2419 HW 3 Prob 1

# This is not a hypotrochoid. reset() var('t') R=5;r=3;d=5;a=0; @interact def _(b=slider(0,12*pi,pi/12,0)): p=(R-r)*vector([sin((r/R)*t),cos((r/R)*t)]) f=p+d*vector([-sin(t),cos(t)]) html('$d = %s {<} r = %s {<} R = %s$' %(d,r,R)) P = parametric_plot(f,(t,0,b+.0001)) P+=circle((0,0),R,color="red") P+=circle(p(t=b),r)+point(p(t=b),size=20) P+=point(f(t=b),size=20,color="red") P+=line((p(t=b),f(t=b)),color="green",thickness=2) P+=line((p(t=b),p(t=b)+r/2*(p(t=b))),color="red",thickness=1,linestyle=":") show(P) 

# This is not a hypotrochoid. reset() var('t,l') R=5;r=2;d=3;a=0; @interact def _(b=slider(0,4*pi,pi/24,0)): p=(R-r)*vector([sin((r/R)*t),cos((r/R)*t)]) f=p+d*vector([-sin(t),cos(t)]) M=matrix([[cos(t),-sin(t)], [sin(t),cos(t)]]) html('$d = %s {<} r = %s {<} R = %s$' %(d,r,R)) P=parametric_plot(f,(t,0,b+.0001)) P+=circle((0,0),R,color="red") P+=circle(p(t=b),r) P+=point(p(t=b),size=20) P+=point(f(t=b),size=20,color="red") P+=arrow2d(p(t=b),f(t=b),color="green") P+=arrow2d((0,0),p(t=b),color="red") P+=arrow2d(path=[[(p(t=b)+.2*M(t=u)*vector([0,1])) for u in [0..b,step=pi/24]]], width=1,arrowsize=2,color=(.5,.5,.5),zorder=1) P+=line((p(t=b),p(t=b)+r/2*vector([0,1])),color="red",thickness=1,linestyle=":") P+=text("${\\theta}$", p(t=b)+.2*M(t=b/2)*p(t=b),vertical_alignment="bottom",fontsize=14) P+=text('$P(\\theta)$',f(t=b), horizontal_alignment='left',vertical_alignment='bottom', fontsize=14) show(P,xmin=-1.5,xmax=4.5,ymin=-.5,ymax=6.3) 

# This is a hypotrochoid which is different from the above reset() var('t') R=5;r=2.6;d=5;a=0; @interact #def _(b=slider(0,12*pi,pi/12,0)): def _(b=[0..12*pi,step=pi/6]): p=(R-r)*vector([sin((r/R)*t),cos((r/R)*t)]) f=p+d*vector([-sin((R-r)/R*t),cos((R-r)/R*t)]) html('$d = %s {<} r = %s {<} R = %s$' %(d,r,R)) P = parametric_plot(f,(t,0,b+.0001)) P+=circle((0,0),R,color="red") P+=circle(p(t=b),r)+point(p(t=b),size=20) P+=point(f(t=b),size=20,color="red") P+=line((p(t=b),f(t=b)),color="green",thickness=2) P+=line((p(t=b),p(t=b)+r/2*(p(t=b))),color="red",thickness=1,linestyle=":") show(P) 

reset() var('t,l') R=5;r=2;d=3;a=0; #_(b=slider(0,4*pi,pi/24,0)): @interact def _(b=[0..4*pi,step=pi/6]): p=(R-r)*vector([sin((r/R)*t),cos((r/R)*t)]) f=p+d*vector([-sin((R-r)/R*t),cos((R-r)/R*t)]) M=matrix([[cos(t),-sin(t)], [sin(t),cos(t)]]) html('$d = %s {<} r = %s {<} R = %s$' %(d,r,R)) P=parametric_plot(f,(t,0,b+.0001)) P+=circle((0,0),R,color="red") P+=circle(p(t=b),r) P+=point(p(t=b),size=20) P+=point(f(t=b),size=20,color="red") P+=arrow2d(p(t=b),f(t=b),color="green") P+=arrow2d((0,0),p(t=b),color="red") if (b>0): P+=arrow2d(path=[[(p(t=b)+.2*M(t=u)*p(t=b)) for u in [0..b,step=pi/24]]], width=1,arrowsize=2,color=(.5,.5,.5),zorder=1) P+=line((p(t=b),p(t=b)+r/2*p(t=b)),color="red",thickness=1,linestyle=":") P+=text("${\\theta}$", p(t=b)+.2*M(t=b/2)*p(t=b),vertical_alignment="bottom",fontsize=14) P+=text("${\\alpha}$", p(t=b)+.13*M(t=r/R*b/3)*p(t=b),vertical_alignment="bottom",fontsize=14) P+=text("${\\alpha}$", vector([0,0])+.13*M(t=r/R*b/3)*p(t=b),vertical_alignment="bottom",fontsize=14) P+=text('$P(\\theta)$',f(t=b), horizontal_alignment='left',vertical_alignment='bottom', fontsize=14) P+=line((p(t=b),p(t=b)+r/2*vector([0,1])),color="red",linestyle=":") show(P,xmin=-1.5,xmax=4.5,ymin=-.5,ymax=6.3)