#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);