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An envelope of a set of curves is a curve that is tangent to these curves.
Examples
are the following:
- an astroid is the envelope of
straight lines
- an astroid is the envelope
of co-axial ellipses for
which the sum of the major and minor axes is constant
- a cardioid is the envelope of
the chords of a circle
- a cardioid is the envelope of circles
- a catacaustic is the envelope of
reflected rays
- a deltoid is the envelope of the
so-called Simson lines
- a diacaustic is the envelope of
refracted rays
- the lemniscate
is the envelope of circles with their centers on a rectangular hyperbola
- the nephroid is the envelope of a set of
circles with centers on a base circle and tangent to a diameter (of the base
circle)
In fact, the envelope of the normal of a curve is the same as the evolute
of the curve.
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