Hi: Here are a few cool space curves. I'd like to make more from http://www.math.umd.edu/research/bianchi/Gifspacecurves/spcu.html and http://virtualmathmuseum.org/SpaceCurves/ If anyone knows of some parametric equations for them, I'd appreciate it.
#trefoil knot #http://en.wikipedia.org/wiki/Trefoil_knot sage: fx = 0.01*(41*cos(t) - 18*sin(t) - 83*cos(2*t)-83*sin(2*t) - 11*cos(3*t) + 27*sin(3*t)) sage: fy = 0.01*(36*cos(t) + 27*sin(t) - 113*cos(2*t)+30*sin(2*t) + 11*cos(3*t) - 27*sin(3*t)) sage: fz = 0.01*(45*sin(t) - 30*cos(2*t) + 113*sin(2*t)-11*cos(3*t) + 27*sin(3*t)) sage: parametric_plot3d( (fx, fy, fz), (t, 0, 6*pi), plot_points = 500, frame=False) #figure-eight knot #http://en.wikipedia.org/wiki/Figure-eight_knot_%28mathematics%29 sage: fx = (2 + cos(2*t))*cos(3*t) sage: fy = (2 + cos(2*t))*sin(3*t) sage: fz = sin(4*t) sage: parametric_plot3d( (fx, fy, fz), (t, 0, 6*pi), plot_points = 500, frame=False) #Cinquefoil Knot (a=2 is this one): #http://en.wikipedia.org/wiki/Skein_relation #http://virtualmathmuseum.org/SpaceCurves/index.html#Classic fx = cos(t)*(2 - cos(2a*t/(2*a + 1))) fy = sin(t)*(2 - cos(2*t/(2*a + 1))) fz = - sin(2*t/(2*a + 1)) sage: parametric_plot3d( (fx, fy, fz), (t, 0, 20*pi), plot_points = 500, frame=False) #3-leafed space curve sage: a = 1; b = 1; c = 1; d = 3; e = 2 sage: fx = (a + b*cos(d*t))*cos(e*t) sage: fy = (a + b*cos(d*t))*sin(e*t) sage: fz = c*sin(d*t) sage: parametric_plot3d( (fx, fy, fz), (t, 0, 4*pi), plot_points = 100, frame=False) # The Viviani Curve #http://en.wikipedia.org/wiki/Viviani's_curve sage: a = 1 sage: fx = a*2*sin(t/2) sage: fy = a*sin(t) sage: fz = a*(1 + cos(t)) sage: parametric_plot3d( (fx, fy, fz), (t, 0, 4*pi), plot_points = 100, frame=False) #loxodrome #http://en.wikipedia.org/wiki/Loxodrome sage: fx = sin(t)/sqrt(1+t^2) sage: fy = cos(t)/sqrt(1+t^2) sage: fz = t/sqrt(1+t^2) sage: parametric_plot3d( (fx, fy, fz), (t, -4*pi, 4*pi), plot_points = 100, frame=False) --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-forum URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
