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 y-axis.

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 y-axis.

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);