{VERSION 4 0 "IBM INTEL NT" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple P
lot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 
0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "Construct the reflections \+
of a light ray trapped inside a reflective ellipse. There are two case
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "a:=5:b:=3:r:=2.34:s:=5.
9:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "ll:=[a*cos(r),b*sin(r
)]:l:=[a*cos(s),b*sin(s)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
10 "m:=[l,ll]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 195 "for k to
 200 do u:=ll-l: n:=[-b*ll[1]/a,-a*ll[2]/b]:v:=u-2*dotprod(u , n)*n/do
tprod(n,n):t:=-2*(b^2*v[1]*ll[1]+a^2*ll[2]*v[2])/(b^2*v[1]^2+a^2*v[2]^
2):lll:=ll+t*v:m:=[op(m),lll]:l:=ll:ll:=lll:od:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 49 "plot(m,scaling=constrained,axes=none,color=cya
n);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVES
G6#7fw7$$\"3g*****R:#RPY!#<$!33+++%**H;7\"F*7$$!39+++Km\"yZ$F*$\"33+++
zVRb@F*7$$!3l*****R)H)=,%F*$!37+++%=a/z\"F*7$$\"3B+++:'zy]%F*$\"3%****
***\\F'yH\"F*7$$\"3$******f[x5!>F*$!3%)*****fy$puFF*7$$!3,+++8X+<ZF*$
\"3%)******zjj\\**!#=7$$\"3)******z5J)Q;F*$!38+++\"ewU$GF*7$$\"3C+++r*
ySa%F*$\"3!*******[Gf^7F*7$$!31+++pww6RF*$!3!******p\"Q]o=F*7$$!3#)***
**\\(RA=OF*$\"3')******zx^q?F*7$$\"39+++;+*\\h%F*$!3!******R>9W:\"F*7$
$\"3G+++q&>!)[*FF$\"3'******HG\"\\XHF*7$$!3:+++$4Cyq%F*$!3'******H^&\\
55F*7$$\"3=+++W$H7\\#F*$\"3@+++[t5,EF*7$$\"3O+++L*ooR%F*$!3\"******f<'
RG9F*7$$!3n*****zuGu@%F*$\"3(*******QYX6;F*7$$!3-+++(\\^]2$F*$!3A+++8s
blBF*7$$\"3q*****>xQ#zYF*$\"33+++vO@d5F*7$$!39++++z$pg)!#>$!33+++zab**
HF*7$$!3G+++\\H6rYF*$\"3))*****>jr+2\"F*7$$\"3++++h>ovJF*$!38+++*)**><
BF*7$$\"3y*****fKnY<%F*$\"3#******\\m_5l\"F*7$$!3/+++!*[dDWF*$!3%*****
*>><hR\"F*7$$!3-+++yj<iBF*$\"37+++!4'4WEF*7$$\"3#)*****>)z76ZF*$!35+++
cp$\\+\"F*7$$!30+++Sr;86F*$\"3(******4o1Z#HF*7$$!3J+++Vso+YF*$!3-+++Nm
yu6F*7$$\"3++++y:X#p$F*$\"3!)******RAzA?F*7$$\"3A+++tB3]QF*$!3%******>
+sS\">F*7$$!3/+++;TliXF*$\"3-+++>Q-F7F*7$$!3'******HOIX[\"F*$!3/+++j+s
kGF*7$$\"3q*****>#30;ZF*$\"3!*******\\\")*e'**FF7$$!30+++TMuW?F*$!3&**
****\\8swt#F*7$$!3m*****f[F^[%F*$\"3(******fQOfK\"F*7$$\"33+++`VMkSF*$
!3/+++.-MZ<F*7$$\"3!******pg&4#R$F*$\"3*)*****pGDS?#F*7$$!3I+++m8n[YF*
$!30+++ZMp/6F*7$$!3+++++_fZ[FF$\"3%********>ne)HF*7$$\"3))*****\\j][p%
F*$!33+++hg*>.\"F*7$$!3*)*****fA]I#GF*$\"35+++)QtgZ#F*7$$!3f*****R'H$p
I%F*$!3&******4z\\Q_\"F*7$$\"3W+++-@:AVF*$\"3*)*****4Rd#3:F*7$$\"3#)**
***f&4NtFF*$!3/+++v3@'\\#F*7$$!3w*****RAssp%F*$\"3'*******>9-G5F*7$$\"
3!*******p!3Re&FF$!3/+++uKB\")HF*7$$\"3C+++ah\"Rk%F*$\"34+++)>q=6\"F*7
$$!3))*****H?>(HMF*$!3;+++PM'H=#F*7$$!3z******[*H?/%F*$\"3'******4\"f(
ew\"F*7$$\"3'******z-t^\\%F*$!3&******prKOJ\"F*7$$\"3#******fw(3$)>F*$
\"31+++3=&Rv#F*7$$!3n*****Hg[lr%F*$!3?++++OTd**FF7$$\"31+++2%H<b\"F*$
\"3=+++46(=&GF*7$$\"3'********[)yaXF*$!3!******>K*\\P7F*7$$!37+++t*3s(
QF*$\"3#******H9dU*=F*7$$!3))******eH#3m$F*$!3++++EKQV?F*7$$\"30+++,0-
2YF*$\"3!*******=u\"e;\"F*7$$\"3$******RX]B/\"F*$!3!)******4i3MHF*7$$!
3'******>R(y4ZF*$\"3.+++Sl>25F*7$$\"3.+++p5e=CF*$!3$*******zYnDEF*7$$
\"3s******\\OR8WF*$\"3$*******z0$*49F*7$$!3e*****>,,N>%F*$!3&******H;!
yL;F*7$$!30+++$o/F8$F*$\"3-+++:b;QBF*7$$\"35+++LstuYF*$!3!******RkeV1
\"F*7$$\"3'********f5&e6F`q$\"3y*****\\#>****HF*7$$!35+++t1$en%F*$!35+
++]\"GE1\"F*7$$\"3++++[8;>JF*$\"3/+++EZnWBF*7$$\"3#)******faD*>%F*$!3&
******>a]%G;F*7$$!3*)*****zuI&4WF*$\"3#******p*\\F99F*7$$!3/+++:0&fV#F
*$!3&)*****\\!y))>EF*7$$\"38+++8GM4ZF*$\"3!*******HY%z+\"F*7$$!34+++=p
A?5F*$!35+++pU)o$HF*7$$!3%******f9X*3YF*$\"3)******pbvI;\"F*7$$\"3')**
***zdL3l$F*$!3#)*****H12)\\?F*7$$\"3!)*****\\D5b)QF*$\"31+++1Q7))=F*7$
$!31+++O*)G_XF*$!3,+++nf!3C\"F*7$$!3#******>u(\\s:F*$\"3))*****p%GxZGF
*7$$\"38+++Hpn;ZF*$!3!)******f\\Ab**FF7$$!3'******zB^P'>F*$\"3/+++)\\N
*eFF*7$$!3o*****4mM#)\\%F*$!3\"******4Pa)48F*7$$\"3g******H,(\\.%F*$\"
3!******fxy;x\"F*7$$\"3$)*****H]b7W$F*$!3;+++KwTw@F*7$$!32+++(Q)RUYF*$
\"33+++!e\\T6\"F*7$$!3B+++!H6C\"eFF$!3'******zbg'zHF*7$$\"3K+++![&*zp%
F*$\"3,+++>4$o-\"F*7$$!37+++\">8xv#F*$!3z*****z2SC]#F*7$$!31+++@$)zEVF
*$\"32+++TRX.:F*7$$\"3J+++k36-VF*$!3++++ubuG:F*7$$\"31+++&QG$QGF*$\"3)
*******=vxpCF*7$$!3c*****zDnSp%F*$!3'******43yK.\"F*7$$\"3@+++]K5=YFF$
\"3;+++Wk<()HF*7$$\"3/+++V?6]YF*$!3#******\\Q3D5\"F*7$$!3/+++JnA!Q$F*$
\"3>+++K+e5AF*7$$!3A+++8n;rSF*$!3'******H<8;u\"F*7$$\"3w*****HKR>[%F*$
\"3/+++d;\")H8F*7$$\"3/+++:!fP1#F*$!3,+++*eIDt#F*7$$!3#******>Uper%F*$
\"33+++gt)*o**FF7$$\"3'******pB*\\j9F*$!3#******>48'oGF*7$$\"3))*****f
5[]c%F*$\"3*)*****f-9QA\"F*7$$!33+++^z]TQF*$!3$******H,k-#>F*7$$!3))**
***zIQ@q$F*$\"32+++Q\"3k,#F*7$$\"35+++>;n)f%F*$!3#******fCCw<\"F*7$$\"
3++++MH4N6F*$\"3#)*****>Er;#HF*7$$!3?+++Nu^6ZF*$!3.+++?%zU+\"F*7$$\"34
+++u#fWM#F*$\"3#*******Qnw\\EF*7$$\"3')******Q/HHWF*$!3))*****p')o=R\"
F*7$$!3%)*****Hz/(oTF*$\"3!*******HtYc;F*7$$!3++++eQ())=$F*$!3/+++B(o1
J#F*7$$\"3i*****p[^*pYF*$\"3)******H0&*=2\"F*7$$\"3)*******\\VH#4\"FF$
!3#)*****>.%G**HF*7$$!3M+++(ol-o%F*$\"3!******\\&fdb5F*7$$\"3%)*****>.
b61$F*$!3!)*****H\"o.sBF*7$$\"3-+++l/)HA%F*$\"3%******R&>@1;F*7$$!3U++
+^V&GR%F*$!3)******H(f$GV\"F*7$$!3(******HPY#3DF*$\"3y*****RF8_f#F*7$$
\"3x*****HwBtq%F*$!3********\\UL65F*7$$!3u******>r(\\E*FF$\"33+++Ni/[H
F*7$$!3>+++*=Eoh%F*$!31+++U!o<:\"F*7$$\"3(******R$p#zg$F*$\"3/+++Ej(p2
#F*7$$\"3%)*****4U,)>RF*$!35+++5HVi=F*7$$!3S+++x1ZTXF*$\"3++++9j*\\D\"
F*7$$!3%******>$RKf;F*$!3()*****R(3)*HGF*7$$\"3s*****4%*zqr%F*$\"3[***
****H[$[**FF7$$!37+++d(G9)=F*$!3++++f4^zFF*7$$!3;+++p%=3^%F*$\"3/+++`:
=%H\"F*7$$\"3!******H))zX+%F*$!3!*******=-L'z\"F*7$$\"3-+++IX-*[$F*$\"
3;+++#ej)[@F*7$$!3L+++?_zNYF*$!3$******>$R+C6F*7$$!3]++++&yDx'FF$\"39+
++&)=NsHF*7$$\"3J+++a(*)3q%F*$!3$******z?^?-\"F*7$$!3))*****\\)='3p#F*
$\"3)******4O/&GDF*7$$!3e*****ptNfM%F*$!3#******4w\\M[\"F*7$$\"3;+++JZ
J\"G%F*$\"31+++C0i\\:F*7$$\"3-+++G,z,HF*$!3=+++0V3VCF*7$$!3;+++Zgg!p%F
*$\"3\"******p=@*Q5F*7$$\"3%*******>%*f[OFF$!39+++]>+#*HF*7$$\"3k*****
R_))fl%F*$\"3'******p\\VN4\"F*7$$!39+++H1KHLF*$!3'*******e!>#QAF*7$$!3
#******>\")=$*4%F*$\"3++++<fn<<F*7$$\"3%)*****\\(=;oWF*$!31+++x!*RY8F*
7$$\"3y*****4NfI9#F*$\"33+++KhY5FF*7$$!3i*****z&f'\\r%F*$!3!**********
fV)**FF7$$\"3#*******G=>u8F*$\"3!*******48Z%)GF*7$$\"3e*****RSr[d%F*$!
3'*******Qk`57F*7$$!33+++Q*QY!QF*$\"3)******pp4l%>F*7$$!3>+++XS>UPF*$!
35+++F:h*)>F*7$$\"3%******>\">$**e%F*$\"3-+++ec$)*=\"F*7$$\"3,+++gb'pA
\"F*$!3\")*****z$4F3HF*7$$!3:+++On,8ZF*$\"35+++*fV<+\"F*7$$\"3%)*****4
\"3))oAF*$!3#)*****>3ZLn#F*7$$\"3x*****RPyXW%F*$\"3'******fc7UP\"F*7$$
!33+++!f:I9%F*$!3/+++s$4&z;F*7$$!3=+++_7dVKF*$\"3A+++,i4$G#F*7$$\"3k**
****eY([m%F*$!3#******H+C)z5F*7$$\"3'*******fZ%y1#FF$\"3#******RHLu*HF
*7$$!3q*****HPCWo%F*$!3-+++XR\"*[5F*7$$\"32+++7Jl,IF*$\"39+++ddD*R#F*7
$$\"3'******HSmeC%F*$!3/+++QHM%e\"F*7$$!3'******>+EbP%F*$\"3)******H9)
z^9F*7$$!3)******\\u]!zDF*$!3/+++F(3,d#F*7$$\"3e*****p%y10ZF*$\"3)****
**\\T1^,\"F*7$$!3$)*******pk/K)FF$!3))*****zFq\"eHF*7$$!3?+++97MCYF*$
\"33+++RI'39\"F*7$$\"35+++l$3Pc$F*$!32+++Q)zU5#F*7$$\"3))*****Ry\")H&R
F*$\"3*******>#H,P=F*7$$!3v*****H9&=IXF*$!3++++<_fp7F*7$$!3$******4oh
\\u\"F*$\"3$)*****frw8\"GF*7$$\"3#)*****RXgsr%F*$!3Q+++]lEX**FF7$$!3-+
++-=\"yz\"F*$\"3)******\\:j$*z#F*7$$!3B+++P\\*G_%F*$!3)******R8=*y7F*7
$$\"3%)*****H(y9tRF*$\"3/+++OPG@=F*7$$\"3=+++WGUNNF*$!3-+++`pQ@@F*7$$!
3J+++CE&)GYF*$\"3)******>fdU8\"F*7$$!3W+++5SNFxFF$!3%******4DcR'HF*7$$
\"3R+++sw`.ZF*$\"3++++jgl<5F*7$$!3.+++*)**\\AEF*$!3++++:8BaDF*7$$!3%)*
****\\gmVO%F*$\"3%******zgSQY\"F*7$$\"3/+++W8ufUF*$!3!******p#y(3d\"F*
7$$\"3A+++V!QP'HF*$\"3&******fykhT#F*7$$!3w*****zd$)oo%F*$!3)******Rg^
\\/\"F*7$$\"3%********>uhn#FF$\"3%******Ru*p&*HF*7$$\"3O+++dQbhYF*$!3+
+++/W(\\3\"F*7$$!3))*****H'Q)pF$F*$\"33+++UU&eE#F*7$$!3%******HY6l7%F*
$!3'******zZtSp\"F*7$$\"3e******HO#QX%F*$\"35+++dTRj8F*7$$\"3%******pr
f4A#F*$!3)******R!\\z(o#F*7$$!3#)*****4(o$Qr%F*$\"3*******\\P`.+\"F*7$
$\"3!*******QB'QG\"F*$!3'******zg:%**GF*7$$\"3w*****4QrUe%F*$\"3!*****
**=gm(>\"F*7$$!3!)*****z(pdmPF*$!3++++0#yH(>F*7$$!3'******\\?95y$F*$\"
3!******>v6I'>F*7$$\"3I+++X'*y!e%F*$!3-+++CBX-7F*7$$\"32+++Zb!zJ\"F*$
\"3y*****pm6R*GF*7$$!3R+++\"[(G9ZF*$!3O+++Si)e***FF7$$\"3-+++<p'=>#F*$
\"3'*******=)yjp#F*7$$\"33+++'yv#fWF*$!3)*******4K'pN\"F*7$$!3\")*****
H24k6%F*$\"3\"******p[)*Gq\"F*7$$!3%******R\")4oH$F*$!3-+++))oZbAF*7$$
\"3m******R&*\\fYF*$\"3!******z]Y\")3\"F*7$$\"3#)*******>*pTIFF$!31+++
cOW%*HF*7$$!3A+++\\EJ)o%F*$\"3,+++i6kU5F*7$$\"3()*****zT[1%HF*$!3;+++p
)*HECF*7$$\"3g*****4iOzE%F*$\"3#******pG\\Gc\"F*-%*AXESSTYLEG6#%%NONEG
-%'COLOURG6&%$RGBG$\"\"!F_[o$\"*++++\"!\")F`[o-%(SCALINGG6#%,CONSTRAIN
EDG-%+AXESLABELSG6$Q!6\"Fj[o-%%VIEWG6$%(DEFAULTGF_\\o" 1 2 0 1 10 0 2 
6 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "6 0 0" 0 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }