Given a curve , the pedal curve of with respect to a fixed point (the Pedal Point) is the locus of the
point of intersection of the Perpendicular from to a Tangent to . The parametric equations
for a curve relative to the Pedal Point are
Curve | Pedal Point | Pedal Curve |
Astroid | center | Quadrifolium |
Cardioid | cusp | Cayley's Sextic |
Central Conic | Focus | Circle |
Circle | any point | Limaçon |
Circle | on Circumference | Cardioid |
Circle Involute | center of Circle | Archimedean Spiral |
Cissoid of Diocles | Focus | Cardioid |
Deltoid | center | Trifolium |
Deltoid | cusp | simple Folium |
Deltoid | on curve | unsymmetric double folium |
Deltoid | Vertex | double folium |
Epicycloid | center | Rose |
Hypocycloid | center | Rose |
Line | any point | point |
Logarithmic Spiral | pole | Logarithmic Spiral |
Parabola | Focus | Line |
Parabola | foot of Directrix | Right Strophoid |
Parabola | on Directrix | Strophoid |
Parabola | reflection of Focus by Directrix | Maclaurin Trisectrix |
Parabola | Vertex | Cissoid of Diocles |
Sinusoidal Spiral | pole | Sinusoidal Spiral |
Tschirnhausen Cubic | Focus of Pedal | Parabola |
See also Negative Pedal Curve
References
Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 46-49 and 204, 1972.
Lee, X. ``Pedal.''
http://www.best.com/~xah/SpecialPlaneCurves_dir/Pedal_dir/pedal.html.
Lockwood, E. H. ``Pedal Curves.'' Ch. 18 in A Book of Curves. Cambridge, England: Cambridge University Press,
pp. 152-155, 1967.
Yates, R. C. ``Pedal Curves.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 160-165, 1952.
© 1996-9 Eric W. Weisstein