{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 } {PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 8 8 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 34 "Approximating the Area of a Circle" }}{PARA 19 "" 0 "" {TEXT -1 22 "Douglas Wilhelm Harder" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "Since the times of the ancient Gre eks, man has approximated the area of the unit circle (" }{XPPEDIT 18 0 "``=Pi" "6#/%!G%#PiG" }{TEXT -1 35 ") by finding the area of a regul ar " }{XPPEDIT 18 0 "N" "6#%\"NG" }{TEXT -1 65 "-gon inscribed in a ci rcle by using larger and larger values for " }{XPPEDIT 18 0 "N" "6#%\" NG" }{TEXT -1 80 ".\nThis maplet shows such a circle and allows the us er to decide on the value of " }{XPPEDIT 18 0 "N" "6#%\"NG" }{TEXT -1 5 " for " }{XPPEDIT 18 0 "N = 3,4,5,`...`,120;" "6'/%\"NG\"\"$\"\"%\" \"&%$...G\"$?\"" }{TEXT -1 34 ". I choose the upper limit to be " } {XPPEDIT 18 0 "120" "6#\"$?\"" }{TEXT -1 7 " as an " }{XPPEDIT 18 0 "1 14" "6#\"$9\"" }{TEXT -1 36 "-gon is the first inscribed regular " } {XPPEDIT 18 0 "N" "6#%\"NG" }{TEXT -1 36 "-gon which has an area great er than " }{XPPEDIT 18 0 "3.14" "6#-%&FloatG6$\"$9$!\"#" }{TEXT -1 1 " ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2809 "AreaOfCircle := modu le()\n option `Copyright (c) 2003 by Douglas Wilhelm Harder. All rig hts reserved.`;\n export Display;\n local\n circle, triangle, max imum, view,\n makeCircle, update,\n PL, BM, SL, BP, MML;\n\n ma keCircle := proc(n)\n [seq( evalf( [cos( i*2*Pi/n ), sin( i*2*Pi/n \+ )] ), i = 0..n )];\n end proc;\n\n circle := 'CURVES'( makeCircle( 1200 ), 'COLOUR'('RGB', 1, 0, 0) );\n triangle := 'CURVES'( makeCirc le( 3 ), 'COLOUR'('RGB', 0, 0, 0) );\n maximum := 120;\n view := \+ 'VIEW'( -1.05..1.05, -1.05..1.05 );\n\n Display := proc()\n option `Copyright (c) 2003 by Douglas Wilhelm Harder. All rights reserved.` ;\n local maplet, result;\n\n use Maplets:-Elements in\n ma plet := Maplet( Window( \"Area of a Circle\", [\n Plotter[PL]( \+ 'value' = 'PLOT'( circle, triangle, view ) ),\n [\n \" Area: \",\n MathMLViewer[MML](\n 'height' = 50,\n 'width' = 300,\n 'value' = MathML:-ExportPresen tation(\n 3/2*sin(2*Pi/3) = evalf[10]( 3/2*sin(2*Pi/3) ) \n )\n )\n ],\n [\n \"Degre e of polygon: \",\n Button[BM](\n \"-\",\n \+ Evaluate( 'function' = 'update( SL - 1 )' ),\n 'enabled ' = false\n ),\n Slider[SL](\n 0..maximum , 3,\n 'onchange' = Evaluate( 'function' = 'update( SL )' ) ,\n 'majorticks' = 20, 'minorticks' = 1\n ),\n \+ Button[BP](\n \"+\",\n Evaluate( 'function ' = 'update( SL + 1 )' )\n )\n ],\n Button( \"O K\", Shutdown([SL]) )\n ] ) );\n end use;\n\n result := Map lets:-Display( maplet );\n\n if result::['string'] then\n resu lt := parse( result[1] );\n\n 'PLOT'(\n circle,\n ' CURVES'( makeCircle( result ), 'COLOUR'('RGB', 0., 0., 0.) ),\n \+ view,\n TITLE( sprintf( \"A Regular %a-gon Inscribed In A Circ le\", result ) )\n );\n else\n NULL;\n end if;\n end \+ proc;\n\n update := proc(n)\n option `Copyright (c) 2003 by Dougla s Wilhelm Harder. All rights reserved.`;\n\n use Maplets:-Tools in \n Set( BP('enabled') = evalb( n < maximum ) );\n Set( BM('e nabled') = evalb( n > 3 ) );\n Set( SL = n );\n\n if n < 3 t hen\n procname( 3 );\n else\n Set( PL = 'PLOT'(\n \+ circle,\n 'CURVES'( makeCircle( n ), 'COLOUR'('RGB',0 .,0.,0.) ),\n view\n ) );\n\n if n = 4 then\n \+ Set( MML = MathML:-ExportPresentation( 2 ) );\n elif n \+ = 12 then\n Set( MML = MathML:-ExportPresentation( 3 ) );\n \+ else\n Set( MML = MathML:-ExportPresentation(\n \+ simplify( n/2*sin(2*Pi/n), 'radical' ) =\n evalf[10]( n /2*sin(2*Pi/n) )\n ) );\n end if; \n end if;\n \+ end use;\n end proc;\nend module:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "AreaOfCircle:-Display();" }}{PARA 13 "" 1 "" {GLPLOT2D 647 647 647 {PLOTDATA 2 "6&-%'CURVESG6$7]fo7$$\"\"\"\"\"!$F* F*7$$\"+AH')****!#5$\"+LQ'fB&!#77$$\"+%p^%****F/$\"+6%yr/\"!#67$$\"+Dj w)***F/$\"+JC%4#F87$$\"+]Kd'***F/$\"+J[p0ziF87$$\"+)yUo(**F/$\"+p! 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