{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
258 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 18 0 0 
0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 
0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 
0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" 
-1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{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 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 
11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 
-1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 0 "" }{TEXT 
257 0 "" }{TEXT 258 0 "" }{TEXT 259 36 "GRAPHING CURVES IN THREE DIMEN
SIONS " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 
"Of course, we always start with:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}{PARA 12 "" 
1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 71 "Suppose we are given a curve parametrically in thr
ee dimensional space:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 79 "                                    x = x(t),    y = y
(t),    z = z(t),    t = " }{TEXT 260 11 "lower limit" }{TEXT -1 8 " t
o t = " }{TEXT 261 11 "upper limit" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 81 "We can plot this curve us
ing the 'spacecurve' command.  The syntax is as follows:" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "              spac
ecurve( [ " }{TEXT 262 18 "x(t), y(t), z(t), " }{TEXT -1 4 "t = " }
{TEXT 263 11 "lower limit" }{TEXT -1 4 " .. " }{TEXT 264 11 "upper lim
it" }{TEXT -1 5 " ] );" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 84 "Note the use of square brackets inside the parenthes
es!  Try graphing the following:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 93 "                        x = cos 4t,      \+
   y = t,         z = sin 4t,     for t = 0 to 2 Pi." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 44 "spacecurve([cos(4*t),t,sin(4*t),t=0..2*Pi]);" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
140 "Nice picture, but it doesn't tell us much without the axes.  We c
an include a command for the axes to be drawn, but the command is incl
uded " }{TEXT 265 7 "outside" }{TEXT -1 25 " the square brackets and \+
" }{TEXT 266 6 "inside" }{TEXT -1 17 " the parentheses:" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "spacec
urve([cos(4*t),t,sin(4*t),t=0..2*Pi],axes=normal);" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 361 "Note two things:
  First, you cannot easily tell which axis is the x-axis, which is the
 y-axis, and which is the z-axis.  You may have to know a little bit o
f math (horrors!) to figure this out.  Second, the graph seems to be a
 little blocky.  We can make the graph a little more \"smooth\" by usi
ng the 'numpoints' option to control the resolution of the picture:" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 70 "spacecurve([cos(4*t),t,sin(4*t),t=0..2*Pi],axes=normal,numpoints
=100);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 115 "Much nicer!  If you want to get really fancy, you can co
ntrol the color, the thickness, and the scales on the axes:" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "
spacecurve([cos(4*t),t,sin(4*t),t=0..2*Pi],axes=normal,scaling= constr
ained,color=blue,thickness=2,numpoints=100);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }