Mathematical Experiment 1
Construct the surface given by
, in spherical coordinates. 

plot3d(1+sin(t),t=0..Pi,s=0..Pi,coords=spherical, scaling=constrained); 
Construct the surface obtained by
rotating the cardioid about its axis by 180 degrees. In polar coordinates,
the cardioid is given by


r:=1+cos(t); x:=r*cos(t); rho:=r*sin(t); y:=rho*cos(s); z:=rho*sin(s); plot3d([x,y,z],t=0..Pi,s=0..Pi,scaling=constrained, grid=[25,25],lightmodel=light2); 
¡@
Construct the surface obtained by rotating the curve given, in polar coordinates, by
about the yaxis. 

r:=1+cos(2*t); rho:=r*cos(t); y:=r*sin(t); x:=rho*cos(s); z:=rho*sin(s); plot3d([x,y,z],t=0..Pi/2,s=0..Pi, scaling=constrained,grid=[25,25]); 
¡@
The nephroid is given by
Construct the surface obtained by rotating the nephroid about the yaxis. 

r:=3*cos(t)cos(3*t); x:=r*cos(s); y:=r*sin(s); z:=3*sin(t)sin(3*t); plot3d([x,y,z], t=Pi/2..Pi/2, s=0..Pi,scaling=constrained); 