# 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

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