Pedal curve
of a curve with respect to a point
The set of bases to the perpendiculars dropped from the point to the tangents to the curve
. For example, the Pascal limaçon is the pedal of a circle with respect to the point
(see Fig.). The pedal (curve) of a plane curve
relative to the coordinate origin is
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Figure: p071950a
The equation for the pedal of a curve in space relative to the origin is
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The antipedal of a curve with respect to a point
is the name given to the curve with as pedal, with respect to the point
, the curve
.
The pedal of a surface with respect to a point is the set of bases to the perpendiculars dropped from the point
to the tangent planes to the surface. The equation for the pedal of a surface
with respect to the coordinate origin is
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where
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Comments
References
[a1] | M. Berger, "Geometry" , I , Springer (1987) |
[a2] | G. Darboux, "Leçons sur la théorie générale des surfaces et ses applications géométriques du calcul infinitésimal" , 1–4 , Gauthier-Villars (1887–1896) |
Pedal curve. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pedal_curve&oldid=48149