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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 49 "High School Modul
es > Algebra by Gregory A. Moore" }}{PARA 3 "" 0 "" {TEXT -1 4 "    " 
}{TEXT 256 33 "Intervals > Cantor Set [optional]" }}{PARA 0 "" 0 "" 
{TEXT -1 74 "\nThe first few steps in the iterative process of creatin
g the Cantor set.\n" }}{PARA 0 "" 0 "" {TEXT 258 153 "[Directions : Ex
ecute the Code Resource section first. Although there will be no outpu
t immediately, these definitions are used later in this worksheet.]" }
{TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 4 "Code" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "restart:  with(plottools): with(plo
ts):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 586 "intfin1 := proc( a
, b )\n#        description \"plot a finite interval on a number line
\";\nlocal r, M, v1, v2, wid, bar, Axesplot, leftpt, rightpt, pt_color
,\n      leftend, rightend, LT, RT, textpos;\n \nr := b-a ;\nM := eval
f( 1.2 * (b-a) );\nv1 := [a, 0];\nv2 := [b, 0];\nwid := .1 ;\n\nbar :=
 arrow( v1, v2,\n    shape = double_arrow, color = green , difference \+
= true,\n    width = wid, head_width = 0, head_length = 0):\n\ntextpos
 := wid ;\nLT := textplot( [a, textpos, a] ):\nRT := textplot( [b, tex
tpos, b] ):\nif (M > .08) \n    then display(  bar, LT, RT );\n    els
e display( bar);\nfi;\n\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 694 "cantorint := proc( a, b, n  )\n#        plot the nth
 step in Cantor set\";\nlocal    left, right, len, A, Axisplot;\ngloba
l   count, finished;\n\nfinished := false;\n\nleft := a; right := b; l
en := (b-a)/3;\n\n\nif(n = 1) \n    then count :=count + 1; \n        \+
 A||count := intfin1( a, b):\n         print( a, b);\n         finishe
d := true;\n    else\n        cantorint( a, a + len, n-1);  \n        \+
cantorint( b - len, b, n-1); \n    fi;\n\nif( finished) \n    then \n \+
     Axisplot := plot( 0, x = a..b , scaling = constrained, \n        \+
             axes = none, thickness = 2, color = black,\n             \+
        tickmarks = [1,1] ):\n      display( \{Axisplot, seq( A||i, i \+
= 1..(2^(n-1) ))\} );\nfi;\nend proc:\n\n\n\n\n" }}}{PARA 3 "" 0 "" 
{TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 5 "Steps" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "count := 0:\ncantorint( 0, 1, 1);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "count := 0:\ncantorint( 0
, 1, 2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "count := 0:\nca
ntorint( 0, 1, 3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "count
 := 0:\ncantorint( 0, 1, 4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 32 "count := 0:\ncantorint( 0, 1, 5);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "count := 0:\ncantorint( 0, 1, 6);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}}{PARA 0 "" 0 "" {TEXT 259 35 "\n         \251 2002 Waterloo M
aple Inc" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 1" 31 }
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