Demonstration 9: Ordinary and Rhamphoid Cusps
The equation for the curve is X(t) =(3+t)(tm ,tn) , and the values of m and n determine the nature of the cusp. For example, the values m=2 , n=3 yield an ordinary cusp, and the values m=2 , n=4 yield a rhamphoid cusp.
This demo displays a curve that has either an ordinary cusp or a rhamphoid cusp at t=0 .
What relationship do the values of
m
and
n
have to the quadrant in which the curve lies?
Try to establish a rule about
m
and
n
that determines whether or not this curve has an ordinary cusp, a
rhamphoid cusp or neither. In particular, look at high values of
m
and
n.