17-These plots are due to David Joyner.sagews

These plots are due to David Joyner

# M\"obius strip:
u,v = var("u,v")
parametric_plot3d([cos(u)*(1+v*cos(u/2)), sin(u)*(1+v*cos(u/2)), 0.2*v*sin(u/2)], (u,0, 4*pi+0.5), (v,0, 0.3),plot_points=[50,50])

# twisted ribbon
parametric_plot3d([3*sin(u)*cos(v), 3*sin(u)*sin(v), cos(v)], (u,0, 2*pi), (v, 0, pi),plot_points=[50,50])

# ellipsoid
var('u,v')
parametric_plot3d([3*sin(u)*cos(v), 2*sin(u)*sin(v), cos(u)], (u,0, 2*pi), (v, 0, 2*pi),plot_points=[50,50], aspect_ratio=[1,1,1])

# cone
parametric_plot3d([u*cos(v), u*sin(v), u], (u, -1, 1), (v, 0, 2*pi+0.5), plot_points=[50,50])

# paraboloid
parametric_plot3d([u*cos(v), u*sin(v), u^2], (u, 0, 1), (v, 0, 2*pi+0.4), plot_points=[50,50])

# hyperboloid
plot3d(u^2-v^2, (u, -1, 1), (v, -1, 1), plot_points=[50,50])

# weird looking surface - like a M\"obius band but also an O
parametric_plot3d([sin(u)*cos(u)*log(u^2)*sin(v), (u^2)^(1/6)*(cos(u)^2)^(1/4)*cos(v), sin(v)], (u, 0.001, 1), (v, -pi, pi+0.2), plot_points=[50,50])

# a heart, but not a cardioid (for my wife)
p1 = parametric_plot3d([sin(u)*cos(u)*log(u^2)*v*(1-v)/2, 
((u^6)^(1/20)*(cos(u)^2)^(1/4)-1/2)*v*(1-v), v^(0.5)], (u, 0.001, 1),
(v, 0, 1), plot_points=[70,70], color='red')
p2 = parametric_plot3d([-sin(u)*cos(u)*log(u^2)*v*(1-v)/2,
((u^6)^(1/20)*(cos(u)^2)^(1/4)-1/2)*v*(1-v), v^(0.5)], (u, 0.001, 1),
(v, 0, 1), plot_points=[70,70], color='red')
show(p1+p2, frame=False)