\mnb150ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\froman\fprq2 Times New Roman;}{\f4\fswiss\fprq2 Arial;}{\f5\fnil Courier Neu;}{\f6\fmodern\fprq1 Courier New;}{\f7\fmodern Courier New;}{\f8\froman Times New Roman;}{\f9\froman\fprq2 Symbol;}{\f10\froman\fcharset1 Times New Roman;}{\f11\froman\fprq2\fcharset2 Symbol;}} {\colortbl\red0\green0\blue0;\red255\green0\blue0;\red0\green0\blue255;\red0\green128\blue0;\red0\green255\blue0;} \deflang1031\pard\ri4\plain\f4\fs40\cf0\b Einschachtelung von PI durch innere und \'e4u\'dfere n-Ecke \par \plain\f4\fs24\cf0 Prof. Dr. D\'f6rte Haftendorn, Jan 05 www.uni-lueneburg.de/mathe-lehramt\plain\f6\fs32\cf1\b \par \plain\f4\fs24\cf0\b Diese Datei ist f\'fcr die Dreiecks-Familie durchgef\'fchrt, funktioniert aber auch f\'fcr die Vierecksfamilie. \par n und die Startseiten f\'fcr innen und au\'dfen sind dann neu einzutragen. \par Danach reicht "Notebook->Evaluiere->alle Eingaben" \par \par \plain\f4\fs32\cf0\b Version 3-Eck \par \plain\f4\fs24\cf0\b Es geht um n-Ecke innen und aussen am Einheitskreis. \par Tr\'e4gerfunktion der rekursiven Formel f\'fcr die Seitenl\'e4nge des inneren 2n-Ecks, \par wenn s die Seitenl\'e4nge des n-Ecks ist. \plain\f4\fs24\cf0 \plain\f6\fs32\cf1\b \par \plain\f4\fs24\cf0\b Diese Formel ist durch geometrische \'dcberlegungen hergeleitet.\plain\f6\fs32\cf1\b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}f:=s->sqrt(2-sqrt(4-s^2)) \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw3903\pich1369\picwgoal2212\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\ri4\plain\f4\fs32\cf0\b Start mit dem Quadrat im Kreis\plain\f6\fs32\cf1\b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}n:=3: \par \pard\ri4\plain\f4\fs28\cf0 Die L\'e4nge der Startseite muss man geometrisch \'fcberlegen und hier eintragen. \par Beim Start mit dem Dreieck \plain\f6\fs32\cf1\b s0:=sqrt(2) \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}s0:=sqrt(3); \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw1030\pich907\picwgoal583\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}(f@@k)(s) $k=1..4 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw18383\pich1743\picwgoal10421\pichgoal988 010009000003AC0A000008001C0000000000050000000B0200000000050000000C02CF06CF4703 0000001E00030000001E00050000000C02DC03B628050000000B020000000008000000FA020000 0000000000000000040000002D0100001C000000FB0238FF000000000000900100000001070000 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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}(f@@k)(s0) $k=1..4 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw10012\pich1623\picwgoal5676\pichgoal920 0100090000037605000007001C0000000000050000000B0200000000050000000C0257061C2703 0000001E00030000001E00050000000C0298032C16050000000B020000000008000000FA020000 0000000000000000040000002D0100001C000000FB0238FF000000000000900100000001070000 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010200040000002D010300040000002D010400040000002D010300040000002D01020004000000 2D010300040000002D010200040000002D010300040000002D010200040000002D010300040000 002D010200040000002D010300040000002D010200040000002D010300040000002D0102000400 00002D010400040000002D010300040000002D010200040000002D010300040000002D01020004 0000002D010300040000002D010200040000002D010400040000002D010300040000002D010200 040000002D010300040000002D010200040000002D010300040000002D010400040000002D0103 00040000002D010200040000002D010300040000002D010200040000002D010300040000002D01 0400040000002D010200040000002D0104000500000009020000FF00040000002D010200070000 0021050100310276026400040000002D01040007000000210501002C027602E900040000002D01 0200040000002D010300040000002D010200040000002D010300040000002D010200040000002D 0103000700000021050100710216017A010700000021050100C50216016A020700000021050100 C5021601FA020700000021050100C50216018A030700000021050100C50216011A040700000021 050100C5021601AA040700000021050100C5021601DC04040000002D0102000700000021050100 320276026A02040000002D01040007000000210501002D0276022B03040000002D010200040000 002D010300040000002D010200040000002D010300040000002D010200040000002D0103000700 00002105010070026F01EC030700000021050100C5026F01DC04040000002D0102000700000021 05010033027602DC04040000002D01040007000000210501002C0276026C05040000002D010200 040000002D010300040000002D010200040000002D010300040000002D010200040000002D0103 0007000000210501007202BD00FD050700000021050100C502BD00ED060700000021050100C502 BD007D070700000021050100C502BD000D080700000021050100C502BD009D0807000000210501 00C502BD002D090700000021050100C502BD00BD090700000021050100C502BD004D0A07000000 21050100C502BD00DD0A0700000021050100C502BD006D0B0700000021050100C502BD00D10B04 0000002D010200070000002105010032027602ED06040000002D01040007000000210501002D02 7602AE07040000002D010200040000002D010300040000002D010200040000002D010300040000 002D010200040000002D0103000700000021050100710216016F080700000021050100C5021601 5F090700000021050100C5021601EF090700000021050100C50216017F0A0700000021050100C5 0216010F0B0700000021050100C50216019F0B0700000021050100C5021601D10B040000002D01 0200040000002D010300040000002D010200040000002D010300040000002D010200040000002D 010300070000002105010070026F015F090700000021050100C5026F014F0A040000002D010200 0700000021050100330276024F0A040000002D01040007000000210501002B0276021B0B040000 002D010200070000002105010032027602DC0B040000002D01040007000000210501002C027602 610C040000002D010200040000002D010300040000002D010200040000002D010300040000002D 010200040000002D010300070000002105010073026400F20C0700000021050100C5026400E20D 0700000021050100C5026400720E0700000021050100C5026400020F0700000021050100C50264 00920F0700000021050100C502640022100700000021050100C5026400B2100700000021050100 C502640042110700000021050100C5026400D2110700000021050100C502640062120700000021 050100C5026400F2120700000021050100C502640082130700000021050100C502640012140700 000021050100C5026400A2140700000021050100C502640032150700000021050100C502640038 15040000002D010200070000002105010032027602E20D040000002D0104000700000021050100 2D027602A30E040000002D010200040000002D010300040000002D010200040000002D01030004 0000002D010200040000002D01030007000000210501007202BD00640F0700000021050100C502 BD0054100700000021050100C502BD00E4100700000021050100C502BD00741107000000210501 00C502BD0004120700000021050100C502BD0094120700000021050100C502BD00241307000000 21050100C502BD00B4130700000021050100C502BD0044140700000021050100C502BD00D41407 00000021050100C502BD003815040000002D010200040000002D010300040000002D0102000400 00002D010300040000002D010200040000002D0103000700000021050100710216015410070000 0021050100C502160144110700000021050100C5021601D4110700000021050100C50216016412 0700000021050100C5021601F4120700000021050100C502160184130700000021050100C50216 01B613040000002D010200040000002D010300040000002D010200040000002D01030004000000 2D010200040000002D010300070000002105010070026F0144110700000021050100C5026F0134 12040000002D0102000700000021050100330276023412040000002D0104000700000021050100 2B0276020013040000002D010200070000002105010032027602C113040000002D010400070000 00210501002B0276028214040000002D010200070000002105010032027602431508000000FA02 00000000000000000000040000002D0105001C000000FB021000070000000000BC020000000001 02022253797374656D00774000000066120A31B7C5C477C0C5C47720C0C7770000300004000000 2D010600040000002701FFFF04000000F001000004000000F001010004000000F0010200040000 00F001030004000000F0010400040000002701FFFF030000000000 }\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}n*2^k $ k=1..4 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw2762\pich836\picwgoal1565\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}n*2^k*(f@@k)(s0) $k=1..4 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw12250\pich1623\picwgoal6944\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\li600\ri1\fi-300\plain\f6\fs32\cf1\b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}float(n*2^k*(f@@k)(s0)) $k=1..4 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw9100\pich836\picwgoal5159\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\ri4\plain\f6\fs32\cf2\b \par \plain\f4\fs32\cf0\b G\'fcnstig ist, nur den halben Umfang zu nehmen:\plain\f6\fs32\cf1\b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}innen:=float(n/2*2^k*(f@@k)(s0)) $k=1..8 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw19980\pich836\picwgoal11327\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}n*2^k $k=1..8 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw6366\pich836\picwgoal3609\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}DIGITS:=80:float(PI); DIGITS:=10: \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw19004\pich836\picwgoal10773\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\ri4\plain\f4\fs32\cf0\b Au\'dfen-n-Ecke, \plain\f4\fs24\cf0 rekursive Formel (Tr\'e4gerfunktion). \par Berechnet die Seite des umbeschriebenen 2n-Ecks aus der Seite t des n-Ecks. \par Diese Formel ist "von Hand" mit geometrischen \'dcberlegungen hergeleitet.\plain\f6\fs32\cf1\b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}g:=t->2*sqrt((sqrt(4+t^2)-2)/(sqrt(4+t^2)+2)) \par \pard\li600\ri1\fi-300\plain\f6\fs32\cf1\b \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw4371\pich2057\picwgoal2478\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\ri4\plain\f4\fs28\cf0 Die L\'e4nge der Startseite muss man geometrisch \'fcberlegen und hier eintragen. \par Beim Start mit dem Dreieck \plain\f6\fs32\cf1\b t0:=2 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}t0:=2*sqrt(3): \par {\pntext\f1\'b7\tab}(g@@k)(t) $k=1..3 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw16018\pich5761\picwgoal9081\pichgoal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{\pntext\f1\'b7\tab}aussen:=float(n/2*2^k*(g@@k)(t0)) $k=1..8 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw21153\pich836\picwgoal11992\pichgoal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00002105010034024301C51E0700000021050100310243014A1F070000002105010038024301CF 1F0700000021050100370243015420070000002105010033024301D92007000000210501003002 43015E21070000002105010035024301E321040000002D01030007000000210501002C02430168 22040000002D010200070000002105010033024301F92207000000210501002E0243017E230700 00002105010031024301C1230700000021050100340243014624070000002105010031024301CB 240700000021050100360243015025070000002105010036024301D52507000000210501003202 43015A26070000002105010037024301DF26070000002105010034024301642707000000210501 0037024301E927040000002D01030007000000210501002C0243016E28040000002D0102000700 00002105010033024301FF2807000000210501002E0243018429070000002105010031024301C7 290700000021050100340243014C2A070000002105010031024301D12A07000000210501003602 4301562B070000002105010031024301DB2B070000002105010030024301602C07000000210501 0031024301E52C0700000021050100370243016A2D070000002105010037024301EF2D08000000 FA0200000000000000000000040000002D0104001C000000FB021000070000000000BC02000000 000102022253797374656D00774000000000160ABFB7C5C477C0C5C47720C0C777000030000400 00002D010500040000002701FFFF04000000F001000004000000F001010004000000F001020004 000000F0010300040000002701FFFF030000000000 }\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\ri4\plain\f4\fs32\cf0\b Anzeige der Fehlerspanne\plain\f6\fs32\cf1\b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}(op(aussen,k)-op(innen,k) )$k=1..8 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw27017\pich836\picwgoal15316\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}n*2^k $ k=1..8 \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw6366\pich836\picwgoal3609\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect \par \pard\ri4\plain\f4\fs32\cf0\b Also hat man beim beim letzen Vieleck PI zwischen \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}op(innen,8);op(aussen,8) \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw2817\pich836\picwgoal1597\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw2817\pich836\picwgoal1597\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \par \pard\ri4\plain\f4\fs32\cf0\b Fehler: \plain\f6\fs32\cf1\b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab}float(PI)-op(innen,8);op(aussen,8)-float(PI); \par \pard\li50\ri6\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw4225\pich836\picwgoal2395\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \pard\li50\ri2\plain\f6\fs32\cf2\b\protect {\pict\wmetafile8\picw3990\pich836\picwgoal2262\pichgoal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}\plain\f6\fs32\cf2\b\protect \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs32\cf1\b {\pntext\f1\'b7\tab} \par }