\mnb150ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fswiss\fprq2 Arial;}{\f4\fmodern\fprq1 Courier New;}{\f5\fmodern\fprq2 Courier New;}{\f6\fswiss\fprq2 Helvetica;}} {\colortbl\red0\green0\blue0;\red0\green128\blue0;\red0\green0\blue255;\red255\green0\blue0;} \deflang1031\pard\ri4\plain\f4\fs20\cf0\b _________________________________________________________________________________ \par \par \plain\f4\fs20\cf0 Inhalt....: Abbildung regelm\'e4\'dfiger Figuren \par Kategorie.: Arbeitsblatt \par Mathematik: Geometrie R^2, Lineare Algebra \par MuPAD.....: 3.0.0 \par Datum.....: 2003-09-22 \par Autoren...: Kai Gehrs\plain\lang2057\f4\fs20\cf0 \plain\f5\fs20 \plain\lang2057\f4\fs20\cf0 \par Funktionen: matrix, plot, plot::Point, plot::Pointlist, linalg::nrows \par Funktionen: linalg::col\plain\f4\fs20\cf0 \par \plain\f4\fs20\cf0\b _________________________________________________________________________________ \par \plain\f3\fs36\cf0\b \par \plain\f3\fs40\cf0\b Abbildung regelm\'e4\'dfiger Figuren \plain\f3\fs36\cf0\b \par \plain\f3\fs36\cf1\b \par \plain\f3\fs24\cf1 In diesem Arbeitsblatt stellen wir eine Funktion \plain\f4\fs24\cf3 matrix2polygon\plain\f3\fs24\cf1 vor, mit deren Hilfe sich \par \'fcber Matrizen definierte regelm\'e4\'dfige Figuren in MuPAD darstellen lassen. \par \par \plain\f3\fs28\cf0 In der ebenen Geometrie ist es oft hilfreich eine Funktion zur Hand zu haben, \par mit deren Hilfe sich schnell \'fcber eine entsprechende Matrix regelm\'e4\'dfige \par Figuren im Zweidimensionalen zeichnen lassen. Dreiecke z.B. lassen sich \par leicht in Form einer Matrix "codieren": Ist z.B. ein Dreieck durch die Lage \par der Eckpunkte A = (0|0), B = (3|4) und C = (2|1) im Koordinatensystem \par gegeben, so w\'fcrde man gerne auf schnellem und unkompliziertem Wege \par eine Darstellung der Form \par \pard\li1500\ri4\plain\f3\fs28\cf0 {\object\objemb{\*\objclass VCam.Graphics.3}{\*\objname Object1}\objw6809\objh4529\objscalex96\objscaley96{\*\objdata 01050000 02000000 10000000 5643616D2E47726170686963732E3300 00000000 00000000 001E0000 D0CF11E0A1B11AE1000000000000000000000000000000003E000300FEFF090006000000000000 0000000000010000000100000000000000001000000200000001000000FEFFFFFF000000000000 0000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFDFFFFFF07000000FEFFFFFF04000000050000000600000008000000FEFFFFFF0900 00000A0000000B0000000C0000000D000000FEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFF52006F006F007400200045006E00740072007900000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000016000500 FFFFFFFFFFFFFFFF02000000C04907ADB4BBD01193DF0000C059B7AD0000000000000000000000 00E0608CDA1747C50103000000001300000000000001004F006C00650000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000A000201FFFFFFFFFFFFFFFFFFFFFFFF00000000000000000000000000000000 0000000000000000000000000000000000000000000000001400000000000000010043006F006D 0070004F0062006A00000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000120002010100000004000000FFFFFFFF0000000000 000000000000000000000000000000000000000000000000000000000000000100000068000000 0000000043006F006E00740065006E007400730000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000012000200FFFFFFFFFFFF FFFFFFFFFFFF000000000000000000000000000000000000000000000000000000000000000000 000000030000005F05000000000000FEFFFFFF02000000FEFFFFFF040000000500000006000000 0700000008000000090000000A0000000B0000000C0000000D0000000E0000000F000000100000 001100000012000000130000001400000015000000160000001700000018000000FEFFFFFF1A00 00001B0000001C0000001D0000001E0000001F0000002000000021000000220000002300000024 00000025000000260000002700000028000000290000002A0000002B0000002C0000002D000000 2E0000002F00000030000000310000003200000033000000340000003500000036000000370000 0038000000390000003A0000003B0000003C0000003D0000003E0000003F000000400000004100 000042000000430000004400000045000000460000004700000048000000490000004A000000FE FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF01000002000000000000000000000000000000 00C80314000300000001000100020044005C007B005B0000000000000000000000000000000000 0000300030000100FEFF030A0000FFFFFFFFC04907ADB4BBD01193DF0000C059B7AD1000000056 43616D2050726F2047726166696B00100000005643616D2E47726170686963732E330010000000 5643616D2E47726170686963732E3300F439B271000000000000000000000000000000005098D6 01000000000000000000000000000000001F8B0800000000000000CD58DD73DA38107FEF5FE171 1FFAD4601B68C98C710748B86426693207E1F0BD095B015D6DC9238B04FAD7DF4AF2876C43D2E9 BD1CED0469F7B7ABFD9612FFDB214DAC17CC73C2E8D8762F1CDBC2346231A1DBB1FDB49C7F1ED9 DF820FFE0CD117945B0F7B91EDC51325221FDBF7F7B675878E6C2FC6F6126DF609E2B63545D18F 2D677B1ACF58C2F8D8FEF8AC3EC0613CC6BCA48E1CF9AFA4FE4562B11BDB6A2F044BEF11DF1269 8F6D81C03EA5B962CE18CD492E30158A35674C603E49C896A68A36839F98978C3993B44F134E50 F2C9723DEBA3A33ED61D7E16B67583517C525A33DE9526DB1D00A40F926258FCA7E4987BF6AACD 5F6428527105E2926506A4F0DFF50045E2B19D254C3C6CFEC191700776E02F224CB1172FC431C1 70DA16D3F8314111D676EB90BD19FA8AB3E488E619E24AD0F9EDA4FC4F23AF437342B16634158F 5A7A35664572B249B072BB9DC8B3390BFC9E99A2C09F318820A148E0C511EA352D73B78850A23B 0B7A8CE6822342716C5B9303861299EC21CA489048136EE99CB3224F727F07D83253DAF29A5EE6 EAC21D69E29264B932536F44825B61755AEED7262F8F19F80F5AE1BF6DFDC1496C5A22F7A62597 EA53D395A3637BC11212D7D4DA3E6883FD66DB5212A94F83D5D463304C554B12FDC8EFD006276F E756E330DD4A49CFB6D69303D151318AE59AC605A72A0238622D5D30AB625DD8D2A0A903A658BC 62ACAB635D9B567872C338F90956A2A4C16D1EA6E8DFF7E9064358BE339ED66813179EB5BFE63C 700264282739D8CDC3C3B68B61DBC5F0848B61C7C5F04D17C3332E86275D0CDB2E424B9D69A2C0 87C9A8DB6996B01CC7CABC394912B974F5F21109687CB0F38AA02DA3289195936B5E61ECF50BA6 0F712C8B232B485A09F40CE7ECB52C9747CE32C66518A5A18B1DD277E3228551B7B3AD4746A868 C8CF088F127958B78CE1A809DDAA885E0CDCD1E82B34CE244699202FF81EE7C5B4052D1B86785C DE153394628EEA70E8DBE48AE4304304A17B228E0B8C78B4ABDCAF2F003D262A9A07C42F83CBA1 F4B222EA86BF22D18E97F367CEE14C386708C27556CF4ED66B2AF8515975276766FBFE694FAE06 CD53407770D93788DAA479828426564DDF1F6A42A3A664E8CC5A7DE062C754DA2179F216553DE0 14C92A2D712FDDCBAF2571417E4A5D17C3629F9BFA96F8205AE3D3ED4C98144FB1BA1B1CBD8376 04856A9395B53490BB66D796813C35A33B87EC37180A3AC542F68E278D05927C78E953751EF133 DA27807EEAC4E949D79807724FD0E2695971AB0E725523570D24864E881A9530453996F206333F A699808740DE7E587411457F5CA17C276BB20B6858D5E156750143BD404E9E213A3AF8156D8A9F 192FF323E76CC7E1B576D875F580AF1C0E3BC8B0468626F2EF8A0EB3AB1C51C6B02A279453364D 119CAAE6CB043EB2E408C5EBC54D45C50B439582F12A3BF5306E3D2187F6D917C92F8DD9DF32B7 ABB67EFDCC1A6F1F78F5AC087E05CE941DC0FE61C79FE61DDCB9B1BA1E7F015BE4C307EE4048F9 DA5AA144C62970FC9E413631E1694C18F8F55B2138F83D63E7D7776D70F47BC6CED737F684463B C64DC526BD44C11C178846B88B2B3970D2197D61435F78565FD8D2F7DF520B2BC8662B47ADA9E9 7675588DEB5DE3BDB858C9C5EDF521E3D25CBDE8EC7B15B225D26F890CDE17F15A22EEFB22BF62 58AF76EB36DD6A25C9517D7B816381087CCB75DF1A546BCF72AB7585E99582BD42514F853DF0EB 5E59DF135A67F902049BBC26161D34B66F07FD36161D4C6CF886DEB0A537ACF4C22FAA833656EA BD910139DDFBE094E29E9C42FA142834F9258F1DDB9FC118C719D80509C1B4181894B501EA9724 09EA6B4AA08D53C12CA6A93C59FD6923F8F02FB612F85D0B110000000000000000000000000000 000000000000000000000000000000000000000000FFFFFFFF030000000400000001000000FFFF FFFF0000000000000000EC2E0000361F0000420C00000100090000032106000007001C00000000 000400000003010800050000000B0200000000050000000C02B811941A14000000FF0600000600 F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D01000004 000000F001000008000000FA0200000000000000000000040000002D01000007000000FC020000 000000000000040000002D0101001C000000FB0210FF0000000000009001000000010700000041 7269616C00C47740000000B1040A47B7C5C477C0C5C47720C0C77700003000040000002D010200 05000000020101000000050000000102FFFFFF00050000002E0118000000050000000902000000 000400000008010000050000000102FFFFFF000B000000320A000000000000020000000000941A B811050000000102FFFFFF000B000000320A000000000000020000000000941AB8110700000016 04B811941A00000000050000000102FFFFFF000B000000320A0000000000000200380038005C1A 80111C000000FB0260FF00000000000090010000000107000000417269616C00C47740000000B3 1002004F006C006500500072006500730030003000300000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000180002010300000005000000FF FFFFFF000000000000000000000000000000000000000000000000000000000000000000000000 190000006A0C0000000000005200690063006800450064006900740046006C0061006700730000 000000000000000000000000000000000000000000000000000000000000000000000000001C00 0200FFFFFFFFFFFFFFFFFFFFFFFF00000000000000000000000000000000000000000000000000 00000000000000000000004B0000000C0000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF0000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF000000 000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000AEFB7C5C477C0C5C47720C0C77700003000040000002D0103001C000000FB0238 FF00000000000090010000000107000000417269616C00C47740000000AB090AC5B7C5C477C0C5 C47720C0C77700003000040000002D010400040000002D01030008000000FA0200000500000099 999900040000002D010500050000001402870F310805000000130285013108040000002D010000 04000000F001050008000000FA0200000500000099999900040000002D01050005000000140287 0FB10B0500000013028501B10B040000002D01000004000000F001050008000000FA0200000500 000099999900040000002D010500050000001402870F310F0500000013028501310F040000002D 01000004000000F001050008000000FA0200000500000099999900040000002D01050005000000 1402870FB1120500000013028501B112040000002D01000004000000F001050008000000FA0200 000500000099999900040000002D010500050000001402860F3108050000001302860FB2120400 00002D01000004000000F001050008000000FA0200000500000099999900040000002D01050005 0000001402060C3108050000001302060CB212040000002D01000004000000F001050008000000 FA0200000500000099999900040000002D010500050000001402860831080500000013028608B2 12040000002D01000004000000F001050008000000FA0200000500000099999900040000002D01 0500050000001402050531080500000013020505B212040000002D01000004000000F001050008 000000FA0200000500000099999900040000002D01050005000000140285013108050000001302 8501B212040000002D01000004000000F001050008000000FA0200000A00000000000000040000 002D01050004000000F001000008000000FA0200000A00000000000000040000002D0100000500 00001402860F3108050000001302860FB212040000002D01050004000000F001000008000000FA 0205000100000000000000040000002D01000007000000FC020000000000000000040000002D01 0600050000000601020000000A00000024030300C713860FEA12570FEA12B50F05000000060101 000000040000002D010100040000002D01050004000000F001060008000000FA0200000A000000 00000000040000002D010600050000001402860FC713050000001302570FEA12040000002D0105 0004000000F001060008000000FA0200000A00000000000000040000002D010600050000001402 860FC713050000001302B50FEA12040000002D01050004000000F001060008000000FA0200000A 00000000000000040000002D010600050000001402570FEA12050000001302B50FEA1204000000 2D01050004000000F001060008000000FA0200000A00000000000000040000002D010600050000 001402860FB212050000001302860FC713040000002D01050004000000F001060008000000FA02 00000A00000000000000040000002D010600050000001402870F31080500000013028501310804 0000002D01050004000000F0010600040000002D01000007000000FC0200000000000000000400 00002D010600050000000601020000000A000000240303003108700060084D0102084D01050000 00060101000000040000002D010100040000002D01050004000000F001060008000000FA020000 0A00000000000000040000002D010600050000001402700031080500000013024D016008040000 002D01050004000000F001060008000000FA0200000A00000000000000040000002D0106000500 00001402700031080500000013024D010208040000002D01050004000000F001060008000000FA 0200000A00000000000000040000002D0106000500000014024D0160080500000013024D010208 040000002D01050004000000F001060008000000FA0200000A00000000000000040000002D0106 000500000014028501310805000000130270003108040000002D01050004000000F00106000500 00001402BE0F31080500000013024E0F31080700000021050100300070100508050000001402BE 0FB10B0500000013024E0FB10B070000002105010031007010850B050000001402A20FF1090500 000013026A0FF109050000001402BE0F310F0500000013024E0F310F0700000021050100320070 10050F050000001402A20F710D0500000013026A0F710D050000001402BE0FB112050000001302 4E0FB1120700000021050100330070108512050000001402A20FF1100500000013026A0FF11005 0000001402860F6908050000001302860FF90707000000210501003000CE0F6807050000001402 060C6908050000001302060CF907070000002105010031004E0C6807050000001402C60D4D0805 0000001302C60D1508050000001402860869080500000013028608F90707000000210501003200 CE086807050000001402460A4D08050000001302460A1508050000001402050569080500000013 020505F907070000002105010033004D056807050000001402C5064D08050000001302C5061508 050000001402850169080500000013028501F90707000000210501003400CD0168070500000014 0245034D0805000000130245031508040000002D010400070000002105010078001C112C130700 00002105010079005B01CC06040000002D01030008000000FA0200000000000000000000040000 002D01060004000000F001050014000000FF0600000600F602000024000100020000800080FF7F FF7F02000080FF7F0080FF7F0200040000002D01050004000000F0010500070000001604B81194 1A0000000008000000FA020000130000000000FF00040000002D01050004000000F00106000500 00001402860F31080500000013028501B1120500000014028501B112050000001302060C310F05 0000001402060C310F050000001302860F310807000000FC0200000000FF000000040000002D01 060004000000F001010008000000FA020000010000000000FF00040000002D01010004000000F0 010500040000002D010000070000001804B10F5C085D0F0808040000002D010100040000002D01 0000070000001804B001DC125C018812040000002D010100040000002D01000007000000180431 0C5C0FDD0B080F040000002D010100040000002D010000070000001804B10F5C085D0F08080400 00002D01010008000000FA0200000000000000000000040000002D01050004000000F001010007 000000FC020000000000000000040000002D01010004000000F001060014000000FF0600000600 F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D01060004 000000F0010600070000001604B811941A0000000014000000FF0600000600F602000024000100 020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D01060004000000F001060007 0000001604B811941A0000000014000000FF0600000600F602000024000100020000800080FF7F FF7F02000080FF7F0080FF7F0200040000002D01060004000000F001060008000000FA02000000 00000000000000040000002D01060004000000F001050007000000FC020000FFFFFF0000000400 00002D01050004000000F00101001C000000FB021000070000000000BC02000000000102022253 797374656D000000000A0021008A010000000001000000C0F11200B9C1C477040000002D010100 030000000000000000000000000000000000000000000000000000002100000000000000010000 000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 01050000 05000000 0D000000 4D45544146494C455049435400 EC2E0000 CAE0FFFF 4A0C0000 0800EC2E361F0000 0100090000032106000007001C00000000000400000003010800050000000B0200000000050000 000C02B811941A14000000FF0600000600F602000024000100020000800080FF7FFF7F02000080 FF7F0080FF7F0200040000002D01000004000000F001000008000000FA02000000000000000000 00040000002D01000007000000FC020000000000000000040000002D0101001C000000FB0210FF 00000000000090010000000107000000417269616C00C47740000000B1040A47B7C5C477C0C5C4 7720C0C77700003000040000002D01020005000000020101000000050000000102FFFFFF000500 00002E0118000000050000000902000000000400000008010000050000000102FFFFFF000B0000 00320A000000000000020000000000941AB811050000000102FFFFFF000B000000320A00000000 0000020000000000941AB811070000001604B811941A00000000050000000102FFFFFF000B0000 00320A0000000000000200380038005C1A80111C000000FB0260FF000000000000900100000001 07000000417269616C00C47740000000B3100AEFB7C5C477C0C5C47720C0C77700003000040000 002D0103001C000000FB0238FF00000000000090010000000107000000417269616C00C4774000 0000AB090AC5B7C5C477C0C5C47720C0C77700003000040000002D010400040000002D01030008 000000FA0200000500000099999900040000002D010500050000001402870F3108050000001302 85013108040000002D01000004000000F001050008000000FA0200000500000099999900040000 002D010500050000001402870FB10B0500000013028501B10B040000002D01000004000000F001 050008000000FA0200000500000099999900040000002D010500050000001402870F310F050000 0013028501310F040000002D01000004000000F001050008000000FA0200000500000099999900 040000002D010500050000001402870FB1120500000013028501B112040000002D010000040000 00F001050008000000FA0200000500000099999900040000002D010500050000001402860F3108 050000001302860FB212040000002D01000004000000F001050008000000FA0200000500000099 999900040000002D010500050000001402060C3108050000001302060CB212040000002D010000 04000000F001050008000000FA0200000500000099999900040000002D01050005000000140286 0831080500000013028608B212040000002D01000004000000F001050008000000FA0200000500 000099999900040000002D010500050000001402050531080500000013020505B212040000002D 01000004000000F001050008000000FA0200000500000099999900040000002D01050005000000 1402850131080500000013028501B212040000002D01000004000000F001050008000000FA0200 000A00000000000000040000002D01050004000000F001000008000000FA0200000A0000000000 0000040000002D010000050000001402860F3108050000001302860FB212040000002D01050004 000000F001000008000000FA0205000100000000000000040000002D01000007000000FC020000 000000000000040000002D010600050000000601020000000A00000024030300C713860FEA1257 0FEA12B50F05000000060101000000040000002D010100040000002D01050004000000F0010600 08000000FA0200000A00000000000000040000002D010600050000001402860FC7130500000013 02570FEA12040000002D01050004000000F001060008000000FA0200000A000000000000000400 00002D010600050000001402860FC713050000001302B50FEA12040000002D01050004000000F0 01060008000000FA0200000A00000000000000040000002D010600050000001402570FEA120500 00001302B50FEA12040000002D01050004000000F001060008000000FA0200000A000000000000 00040000002D010600050000001402860FB212050000001302860FC713040000002D0105000400 0000F001060008000000FA0200000A00000000000000040000002D010600050000001402870F31 0805000000130285013108040000002D01050004000000F0010600040000002D01000007000000 FC020000000000000000040000002D010600050000000601020000000A00000024030300310870 0060084D0102084D0105000000060101000000040000002D010100040000002D01050004000000 F001060008000000FA0200000A00000000000000040000002D0106000500000014027000310805 00000013024D016008040000002D01050004000000F001060008000000FA0200000A0000000000 0000040000002D010600050000001402700031080500000013024D010208040000002D01050004 000000F001060008000000FA0200000A00000000000000040000002D0106000500000014024D01 60080500000013024D010208040000002D01050004000000F001060008000000FA0200000A0000 0000000000040000002D0106000500000014028501310805000000130270003108040000002D01 050004000000F0010600050000001402BE0F31080500000013024E0F3108070000002105010030 0070100508050000001402BE0FB10B0500000013024E0FB10B070000002105010031007010850B 050000001402A20FF1090500000013026A0FF109050000001402BE0F310F0500000013024E0F31 0F070000002105010032007010050F050000001402A20F710D0500000013026A0F710D05000000 1402BE0FB1120500000013024E0FB1120700000021050100330070108512050000001402A20FF1 100500000013026A0FF110050000001402860F6908050000001302860FF9070700000021050100 3000CE0F6807050000001402060C6908050000001302060CF907070000002105010031004E0C68 07050000001402C60D4D08050000001302C60D1508050000001402860869080500000013028608 F90707000000210501003200CE086807050000001402460A4D08050000001302460A1508050000 001402050569080500000013020505F907070000002105010033004D056807050000001402C506 4D08050000001302C5061508050000001402850169080500000013028501F90707000000210501 003400CD01680705000000140245034D0805000000130245031508040000002D01040007000000 2105010078001C112C13070000002105010079005B01CC06040000002D01030008000000FA0200 000000000000000000040000002D01060004000000F001050014000000FF0600000600F6020000 24000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D01050004000000F0 010500070000001604B811941A0000000008000000FA020000130000000000FF00040000002D01 050004000000F0010600050000001402860F31080500000013028501B1120500000014028501B1 12050000001302060C310F050000001402060C310F050000001302860F310807000000FC020000 0000FF000000040000002D01060004000000F001010008000000FA020000010000000000FF0004 0000002D01010004000000F0010500040000002D010000070000001804B10F5C085D0F08080400 00002D010100040000002D010000070000001804B001DC125C018812040000002D010100040000 002D010000070000001804310C5C0FDD0B080F040000002D010100040000002D01000007000000 1804B10F5C085D0F0808040000002D01010008000000FA0200000000000000000000040000002D 01050004000000F001010007000000FC020000000000000000040000002D01010004000000F001 060014000000FF0600000600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF 7F0200040000002D01060004000000F0010600070000001604B811941A0000000014000000FF06 00000600F602000024000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D 01060004000000F0010600070000001604B811941A0000000014000000FF0600000600F6020000 24000100020000800080FF7FFF7F02000080FF7F0080FF7F0200040000002D01060004000000F0 01060008000000FA0200000000000000000000040000002D01060004000000F001050007000000 FC020000FFFFFF000000040000002D01050004000000F00101001C000000FB0210000700000000 00BC02000000000102022253797374656D000000000A0021008A010000000001000000C0F11200 B9C1C477040000002D010100030000000000 }{\result {\pict\wmetafile8\picw11649\pich7748\picscalex96\picscaley96\picwgoal6809\pichgoal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}}}\plain\f3\fs28\cf0 \par \pard\ri4\plain\f3\fs28\cf0 mit MuPAD erstellen. Ist das Dreieck erst \'fcber eine Matrix definiert, so \par bietet sich der Vorteil, dass Abbildungen der Ebene wie \plain\f3\fs28\cf0\i Streckungen\plain\f3\fs28\cf0 \par und \plain\f3\fs28\cf0\i Drehungen\plain\f3\fs28\cf0 einerseits auf algebraischer Ebene mit dem CAS durch \par Matrixmulitiplikationen realsiert werden k\'f6nnen, man aber andererseits \par auch sofort die Visualisierung der Transformation, die man gerade \par durchgef\'fchrt hat, darstellen lassen kann. \par \par Im folgenden stellen wir die Prozedur \plain\f4\fs28\cf3 matrix2polygon\plain\f3\fs28\cf0 vor, mit deren \par Hilfe sich leicht geometrische Objekte wie Dreiecke, Vierecke etc. und \par auch ganz allgemeine Streckenkz\'fcge ("Polygone") zeichnen lassen. \par \par Die Prozedur \plain\f4\fs28\cf3 matrix2polygon\plain\f3\fs28\cf0 soll als Eingabe eine Matrix mit zwei \par Zeilen und beliebig vielen Spalten der Form \par \par \pard\li3000\ri4\plain\f3\fs28\cf0 {\pict\wmetafile8\picw5658\pich1607\picscalex99\picscaley99\picwgoal3212\pichgoal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}\plain\f3\fs28\cf0 \par \par \pard\ri4\plain\f3\fs28\cf0 erhalten. Jede Spalte der Matrix steht dabei f\'fcr einen Punkt, dessen \par x-Koordinate durch den entsprechenden Eintrag in der ersten Zeile \par und dessen y-Koordinate durch den entsprechenden Eintrag in der \par zweiten Zeile gegeben ist. \par \par Hier also zun\'e4chst die Prozedur: \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf3 {\pntext\f1\'b7\tab}matrix2polygon:= (A) -> \par \pard\li600\ri1\fi-300\plain\f4\fs28\cf3 if linalg::nrows(A) = 2 then \par plot::Polygon2d(linalg::transpose(A), \par PointsVisible = TRUE, \par GridVisible = TRUE, \par Scaling = Constrained) \par else \par error("n x 2 matrix erwartet"); \par end_if: \par \pard\ri4\plain\f3\fs28\cf0 \par Wir sehen im Programmcode bereits, dass sinnvolle \plain\f4\fs28\cf3 plot\plain\f3\fs28\cf0 -Optionen wie \par \plain\f4\fs28\cf3 GridVisible =\plain\f3\fs28\cf0 \plain\f4\fs28\cf3 Automatic\plain\f3\fs28\cf0 und \plain\f4\fs28\cf3 Scaling = Constrained\plain\f3\fs28\cf0 (\'fcber das \par Koordinatensystem werden Gitterlinien gelegt und die Skalierung der \par Graphik bleibt "originalgetreu") fest eingebaut sind. M\'f6chte man auf eine \par dieser Optionen verzichten, so ist es ein Leichtes schlicht die entsprechende \par Zeile im Programmcode der Prozedur \plain\f4\fs28\cf3 matrix2polygon\plain\f3\fs28\cf0 zu l\'f6schen. \par \par R\'fcckgabewert der Prozedur ist entweder ein grafisches Objekt, das \par wir dann mit dem \plain\f4\fs28\cf3 plot\plain\f3\fs28\cf0 -Befehl von MuPAD zeichnen lassen k\'f6nnen, \par oder die Fehlermeldung \plain\f4\fs28\cf3 "n x 2 matrix erwartet"\plain\f3\fs28\cf0 , wenn wir \par eine Matrix von einem falschen Format eingegeben haben. \par \par Nun testen wir die Prozedur an dem obigen Beispiel des Dreiecks \par mit den Eckpunkten \plain\f3\fs28\cf0\b A = (0|0)\plain\f3\fs28\cf0 , \plain\f3\fs28\cf0\b B = (3|4)\plain\f3\fs28\cf0 und \plain\f3\fs28\cf0\b C = (2|1)\plain\f3\fs28\cf0 . Die Spalten \par der Matrix sollen die Eckpunkte des Dreiecks definieren: \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf3 {\pntext\f1\'b7\tab}Dreieck:= matrix([[0,3,2], \par \pard\li600\ri1\fi-300\plain\f4\fs28\cf3 [0,4,1]]) \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf3 {\pntext\f1\'b7\tab}plot(matrix2polygon(Dreieck)): \par \pard\ri4\plain\f3\fs28\cf0 Offensichtlich ist dies nicht ganz das, was wir uns vorgestellt hatten. \par Es gen\'fcgt nicht, die Eckpunkte anzugeben, sondern wir m\'fcssen, wenn \par wir eine geschlossene Figur zeichnen wollen, vom "letzten" Eckpunkt \par nochmals zur\'fcck zum "Startpunkt" laufen. In unserem Fall bedeutet \par dies einfach, dass wir den Eckpunkt \plain\f3\fs28\cf0\b A\plain\f3\fs28\cf0 \plain\f3\fs28\cf0\b = (0|0) \plain\f3\fs28\cf0 noch einmal als letzten \par Punkt in die Matrix \plain\f4\fs28\cf3 Dreieck\plain\f3\fs28\cf0 hineinschreiben m\'fcssen: \par \plain\f4\fs28\cf3 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf3 {\pntext\f1\'b7\tab}Dreieck:= Dreieck . matrix([0,0]) \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf3 {\pntext\f1\'b7\tab}plot(matrix2polygon(Dreieck)): \par \pard\ri4\plain\f3\fs28\cf0 Dies ist genau die Zeichnung, die wir oben in der Einleitung schon als \par Beispiel gesehen hatten. \par \par Auch zuf\'e4llige Figuren k\'f6nnen wir leicht mit Hilfe der Prozedur \par \plain\f4\fs28\cf3 matrix2polygon\plain\f3\fs28\cf0 darstellen: Z.B. k\'f6nnen wir Zufallszahlen im \par Bereich von 1 bis 6 erzeugen und so beliebige Streckenz\'fcge \par zeichnen: \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf3 {\pntext\f1\'b7\tab}zufallsEcken:= random(1..6): \par {\pntext\f1\'b7\tab}n:= 5: \par {\pntext\f1\'b7\tab}zufallsFigur:= matrix2polygon( \par \pard\li600\ri1\fi-300\plain\f4\fs28\cf3 matrix([[zufallsEcken() $ i = 1..n], \par [zufallsEcken() $ i = 1..n]])): \par plot(zufallsFigur): \par \pard\ri4\plain\f3\fs28\cf0 Auch mehrere verschiedene Figuren lassen sich leicht in ein \par gemeinsames Koordinatensystem zeichnen, indem man z.B. die \par Matrizen, die einzelne Figuren definieren, in einer Liste zusammen- \par fasst und anschlie\'dfend mit dem Sequenzoperator \plain\f4\fs28\cf3 $\plain\f3\fs28\cf0 \'fcber die \par Elemente der Liste iteriert: \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf3 {\pntext\f1\'b7\tab}MuPAD:= [ \par \pard\li600\ri1\fi-300\plain\f4\fs28\cf3 matrix([[0,0,1,2,2,1.5,1.5,1,0.5,0.5,0], \par [0,3,2,3,0,0,2,1.5,2,0,0]]), \par matrix([[2.5,2.5,3,3,4,4,4.5,4.5,2.5], \par [0,1.5,1.5,0.5,0.5,1.5,1.5,0,0]]), \par matrix([[5,5,6.5,6.5,5.5,5.5,6,6,5.5,5.5,5], \par [0,3,3,1.5,1.5,2.5,2.5,2,2,0,0]]), \par matrix([[7,8,9,10,9.5,8.75,8.25,8,9,8,7.95,9.05,7.95,7.5,7], \par [0,3,3,0,0,2.5,2.5,1.75,1.75,1.75,1.5,1.5,1.5,0,0]]), \par matrix([[10.5,10.5,11,12,12,11,11,11.5,11.5,11,11,10.5], \par [0,3,3,2,1,0,2.5,2,1,0.5,0,0]])]: \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf3 {\pntext\f1\'b7\tab}plot(matrix2polygon(MuPAD[k]) $ k = 1..5):\plain\f3\fs28\cf3 \par \pard\ri4\plain\f4\fs20\cf0\b ________________________________________________________________________________ \par \plain\f3\fs22\cf0 \par \plain\f3\fs22\cf1\b Anmerkungen:\plain\f3\fs22\cf1 \par \plain\f3\fs20\cf1\b 1\plain\f3\fs20\cf1 . Weitere Anregungen finden Sie in der Buchreihe \plain\f3\fs20\cf3 Mathematik 1 x anders\plain\f3\fs20\cf1 . In dieser Reihe \par wird eine Vielzahl unterschiedlichster mathematischer Probleme mit MuPAD gel\'f6st. Die \par B\'fccher k\'f6nnen unter \plain\f6\fs20\cf2 www.schule.mupad.de/literatur\plain\f3\fs20\cf1 kostenfrei kopiert werden. \par \plain\f3\fs20\cf2 \par \plain\f4\fs20\cf0\b _______________________________________________________________________________ \par \plain\f4\fs28\cf3 \par }