#A # sign indicates a comment 
#Click  Edit ---> Execute --> Worksheet  to re-execute the sheet
#Press the enter key on each line to execute that line

restart; # Restart clears out Maple's memory 

with(plots): #We'll use the display command from the "plots" package

r := [cos(t),sin(t)]; # := means assignment, the brackets mean a list
q := [cos(t)+t*sin(t),sin(t)-t*cos(t)];  #Commands end with a semicolon or colon
C := plot([r[1],r[2],t=0..2*Pi],color=blue):  #Parametric plot of the above circle
Inv :=plot([q[1],q[2],t=0..2*Pi],color=green): #Parametric plot of the involute
Q := display([C,Inv],scaling=constrained):  #Display them together
Q; #Show the picture stored in Q



###############################################################
#Next we work on animating the string constructing the involute
L := expand((1-s)*r + s*q);  #A line from the circle r at t to the involute q at t
                       L := r - r s + s q

#The next loop makes a sequence of plots of the above lines on top of the plot Q
n := 32: # Number of frames in the animation
for i from 1 to n do  #Begin the loop
   Lt := subs(t=(2*Pi)*(i/n),L);  #The line for the given t value
    P[i] := plot([Lt[1],Lt[2],s=0..1],color=magenta);  #Plot the line
    PQ[i] := display([P[i],Q]);  #Display on top of Q
od:  #End the for loop

#In the next command we give the display command the sequence of plots
#defined in the loop and ask for them to be displayed "insequence" for
#an animation. Click on the plot to get a top bar of playback controls.

display([PQ[j] $j=1..n],scaling=constrained,insequence=true);