{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 "Highlight" -1 256 "" 0 0 0 255 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "Define" -1 257 "Times" 1 12 0 0 0 1 1 1 2 0 0 2 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 "" 0 256 1 {CSTYLE "" -1 -1 "" 1 14 116 114 97 0 0 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 256 "" 0 "" {TEXT -1 14 "Art Gallery II" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart; with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "a:=8: b:=3: c:=1: d:=0: m:=9: n:=1:\nr := \+ theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\npolarplot(r, 0..2*Pi) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "a:=0: b:=8: c:=0: d:= 4: m:=6: n:=4:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\n polarplot(r, 0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 " a:=0: b:=8: c:=0: d:=4: m:=7: n:=4:\nr := theta -> (a+b*cos(m*theta))* (c+d*sin(n*theta)):\npolarplot(r, 0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "a:=1: b:=0: c:=1: d:=20: m:=1: n:=1:\nr := theta \+ -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\npolarplot(r, 0..2*Pi);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "a:=3: b:=1: c:=1: d:=0: m:= 2: n:=1:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\npolarp lot(r, 0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "a:=0: \+ b:=5: c:=0: d:=0.5: m:=.1: n:=15:\nr := theta -> (a+b*cos(m*theta))*(c +d*sin(n*theta)):\npolarplot(r, 0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 111 "a:=0: b:=1: c:=0: d:=1: m:=1: n:=2:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\npolarplot(r, 0..2*Pi);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "a:=2: b:=3: c:=1: d:=0: m:= 2: n:=1:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\npolarp lot(r, 0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "a:=1: \+ b:=0: c:=-4: d:=20: m:=1: n:=50:\nr := theta -> (a+b*cos(m*theta))*(c+ d*sin(n*theta)):\npolarplot(r, 0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "a:=0: b:=9: c:=0: d:=.45632: m:=1: n:=7:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\npolarplot(r, 0..2*Pi);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "a:=1: b:=0: c:=17: d:=3: m :=1: n:=-10:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\npo larplot(r, 0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "a: =25: b:=10: c:=1: d:=0: m:=22: n:=1:\nr := theta -> (a+b*cos(m*theta)) *(c+d*sin(n*theta)):\npolarplot(r, 0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "a:=0: b:=9: c:=0: d:=9: m:=2: n:=18:\nr := thet a -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\npolarplot(r, 0..2*Pi);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "a:=1: b:=8: c:=1: d:=6: m :=3: n:=9:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\npola rplot(r, 0..2*Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Interesting , but not as in assignment:" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "a:=0: b:=1: c:=0: d:=3: m:=14: n:=4:\nr := theta -> \+ (a+b*cos(m*theta))+(c+d*sin(n*theta)):\npolarplot(r, 0..2*Pi);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "a:=0: b:=23: c:=0: d:=13: m :=9: n:=7:\nr := theta -> (a+b*cos(m*theta))+(c+d*sin(n*theta)):\npola rplot(r, 0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "a:=0 : b:=1: c:=0: d:=1: m:=2: n:=1:\nr := theta -> (a+b*cos(m*theta))+(c+d *sin(n*theta)):\npolarplot(r, 0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "a:=0: b:=1: c:=0: d:=1: m:=1: n:=2:\nr := theta -> ( a+b*cos(m*theta))+(c+d*sin(n*theta)):\npolarplot(r, 0..2*Pi);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "And now some absolutely teriffic g raphs:" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 576 "a:=1: b:= 0: c:=1: d:=1/4: m:=1/2: n:=1/2:\nr := theta -> (a+b*cos(m*theta))*(c+ d*sin(n*theta)):\np1:=polarplot(r, -2*Pi..2*Pi, color=blue):\na:=1: b: =0: c:=1: d:=2: m:=1/2: n:=3:\nr := theta -> (a+b*cos(m*theta))*(c+d*s in(n*theta)):\np2:=polarplot(r, -2*Pi..2*Pi, color=black):\na:=1: b:=0 : c:=1: d:=(3/2): m:=1/2: n:=6:\nr := theta -> (a+b*cos(m*theta))*(c+d *sin(n*theta)):\np3:=polarplot(r, -2*Pi..2*Pi, color=navy):\na:=1: b:= 0: c:=2: d:=(1/4): m:=1/2: n:=1/4:\nr := theta -> (a+b*cos(m*theta))*( c+d*sin(n*theta)):\np4:=polarplot(r, -2*Pi..2*Pi, color=sienna):\ndisp lay(\{p1,p2,p3,p4\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 554 "a :=4: b:=1/4: c:=1: d:=0: m:=1/8: n:=1/2:\nr := theta -> (a+b*cos(m*the ta))*(c+d*sin(n*theta)):\np1:=polarplot(r, -Pi..Pi, color=blue):\na:=0 : b:=3: c:=1: d:=0: m:=6: n:=1/2:\nr := theta -> (a+b*cos(m*theta))*(c +d*sin(n*theta)):\np2:=polarplot(r, -Pi..Pi, color=black):\na:=1: b:=1 /8: c:=1: d:=0: m:=1/8: n:=1/2:\nr := theta -> (a+b*cos(m*theta))*(c+d *sin(n*theta)):\np3:=polarplot(r, -Pi..Pi, color=navy):\na:=5: b:=2: c :=1: d:=0: m:=4: n:=1/2:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n* theta)):\np4:=polarplot(r, -Pi..Pi, color=sienna):\ndisplay(\{p1,p2,p3 ,p4\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 552 "a:=0: b:=2: c:= 0: d:=3: m:=4: n:=2:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*thet a)):\np1:=polarplot(r, -Pi..Pi, color=blue):\na:=0: b:=3: c:=0: d:=3: \+ m:=1/2: n:=1/2:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)): \np2:=polarplot(r, -Pi..Pi, color=black):\na:=0: b:=3/2: c:=0: d:=2: m :=5: n:=3:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\np3:= polarplot(r, -Pi..Pi, color=navy):\na:=0: b:=3: c:=0: d:=3: m:=1/3: n: =1/3:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\np4:=polar plot(r, -4*Pi..4*Pi, color=sienna):\ndisplay(\{p1,p2,p3,p4\});" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 564 "a:=1: b:=0: c:=1: d:=0: m:= 1/2: n:=1/2:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\np1 :=polarplot(r, -2*Pi..2*Pi, color=blue):\na:=1: b:=0: c:=1: d:=1: m:=1 /2: n:=2:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\np2:=p olarplot(r, -2*Pi..2*Pi, color=black):\na:=1: b:=0: c:=3: d:=2: m:=1/2 : n:=3:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\np3:=pol arplot(r, -2*Pi..2*Pi, color=red):\na:=1: b:=0: c:=1: d:=2: m:=1/2: n: =4:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\np4:=polarpl ot(r, -2*Pi..2*Pi, color=magenta):\ndisplay(\{p1,p2,p3,p4\});" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 550 "a:=2: b:=2: c:=1: d:=0: m:= 1/2: n:=1/2:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\np1 :=polarplot(r, -Pi..Pi, color=blue):\na:=1: b:=3: c:=1: d:=0: m:=4: n: =1/2:\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\np2:=polar plot(r, -Pi..Pi, color=black):\na:=1: b:=4: c:=1: d:=0: m:=1/3: n:=1/2 :\nr := theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\np3:=polarplot (r, -Pi..Pi, color=red):\na:=4: b:=1: c:=1: d:=0: m:=3: n:=1/2:\nr := \+ theta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\np4:=polarplot(r, -Pi. .Pi, color=magenta):\ndisplay(\{p1,p2,p3,p4\});" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 548 "a:=0: b:=1: c:=0: d:=1: m:=4: n:=2:\nr := the ta -> (a+b*cos(m*theta))*(c+d*sin(n*theta)):\np1:=polarplot(r, -Pi..Pi , color=blue):\na:=0: b:=2: c:=0: d:=2: m:=2: n:=4:\nr := theta -> (a+ b*cos(m*theta))*(c+d*sin(n*theta)):\np2:=polarplot(r, -Pi..Pi, color=b lack):\na:=0: b:=1: c:=0: d:=3: m:=1/4: n:=3:\nr := theta -> (a+b*cos( m*theta))*(c+d*sin(n*theta)):\np3:=polarplot(r, -Pi..Pi, color=red):\n a:=0: b:=1: c:=0: d:=2: m:=1/2: n:=1/3:\nr := theta -> (a+b*cos(m*thet a))*(c+d*sin(n*theta)):\np4:=polarplot(r, -8*Pi..8*Pi, color=magenta): \ndisplay(\{p1,p2,p3,p4\});" }}}}{MARK "26" 0 }{VIEWOPTS 1 1 0 1 1 1803 }