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{SECT 0 {EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 208 30 "#A # sign indica
tes a comment " }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 65 "#Begin by click
ing Edit ---> Execute --> Worksheet  to re-execute" }}{PARA 206 "> " 0
 "" {MPLTEXT 1 0 46 "#Press enter on each line to execute that line" }
}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 205 "> \+
" 0 "" {MPLTEXT 1 208 45 "restart; # Restart clears out Maple's memory
 " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
205 "> " 0 "" {MPLTEXT 1 208 68 "with(plots): #We'll use the display c
ommand from the \"plots\" package" }}{PARA 207 "" 1 "" {TEXT 209 49 "W
arning, the name changecoords has been redefined" }{TEXT 209 0 "" }}}
{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 205 "> " 
0 "" {MPLTEXT 1 208 69 "r := [cos(t),sin(t)]; # := means assignment, t
he brackets mean a list" }}{PARA 208 "" 1 "" {XPPMATH 20 "6#>I\"rG6\"7
$-I$cosG6$I*protectedGF*I(_syslibGF%6#I\"tGF%-I$sinGF)F," }{TEXT 210 
0 "" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 208 80 "q := [cos(t)+t*s
in(t),sin(t)-t*cos(t)];  #Commands end with a semicolon or colon" }}
{PARA 208 "" 1 "" {XPPMATH 20 "6#>I\"qG6\"7$,&-I$cosG6$I*protectedGF+I
(_syslibGF%6#I\"tGF%\"\"\"*&F.F/-I$sinGF*F-F/F/,&F1F/*&F.F/F(F/!\"\"" 
}{TEXT 210 0 "" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 208 82 "C := \+
plot([r[1],r[2],t=0..2*Pi],color=blue):  #Parametric plot of the above
 circle" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 208 79 "Inv :=plot([
q[1],q[2],t=0..2*Pi],color=green): #Parametric plot of the involute" }
{MPLTEXT 1 208 0 "" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 208 66 "Q
 := display([C,Inv],scaling=constrained):  #Display them together" }
{MPLTEXT 1 208 0 "" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 0 32 "Q; \+
#Show the picture stored in Q" }}{PARA 209 "" 1 "" {GLPLOT2D 580 420 
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NSTRAINEDG" 1 2 2 0 10 1 2 6 1 4 1 1.0 45.0 45.0 1 0 "Curve 1" "Curve \+
2" }}{TEXT 211 0 "" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 208 82 "L := expand((1-s)*r + s
*q);  #A line from the circle r at t to the involute q at t" }}{PARA 
208 "" 1 "" {XPPMATH 20 "6#>I\"LG6\"7$,&*(I\"tGF%\"\"\"-I$sinG6$I*prot
ectedGF.I(_syslibGF%6#F)F*I\"sGF%F*F*-I$cosGF-F0F*,&*(F)F*F2F*F1F*!\"
\"F+F*" }{TEXT 210 0 "" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 0 80 "#The next loop makes \+
a sequence of plots of the above lines on top of the plot Q" }}{PARA 
205 "> " 0 "" {MPLTEXT 1 208 26 "n := 32: # Number of lines" }}{PARA 
205 "> " 0 "" {MPLTEXT 1 208 37 "for i from 1 to n do  #Begin the loop
" }{MPLTEXT 1 208 0 "" }}{PARA 205 "> " 0 "" {MPLTEXT 1 208 65 "   Lt \+
:= subs(t=(2*Pi)*(i/n),L);  #The line for the given t value" }}{PARA 
205 "> " 0 "" {MPLTEXT 1 208 68 "   P[i] := plot([Lt[1],Lt[2],s=0..1],
color=magenta);  #Plot the line" }{MPLTEXT 1 208 0 "" }}{PARA 205 "> "
 0 "" {MPLTEXT 1 208 52 "   PQ[i] := display([P[i],Q]);  #Display on t
op of Q" }{MPLTEXT 1 208 0 "" }}{PARA 205 "> " 0 "" {MPLTEXT 1 208 23 
" od:  #End the for loop" }{MPLTEXT 1 208 0 "" }}}{EXCHG {PARA 205 "> \+
" 0 "" {MPLTEXT 1 208 0 "" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 0 
70 "#In the next command we give the display command the sequence of p
lots" }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 70 "#defined in the loop and \+
ask for them to be displayed \"insequence\" for" }}{PARA 206 "> " 0 ""
 {MPLTEXT 1 0 71 "#an animation. Click on the plot to get a top bar of
 playback controls." }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 
205 "> " 0 "" {MPLTEXT 1 208 63 "  display([PQ[j] $j=1..n],scaling=con
strained,insequence=true);" }{MPLTEXT 1 208 0 "" }}{PARA 209 "" 1 "" 
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