WOLFRAM|DEMONSTRATIONS PROJECT

Envelope of Two Families of Plane Curves

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radius
position
generatrix
circle
figure eight
fill
The equation of the envelope of the family of curves {
x(t,a)
,
y(t,a)
} is symmetric with respect to
t
and
a
. In this case the same curve is the envelope of the family of circles sliding along a figure-eight curve and the family of figure-eight curves sliding along a circle.