Copy and paste the formulas below for x(t) and y(t) into the input boxes of the action figure to give a variety of interesting examples. Hit the enter key with the curser in one of the input boxes to tell the figure to read your new formulas.
cos[a*t]
sin[b*t]
Try varying a and b.
Set tmax=6.28.
Lissajous Figures
a*(t^2-1)
a*t*(t^2-3)/3
Tschirnhausen's
cubic
. Set tmin=-10
and tmax=10
cos[t]*sin[a*t]
sin[t]*sin[a*t]
Try varying a.
Set tmax=6.28.
(1+1/a)*cos[t]+b*cos[(a-1)*t]/a
(1+1/a)*sin[t]-b*sin[(a-1)*t]/a
Try a=3 and b=1.1.
Try a=4 and b=0.6.
Set tmax=6.28.
3*a*t/(1+t^3)
3*a*t^2/(1+t^3)
Try tmin = -n, tmax = n with
n = 5, 10, 20
Folium of Descartes
cos[t]*c*d/(1+c*cos[t])-d
sin[t]*c*d/(1+c*cos[t])
c is the eccentricity.
The y-axis is the directrix
and a focus is at -d.
Set tmax=6.28.
a*tan[t]
a*(cos[t])^2
Witch of Agnesi
cos[t]*(2*a*cos[t]+b)
sin[t]*(2*a*cos[t]+b)
Limacon of Pascal
tmin=-3.14
tmax=3.14
a*cos[t]*(1+b*cos[t])
a*sin[t]*(1+b*cos[t])
Cardioid. Set tmax=6.28,
tmin=0
a*cos[t]/(1+(sin[t])^2)
a*sin[t]*cos[t]/(1+(sin[t])^2)
Leminscate of Bernoulli
tmin=-3.14, tmax=3.14
a*cos[t]
a*sin[t]*cos[t]
Another figure eight
tmin=-3.14, tmax=3.14
a*cos[t]
b*cot[t]
Bullet Nose
tmin=-3.14, tmax=3.14
a/cos[t]
b/sin[t]
The cross curve
tmin=-3.14, tmax=3.14
a*cos[t]*(1+cos[t])-a/2
a*sin[t]*(1-cos[t])
Deltoid
tmin=-3.14, tmax=3.14
b+a*cos[t]
tan[t]*(b+a*cos[t])
Conchoid of Nicomedes
tmin=-1.57, tmax=4.71
a*cos[t]*cot[t]
a*cos[t]
Kappa Curve
tmax=6.28
a*sec[t]
a*sec[t]*tan[t]
Kampyle of Eudoxus
tmin=-1.57, tmax=4.71
x4=a2(x2+y2)