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{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 14 "1. The middle " }{TEXT 
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{TEXT -1 69 ") is obtained by starting with the unit interval, removin
g a fraction" }{TEXT 258 2 " t" }{TEXT -1 44 " from the middle of it, \+
removing a fraction " }{TEXT 259 1 "t" }{TEXT -1 99 " from the middle \+
of what's left, and so forth.  For example, here is the first level of
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261 59 "while here is the first level of the middle 0.1 Cantor set:" }
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{TEXT -1 109 "Draw the first three levels of the middle 0.9 and the mi
ddle 0.1 Cantor sets.  What are their box dimensions?" }}}{EXCHG 
{PARA 256 "" 0 "" {TEXT -1 86 "2. What is the box dimension of the Sie
rpinski carpet?  Here are the first few levels." }}}{EXCHG {PARA 0 "" 
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}{EXCHG {PARA 0 "" 0 "" {TEXT 287 40 "3. Write a Maple routine that dr
aws the " }{TEXT 288 1 "n" }{TEXT 289 59 "'th level of the Sierpinski \+
carpet (see previous question)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 
11 "4. Suppose " }{TEXT 263 1 "A" }{TEXT 265 1 "1" }{TEXT 266 3 ", A" 
}{TEXT 267 1 "2" }{TEXT 268 8 ", ..., A" }{TEXT 269 1 "n" }{TEXT 264 
38 " is a finite collection of subsets of " }{TEXT 270 1 "R" }{TEXT 
272 1 "m" }{TEXT 271 46 " (this m should be a superscript, sorry). Let
 " }{TEXT 273 1 "A" }{TEXT 274 17 " be the union of " }{TEXT 275 1 "A
" }{TEXT 277 1 "1" }{TEXT 278 8 ", ..., A" }{TEXT 276 1 "n" }{TEXT 
279 35 ".  Prove that the box dimension of " }{TEXT 280 1 "A" }{TEXT 
281 41 " is the maximum of the box dimensions of " }{TEXT 282 1 "A" }
{TEXT 284 1 "1" }{TEXT 285 8 ", ..., A" }{TEXT 286 1 "n" }{TEXT 283 1 
"." }}}}{MARK "6 0 10" 12 }{VIEWOPTS 1 1 0 1 1 1803 }