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{SECT 0 {PARA 3 "" 0 "" {TEXT -1 19 "Module 2 : Geometry" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 23 "201 : Points & Pol
ygons" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 256 "" 0 "" {TEXT -1 17 "O B J E C T I V E" }}{PARA 0 "" 0 "
" {TEXT -1 55 "In this project we will learn some basic concepts......
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 11 " S \+
E T  U P" }}{PARA 0 "" 0 "" {TEXT -1 252 "In this project we will use \+
the following command packages. Type and execute this line before begi
ning the project below. If you re-enter the worksheet for this project
, be sure to re-execute this statement before jumping to any point in \+
the worksheet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 52 "restart; with(plots): with(geometry): with(stude
nt):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords ha
s been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 68 "Warning, the names \+
distance, midpoint and slope have been redefined\n" }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "_________________________
__________________________________________________________" }}{PARA 4 
"" 0 "" {TEXT -1 20 "A. Points & Segments" }}{PARA 0 "" 0 "" {TEXT -1 
83 "__________________________________________________________________
_________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 285 "Were going to define and graph points and line segments. Were \+
going to use this straight forward method, but it should be noted that
 Maple offers an alternative way of doing these same things in the geo
metry package using a slightly different syntax which we will use in l
ater modules." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 6 "POINTS" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 110 "We will define points by specifying coordinates using sq
uare brackets. We can also name points and graph them." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "A := [-
5,2];   B := [-1,7];   C:=[6,2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"AG7$!\"&\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG7$!\"\"\"\"(
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG7$\"\"'\"\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "plot( \{A, B, C\}, x = -8..8, y = -
4..12, style = point);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
{PLOTDATA 2 "6&-%'CURVESG6$7%7$$\"\"'\"\"!$\"\"#F*7$$!\"\"F*$\"\"(F*7$
$!\"&F*F+-%'COLOURG6&%$RGBG$\"#5F/$F*F*F;-%+AXESLABELSG6$Q\"x6\"Q\"yF@
-%&STYLEG6#%&POINTG-%%VIEWG6$;$!\")F*$\"\")F*;$!\"%F*$\"#7F*" 1 5 0 1 
10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 "We can also plot \+
points directly." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 61 "plot( \{[-3,2], [6,4] \}, x = -8..8, y= -4..12
, style = point);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 
2 "6&-%'CURVESG6$7$7$$\"\"'\"\"!$\"\"%F*7$$!\"$F*$\"\"#F*-%'COLOURG6&%
$RGBG$\"#5!\"\"$F*F*F9-%+AXESLABELSG6$Q\"x6\"Q\"yF>-%&STYLEG6#%&POINTG
-%%VIEWG6$;$!\")F*$\"\")F*;$!\"%F*$\"#7F*" 1 5 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "SEGMENTS" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "Just as easily we can def
ine line segments as two points enclosed in square brackets." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "seg := [[ -3, -2],[4,5]];" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$segG7$7$!\"$!\"#7$\"\"%\"\"&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "plot( seg, x = -5..5, thickn
ess = 4, color = gold, scaling = constrained);" }}{PARA 13 "" 1 "" 
{GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6#7$7$$!\"$\"\"!$!\"#F*
7$$\"\"%F*$\"\"&F*-%(SCALINGG6#%,CONSTRAINEDG-%*THICKNESSG6#F/-%+AXESL
ABELSG6$Q\"x6\"Q!6\"-%'COLOURG6&%$RGBG$\")+++!)!\")$\")AR!)\\FF$\")Vyg
>FF-%%VIEWG6$;$!\"&F*F0%(DEFAULTG" 1 2 0 1 10 4 2 6 1 4 1 1.000000 
45.000000 45.000000 0 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 95 "We can also several segments at the same \+
time directly by enclosing the segments in set braces." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "plot( \+
\{ [[-7,2],[6,2]], [[-4,10],[7,4]],[[-4,1],[5,8]] \}, x = -8..8, y = -
4..12, thickness = 4, color = [gold, khaki, plum], scaling = constrain
ed);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6)-%'CURVE
SG6$7$7$$!\"(\"\"!$\"\"#F*7$$\"\"'F*F+-%'COLOURG6&%$RGBG$\")+++!)!\")$
\")AR!)\\F6$\")Vyg>F6-F$6$7$7$$!\"%F*$\"#5F*7$$\"\"(F*$\"\"%F*-F16&F3$
\")THNiF6FJ$\")-\\DPF6-F$6$7$7$F?$\"\"\"F*7$$\"\"&F*$\"\")F*-F16&F3$\"
)1Zw\"*F6$\")PJ%y'F6Fen-%(SCALINGG6#%,CONSTRAINEDG-%*THICKNESSG6#FG-%+
AXESLABELSG6$Q\"x6\"Q\"yFdo-%%VIEWG6$;$F6F*FW;F?$\"#7F*" 1 2 0 1 10 4 
2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve \+
3" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 141 "T
o keep organized, the best way is to define points, as we did above, a
nd then define segments as the two points enclosed in square brackets.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "As yo
u can see, this creates a triangle!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "AB := [ A, B]; BC := [B, C]
; AC := [A, C];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ABG7$7$!\"&\"\"#
7$!\"\"\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#BCG7$7$!\"\"\"\"(7$
\"\"'\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ACG7$7$!\"&\"\"#7$\"
\"'F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "plot( \{AB, BC, AC
\}, x = -8..8, y = -4..12, thickness = 4, color = khaki, scaling = con
strained );" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6*-
%'CURVESG6#7$7$$!\"&\"\"!$\"\"#F*7$$!\"\"F*$\"\"(F*-F$6#7$F-7$$\"\"'F*
F+-F$6#7$F'F5-%(SCALINGG6#%,CONSTRAINEDG-%*THICKNESSG6#\"\"%-%+AXESLAB
ELSG6$Q\"x6\"Q\"yFG-%'COLOURG6&%$RGBG$\")THNi!\")FM$\")-\\DPFO-%%VIEWG
6$;$FOF*$\"\")F*;$!\"%F*$\"#7F*" 1 2 0 1 10 4 2 6 1 4 1 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" }}}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 8 "DISTANCE" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "Line segments h
ave length which is the same thing as the distance between the points.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "with( student):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "
distance( [1,5], [-7, 4] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sq
rtG6#\"#l\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "distance
( A, B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#\"#T\"\"\"" }}
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 67 "We can f
ind the distance between each pair of points defined above." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "dA
B := distance( A, B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dABG*$-%%s
qrtG6#\"#T\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "dBC := \+
distance( B, C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dBCG*$-%%sqrtG6
#\"#u\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "dAC := dista
nce( A, C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dACG\"#6" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "perimeter := dAB + dBC + dAC;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*perimeterG,(*$-%%sqrtG6#\"#T\"\"\"F
+*$-F(6#\"#uF+F+\"#6F+" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 83 "_________________________________________________________
__________________________" }}{PARA 4 "" 0 "" {TEXT -1 12 "B. Triangle
s" }}{PARA 0 "" 0 "" {TEXT -1 83 "____________________________________
_______________________________________________" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
273 "Above we defined a triangle by first defining three points, then \+
the three segments that join them. Here we will use a little more soph
isticated block of commands to do all of that, plus graph the triangle
 and automatically adjust the size of the graph to fit the triangle." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 19 "AUTOM
ETIC TRIANGLES" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 511 " tri_plot := proc( A, B, C)    local AB,BC,AC, \+
mx, Mx, my, My ;\n   AB:=[ A, B]; BC:=[ B, C ]; AC:=[ A, C ];\n   mx :
= min( A[1], B[1], C[1]);   \n   Mx := max( A[1], B[1], C[1]);\n   my \+
:= min( A[2], B[2], C[2]);  \n   My := max( A[2], B[2], C[2]);\n   plo
ts[display]( plot(\{AB, BC, AC \}, x = (mx-1)..(Mx+1), y = (my-1)..(My
+1), \n   thickness= 4, color = green, axes = boxed, scaling = constra
ined ),\n   plots[textplot](\{[A[1], A[2],\"A\"],[ B[1],B[2],\"B\"],[C
[1],C[2],\"C\"]\},\n   font=[HELVETICA,BOLD,14])   );      end:" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "To use th
is triangle graphing procedure, simply type its name and three points
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "Notic
e that it labels the points A, B, C in the same order you specified th
em." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "tri_plot( [-5,2], [-1,7],[6,2] );" }}{PARA 13 "" 1 "
" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6,-%'CURVESG6%7$7$$!\"&\"\"!$\"\"
#F*7$$!\"\"F*$\"\"(F*-%'COLOURG6&%$RGBG$F*F*$\"*++++\"!\")F6-%*THICKNE
SSG6#\"\"%-F$6%7$F-7$$\"\"'F*F+F2F:-F$6%7$F'FAF2F:-%%TEXTG6%F'Q\"A6\"-
%%FONTG6%%*HELVETICAG%%BOLDG\"#9-FH6%F-Q\"BFKFL-FH6%FAQ\"CFKFL-%*AXESS
TYLEG6#%$BOXG-%(SCALINGG6#%,CONSTRAINEDG-%+AXESLABELSG6$Q\"xFKQ\"yFK-%
%VIEWG6$;$!\"'F*F0;$\"\"\"F*$\"\")F*" 1 2 0 1 10 0 2 9 1 2 1 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve
 5" "Curve 6" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 70 "Here is another version of the triangle plot command we c
reated above." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 918 " tri_plot := proc( A, B, C) local AB,BC,AC,mx,M
x,my,My,x1,x2,x3,y1,y2,y3,dAB,dBC,dAC;\n  AB:=[ A, B ]; BC:=[ B, C ]; \+
AC:=[ A, C ]; \n  mx := min( A[1], B[1], C[1]);    Mx := max( A[1], B[
1], C[1]); \n  my := min( A[2], B[2], C[2]);    My := max( A[2], B[2],
 C[2]); \n  x1 := (A[1]+B[1])/2;  y1 := (A[2]+B[2])/2;\n  x2 := (B[1]+
C[1])/2;  y2 := (B[2]+C[2])/2;\n  x3 := (A[1]+C[1])/2;  y3 := (A[2]+C[
2])/2;\n  dAB := student[distance]( A, B ); \n  dBC := student[distanc
e]( B, C ); \n  dAC := student[distance]( A, C );\n  plots[display]( p
lot(\{AB, BC, AC \}, x = (mx-1)..(Mx+1), y = (my-1)..(My+1), \n      t
hickness= 4, color = coral, axes = boxed, scaling = constrained ),\n  \+
plots[textplot](\{[A[1],A[2],\"A\"],[B[1],B[2],\"B\"],[C[1],C[2],\"C\"
]\},\n      font=[HELVETICA,BOLD,14]),\n  plots[textplot](\{[x1,y1, co
nvert(evalf(dAB,5), string)], \n      [x2,y2 ,convert(evalf(dBC,5), st
ring)], [x3,y3 ,convert(evalf(dAC,5), string)]\}));\n  end:" }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 81 "We use this in \+
the same way. Lets use the command see what this new version does." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "The lengt
h of each edge is now labeled also!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "tri_plot( [-5,2],[-1,7],[6,
2] );" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6/-%'CURV
ESG6%7$7$$!\"&\"\"!$\"\"#F*7$$!\"\"F*$\"\"(F*-%'COLOURG6&%$RGBG$\"*+++
+\"!\")$\")AR!)\\F8$F*F*-%*THICKNESSG6#\"\"%-F$6%7$F-7$$\"\"'F*F+F2F<-
F$6%7$F'FCF2F<-%%TEXTG6%F'Q\"A6\"-%%FONTG6%%*HELVETICAG%%BOLDG\"#9-FJ6
%F-Q\"BFMFN-FJ6%FCQ\"CFMFN-FJ6$7$$!\"$F*$\"+++++X!\"*Q'6.4031FM-FJ6$7$
$\"+++++DF[oFinQ'8.6023FM-FJ6$7$$\"+++++]!#5F+Q$11.FM-%*AXESSTYLEG6#%$
BOXG-%(SCALINGG6#%,CONSTRAINEDG-%+AXESLABELSG6$Q\"xFMQ\"yFM-%%VIEWG6$;
$!\"'F*F0;$\"\"\"F*$\"\")F*" 1 2 0 1 10 0 2 9 1 2 1 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve
 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" }}}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 83 "_____
______________________________________________________________________
________" }}{PARA 4 "" 0 "" {TEXT -1 11 "C. Polygons" }}{PARA 0 "" 0 "
" {TEXT -1 83 "_______________________________________________________
____________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 115 "Triangles are polygons of three sides. We can use M
aple's built - in capabilities to display more general polygons." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
66 "polygonplot( [ [-2,0],[-3,12],[4,8],[7,1],[3,-3] ], color = gold);
" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%)POLYGONSG
6#7'7$$!\"#\"\"!$F*F*7$$!\"$F*$\"#7F*7$$\"\"%F*$\"\")F*7$$\"\"(F*$\"\"
\"F*7$$\"\"$F*F--%'COLOURG6&%$RGBG$\")+++!)!\")$\")AR!)\\FD$\")Vyg>FD
" 1 2 0 1 10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 14 "QUADR
ILATERALS" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
183 "Quadrilaterals, which are four sided polygons, come in many varie
ties : squares, rectangles, parallelograms, trapezoids, rhombuses and \+
otehr shapes which do not have any special name." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "polygonplot(
 [ [-7,-4],[-4,11],[7,11],[4,-4] ], color = gold);" }}{PARA 13 "" 1 "
" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%)POLYGONSG6#7&7$$!\"(\"\"!$!
\"%F*7$F+$\"#6F*7$$\"\"(F*F.7$$\"\"%F*F+-%'COLOURG6&%$RGBG$\")+++!)!\"
)$\")AR!)\\F<$\")Vyg>F<" 1 2 0 1 10 0 2 6 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "
polygonplot( [ [-5,-1],[-2,11],[7,-1],[1,-3] ], color = gold, scaling \+
= constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 
"6%-%)POLYGONSG6#7&7$$!\"&\"\"!$!\"\"F*7$$!\"#F*$\"#6F*7$$\"\"(F*F+7$$
\"\"\"F*$!\"$F*-%(SCALINGG6#%,CONSTRAINEDG-%'COLOURG6&%$RGBG$\")+++!)!
\")$\")AR!)\\FD$\")Vyg>FD" 1 2 0 1 10 0 2 6 1 4 1 1.000000 45.000000 
45.000000 0 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 
"" 0 "" {TEXT -1 14 "OTHER POLYGONS" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 42 "There are much more general polygons als
o." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 86 "polygonplot( [ [-20,-3],[-17,6],[-10,8],[-2,15],[5,3]
,[10,3],[13,-7] ], color = gold);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 
300 300 {PLOTDATA 2 "6$-%)POLYGONSG6#7)7$$!#?\"\"!$!\"$F*7$$!#<F*$\"\"
'F*7$$!#5F*$\"\")F*7$$!\"#F*$\"#:F*7$$\"\"&F*$\"\"$F*7$$\"#5F*F?7$$\"#
8F*$!\"(F*-%'COLOURG6&%$RGBG$\")+++!)!\")$\")AR!)\\FO$\")Vyg>FO" 1 2 
0 1 10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }