a point if they have a common tangent line at that point.
The envelope of a family of plane curves is a curve which touches in each of its points one of the curves of the family.
For example, the envelope of the family
 , with  the parameter, may be justified geometrically. It is the open lower semicircle of the unit circle. Indeed, the distance of any line
of the family from the center of the unit circle is
whence the line is the tangent to the circle.
Below, the red curve is the lower semicircle of the unit circle, the black lines belong to the family
 , and the equation of each line is given.
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"envelope" is owned by pahio. [ full author list (3) ]
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(view preamble)
Cross-references: equation, circle, tangent, center, line, distance, unit circle, parameter, curve, tangent line, point, plane curves
There are 13 references to this entry.
This is version 20 of envelope, born on 2007-05-29, modified 2007-10-13.
Object id is 9484, canonical name is Envelope.
Accessed 1366 times total.
Classification:
| AMS MSC: | 51N20 (Geometry :: Analytic and descriptive geometry :: Euclidean analytic geometry) |
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Pending Errata and Addenda
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