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Pedal curve

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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

Figure: p071950a

The equation for the pedal of a curve in space relative to the origin is

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

where


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)
How to Cite This Entry:
Pedal curve. A.B. Ivanov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Pedal_curve&oldid=17030
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098