Previous: Smooth Curves and Curves with Singular Points
5. Pedal CurvesA point of the pedal curve ZC(t) of a plane curve X(t) is defined to be the foot of the perpendicular from C to the tangent line to the curve at X(t) . We may express this by the following formula: | |
Pedal Curves Demo
What happens to the curve
ZC(t)
as
C
changes? What is the nature of the pedal curve if the original curve has
an inflection point? What if the original curve has an ordinary or
rhamphoid cusp? | |
What is the condition for the pedal curve to intersect the original curve? | |
What familty of curves arise as the pedal curves of a circle? | |
What types of cusps does the pedal curve to [t2, t3 - t/2] have for various positions of the pedal point? |