parametric equations

2354 days ago by chrisphan

var('t') x = lambda t: sin(t)*sin(5*t) y = lambda t: cos(t)*sin(5*t) frames =[] curback = parametric_plot((x(t), y(t)), (t, 0, pi), rgbcolor=(1, 0.5, 0.5)) totalnum = 100 deltat = pi/totalnum for i in range(1, totalnum+1): curback = curback + parametric_plot((x(t),y(t)), (t, (i-1)*deltat, i*deltat)) curframe = curback + point([x(i*deltat), y(i*deltat)], rgbcolor=(0, 0.5, 0), size=25) frames.append(curframe) a = animate(frames, xmin=-1, xmax=1, ymin=-1, ymax=1, figsize=[5, 5]) show(a) show(plot(x(t), t, 0, pi, rgbcolor=(0.5, 0, 0))+ plot(y(t), t, 0, pi, rgbcolor=(0, 0.5, 0))) 
       

                                
                            

                                
var('t') x = lambda t: sin(t) y = lambda t: cos(t) frames =[] curback = parametric_plot((x(t), y(t)), (t, 0, 2*pi), rgbcolor=(1, 0.5, 0.5)) totalnum = 100 deltat = 2*pi/totalnum for i in range(1, totalnum+1): curback = curback + parametric_plot((x(t),y(t)), (t, (i-1)*deltat, i*deltat)) curframe = curback + point([x(i*deltat), y(i*deltat)], rgbcolor=(0, 0.5, 0), size=25) frames.append(curframe) a = animate(frames, xmin=-1, xmax=1, ymin=-1, ymax=1, figsize=[5, 5]) show(a) show(plot(x(t), t, 0, 2*pi, rgbcolor=(0.5, 0, 0))+ plot(y(t), t, 0, 2*pi, rgbcolor=(0, 0.5, 0))) 
       

                                
                            

                                
var('t') x = lambda t: 2*sin(t) y = lambda t: 3*cos(t) frames =[] curback = parametric_plot((x(t), y(t)), (t, 0, 2*pi), rgbcolor=(1, 0.5, 0.5)) totalnum = 100 deltat = 2*pi/totalnum for i in range(1, totalnum+1): curback = curback + parametric_plot((x(t),y(t)), (t, (i-1)*deltat, i*deltat)) curframe = curback + point([x(i*deltat), y(i*deltat)], rgbcolor=(0, 0.5, 0), size=25) frames.append(curframe) a = animate(frames, xmin=-3, xmax=3, ymin=-3, ymax=3, figsize=[5, 5]) show(a) show(plot(x(t), t, 0, 2*pi, rgbcolor=(0.5, 0, 0))+ plot(y(t), t, 0, 2*pi, rgbcolor=(0, 0.5, 0))) 
       

                                
                            

                                
var('t') x = lambda t: 4*t-5 y = lambda t: 3*t^2 frames =[] curback = parametric_plot((x(t), y(t)), (t, -3, 3), rgbcolor=(1, 0.5, 0.5)) totalnum = 100 deltat = 6/totalnum for i in range(1, totalnum+1): curback = curback + parametric_plot((x(t),y(t)), (t, (i-1)*deltat-3, i*deltat-3)) curframe = curback + point([x(i*deltat-3), y(i*deltat-3)], rgbcolor=(0, 0.5, 0), size=25) frames.append(curframe) a = animate(frames, xmin=-17, xmax=7, ymin=0, ymax=36, figsize=[4, 6]) show(a) show(plot(x(t), t, -3, 3, rgbcolor=(0.5, 0, 0))+ plot(y(t), t, -3, 3, rgbcolor=(0, 0.5, 0))) 
       

                                
                            

                                
var('t') x = lambda t: t^3 y = lambda t: t^6 frames =[] curback = parametric_plot((x(t), y(t)), (t, -2, 2), rgbcolor=(1, 0.5, 0.5)) totalnum = 100 deltat = 4/totalnum for i in range(1, totalnum+1): curback = curback + parametric_plot((x(t),y(t)), (t, (i-1)*deltat-2, i*deltat-2)) curframe = curback + point([x(i*deltat-2), y(i*deltat-2)], rgbcolor=(0, 0.5, 0), size=25) frames.append(curframe) a = animate(frames, xmin=-8, xmax=8, ymin=0, ymax=64, figsize=[5, 5]) show(a) show(plot(x(t), t, -2, 2, rgbcolor=(0.5, 0, 0))+ plot(y(t), t, -2, 2, rgbcolor=(0, 0.5, 0))) 
       

                                
                            

                                
var('t') x = lambda t: t^2 y = lambda t: t^4 frames =[] curback = plot(t^2, (t, -8, 8), rgbcolor=(1, 0.5, 0.5)) totalnum = 100 deltat = 2*sqrt(8)/totalnum for i in range(1, totalnum+1): curback = curback + parametric_plot((x(t),y(t)), (t, (i-1)*deltat-sqrt(8), i*deltat-sqrt(8))) curframe = curback + point([x(i*deltat-sqrt(8)), y(i*deltat-sqrt(8))], rgbcolor=(0, 0.5, 0), size=25) frames.append(curframe) a = animate(frames, xmin=-8, xmax=8, ymin=0, ymax=64, figsize=[5, 5]) show(a) show(plot(x(t), t, -3, 3, rgbcolor=(0.5, 0, 0))+ plot(y(t), t, -3, 3, rgbcolor=(0, 0.5, 0))) 
       

                                
                            

                                
var('t') x = lambda t: 4*cos(t) y = lambda t: 16*cos(t)^2 frames =[] curback = plot(t^2, (t, -8, 8), rgbcolor=(1, 0.5, 0.5)) totalnum = 100 deltat = 6*pi/totalnum for i in range(1, totalnum+1): curback = curback + parametric_plot((x(t),y(t)), (t, (i-1)*deltat-3*pi, i*deltat-3*pi)) curframe = curback + point([x(i*deltat-3*pi), y(i*deltat-3*pi)], rgbcolor=(0, 0.5, 0), size=25) frames.append(curframe) a = animate(frames, xmin=-8, xmax=8, ymin=0, ymax=64, figsize=[5, 5]) show(a) show(plot(x(t), t, -3*pi, 3*pi, rgbcolor=(0.5, 0, 0))+ plot(y(t), t, -3*pi, 3*pi, rgbcolor=(0, 0.5, 0))) 
       

                                
                            

                                
var('t') show(parametric_plot((sin(t)*sin(5*t), cos(t)*sin(5*t)), (t, 0, 2*pi), rgbcolor=(0.75, 0.25, 0.25)) + plot((4*sqrt(3)/4)/(5*sqrt(3)/4 - 3/4)*(t - sin(pi/3)*sin(5*pi/3)) + cos(pi/3)*sin(5*pi/3), t, -1, 1), figsize=[5,5], xmin=-1, xmax=1, ymin=-1, ymax=1)