{VERSION 3 0 "SUN SPARC SOLARIS" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 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 "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "" 3 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 30 "Reparametrization of a c ircle." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "with(plots):with(plottools): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "Q:=k->disk([cos(2*Pi*k ^2/400)+1,sin(2*Pi*k^2/400)+1],0.04,color=green):Q1:=k->disk([2*Pi*k^2 /400,0],0.04,color=green):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "P:=k->disk([cos(2*Pi*k/20)+1,sin(2*Pi*k/20)+1],0.04,color=blue):P 1:=k->disk([2*Pi*k/20,0],0.04,color=blue):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 35 "circle1:=circle([1,1],1,color=red):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 129 "There are two blue points running: One o n the real axis representing t and another on the circle corresponding to (cos(t),sin(t))" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "disp lay([circle1,seq(display(\{circle1,P(k),P1(k)\}),k=1..20)],insequence= true,scaling=constrained);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 179 "There ar e four points running: Two blue points as above and a green point on t he real axis representing t^2 and another green point on the circle re presenting (cos(t^2),sin(t^2))" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "display([circle1,seq(display(\{circle1,P(sqrt(k)),Q(k),P1(sqr t(k)),Q1(k)\}),k=1..20)],insequence=true,scaling=constrained);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 112 "R:=k->disk([cos(4*Pi*k/40)+1,sin(4*Pi*k/40)+1],0.0 4,color=yellow):\nR1:=k->disk([4*Pi*k/40,0],0.04,color=yellow):" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "Here the blue points are as above \+ and the two yellow points represent 2t and (cos(2t),sin(2t))" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "display([circle1,seq(displa y(\{circle1,P(k/2),R(k),R1(k),P1(k/2)\}),k=1..20)],insequence=true,sca ling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "15" 0 }{VIEWOPTS 1 1 0 1 1 1803 }