1433.sagews

##Hurricane candleholder
r,theta,z=var('r'),var('theta'),var('z');
H=parametric_plot3d([(sin(z/2)+5)*cos(theta),(sin(z/2)+5)*sin(theta), z],(theta,0,2*pi),(z,3*pi,8*pi), frame=False, color='black',opacity=0.1);
show(H)

##H as a surface of revolution
r,theta,z=var('r'),var('theta'),var('z');
x,y=var('x'),var('y');
H=parametric_plot3d([x,(sin(x/2)+5)*sin(theta), (sin(x/2)+5)*cos(theta)],(theta,0,2*pi),(x,3*pi,8*pi), color='black',opacity=0.1);
xaxis=parametric_plot3d([x,0,0],(x,0,8*pi), color='black',opacity=0.5);
yaxis=parametric_plot3d([0,y,0],(y,0,6), color='black',opacity=0.5);
zaxis=parametric_plot3d([0,0,z],(z,0,6), color='black',opacity=0.5);
C=parametric_plot3d([x,0 ,(sin(x/2)+5)],(x,3*pi,8*pi), color='blue',opacity=1);
show(H+xaxis+yaxis+zaxis+C)

##Approximation of H by frusta
r,theta,z=var('r'),var('theta'),var('z');
r1=0.3535533*(z-3.5*pi)+4.292893;
F1=parametric_plot3d([z,r1*sin(theta), r1*cos(theta)],(theta,0,2*pi),(z,3*pi,4*pi), frame=False, color='blue',opacity=1);
r2=0.3535533*(z-4.5*pi)+5.7070107;
F2=parametric_plot3d([z,r2*sin(theta), r2*cos(theta),],(theta,0,2*pi),(z,4*pi,5*pi), frame=False, color='red',opacity=1);
r3=-0.3535533*(z-5.5*pi)+5.7070107;
F3=parametric_plot3d([z,r3*sin(theta), r3*cos(theta)],(theta,0,2*pi),(z,5*pi,6*pi), frame=False, color='green',opacity=1);
r4=-0.3535533*(z-6.5*pi)+4.292893;
F4=parametric_plot3d([z,r4*sin(theta), r4*cos(theta)],(theta,0,2*pi),(z,6*pi,7*pi), frame=False, color='yellow',opacity=1);
r5=0.3535533*(z-7.5*pi)+4.292893;
F5=parametric_plot3d([z,r5*sin(theta), r5*cos(theta)],(theta,0,2*pi),(z,7*pi,8*pi), frame=False, color='blue',opacity=1);
show(F1+F2+F3+F4+F5)