L3.html

Curves in polar coordinates

Note: Maple contradicts to our agreement that r> 0; as r≤0 it puts point (t+Pi, -r).
To overcome this we replace r by max(r,0) and the correct curve on two first figures is red; blue one is Maple extra. On the second figure red and blue coincide: Maple runs the same curve twice: correctly and excessively.

> with(plots,polarplot);
polarplot([[max(cos(2*t),0),t,t=0..2*Pi],[min(cos(2*t),0),t,t=0..2*Pi]],color=[red,blue],scaling=CONSTRAINED);

> with(plots,polarplot);
polarplot([[max(cos(3*t),0),t,t=0..2*Pi],[min(cos(3*t),0),t,t=0..2*Pi]],color=[red,blue],scaling=CONSTRAINED);

> with(plots);
animate(polarplot,[[max(cos(t)+s,0),t,t=0..2*Pi]],s=-1..1,frames=20,scaling=CONSTRAINED);

> with(plots);
animate(polarplot,[[max(cos(2*t)+s,0),t,t=0..2*Pi]],s=-1..1,frames=20,scaling=CONSTRAINED);

> with(plots);
animate(polarplot,[[max(cos(3*t)+s,0),t,t=0..2*Pi]],s=-1..1,frames=20,scaling=CONSTRAINED);

> with(plots);
animate(polarplot,[[max(cos(t/2)+s,0),t,t=0..4*Pi]],s=-1..1,frames=20,scaling=CONSTRAINED);

> with(plots);
animate(polarplot,[[max(1/(1-s+s*cos(t)),0),t,t=0..2*Pi]],s=0.1..0.48,frames=20,scaling=CONSTRAINED);

> with(plots,polarplot);
polarplot([[max(t,0),t,t=-8*Pi..8*Pi],[min(t,0),t,t=-8*Pi..8*Pi]],color=[red,blue],scaling=CONSTRAINED);

> with(plots,polarplot);
polarplot([[exp(t/10),t,t=-8*Pi..8*Pi],[exp(-t/10),t,t=-8*Pi..8*Pi]],color=[red,green],scaling=CONSTRAINED);