{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 Output" 2 20 "" 0 1 0 0 255 1 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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple P lot" -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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "with(linalg):\nwith( plots):\nwith(plottools):" }}{PARA 7 "" 1 "" {TEXT -1 98 "Warning, the previous binding of the name arrow has been removed and it now has an assigned value\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "# Zent ralprojektion eines Vierecks auf ein Quadrat" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "# \+ 4 Punkte in y=0 Ebene" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "P1y:=[X1,0,Z1];\nP2y:=[X2, 0,Z2];\nP3y:=[X3,0,Z3];\nP4y:=[X4,0,Z4];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$P1yG7%%#X1G\"\"!%#Z1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$P 2yG7%%#X2G\"\"!%#Z2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$P3yG7%%#X3G \"\"!%#Z3G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$P4yG7%%#X4G\"\"!%#Z4G " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 47 "# gesuchte Eckpunkte des Quadrats in z=-h Eben e" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "Q1:=[x1,y1,-h];\nQ2:=[ x2,y2,-h];\nQ3:=[x3,y3,-h];\nQ4:=[x4,y4,-h];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Q1G7%%#x1G%#y1G,$%\"hG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Q2G7%%#x2G%#y2G,$%\"hG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Q3G7%%#x3G%#y3G,$%\"hG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Q4G7%%#x4G%#y4G,$%\"hG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "# Auge" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "A:=[a,b,0];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG7%%\"aG%\"bG \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "l1:=expand(c1*A+(1-c1)*P1y-Q1);\nl2:=exp and(c2*A+(1-c2)*P2y-Q2);\nl3:=expand(c3*A+(1-c3)*P3y-Q3);\nl4:=expand( c4*A+(1-c4)*P4y-Q4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l1G7%,*%#x1 G!\"\"%#X1G\"\"\"*&F)F*%#c1GF*F(*&%\"aGF*F,F*F*,&%#y1GF(*&%\"bGF*F,F*F *,(%\"hGF*%#Z1GF**&F5F*F,F*F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l2 G7%,*%#x2G!\"\"%#X2G\"\"\"*&F)F*%#c2GF*F(*&%\"aGF*F,F*F*,&%#y2GF(*&%\" bGF*F,F*F*,(%\"hGF*%#Z2GF**&F5F*F,F*F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l3G7%,*%#x3G!\"\"%#X3G\"\"\"*&F)F*%#c3GF*F(*&%\"aGF*F,F*F*,&% #y3GF(*&%\"bGF*F,F*F*,(%\"hGF*%#Z3GF**&F5F*F,F*F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l4G7%,*%#x4G!\"\"%#X4G\"\"\"*&F)F*%#c4GF*F(*&%\"aGF* F,F*F*,&%#y4GF(*&%\"bGF*F,F*F*,(%\"hGF*%#Z4GF**&F5F*F,F*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "# Parallelogramm Bedingung" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "parallelogramm:=\{op(l1),op(l2),op(l3),op(l4)\};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%/parallelogrammG<.,(%\"hG\"\"\"%#Z 4GF(*&F)F(%#c4GF(!\"\",(F'F(%#Z2GF(*&F.F(%#c2GF(F,,(F'F(%#Z1GF(*&F2F(% #c1GF(F,,(F'F(%#Z3GF(*&F6F(%#c3GF(F,,*%#x2GF,%#X2GF(*&F;F(F0F(F,*&%\"a GF(F0F(F(,*%#x3GF,%#X3GF(*&FAF(F8F(F,*&F>F(F8F(F(,*%#x4GF,%#X4GF(*&FFF (F+F(F,*&F>F(F+F(F(,&%#y1GF,*&%\"bGF(F4F(F(,*%#x1GF,%#X1GF(*&FOF(F4F(F ,*&F>F(F4F(F(,&%#y2GF,*&FLF(F0F(F(,&%#y3GF,*&FLF(F8F(F(,&%#y4GF,*&FLF( F+F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "sol:=solve(parall elogramm,\{c1,c2,c3,c4,x1,y1,x2,y2,x3,y3,x4,y4\});" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>%$solG<./%#x3G*&,(*&%#X3G\"\"\"%\"hGF,!\"\"*&%\"aGF, F-F,F,*&F0F,%#Z3GF,F,F,F2F./%#x2G*&,(*&%#X2GF,F-F,F.F/F,*&F0F,%#Z2GF,F ,F,F:F./%#x1G*&,(*&%#X1GF,F-F,F.F/F,*&F0F,%#Z1GF,F,F,FBF./%#x4G*&,(*&% #X4GF,F-F,F.F/F,*&F0F,%#Z4GF,F,F,FJF./%#y3G*(%\"bGF,,&F-F,F2F,F,F2F./% #y2G*(FNF,,&F-F,F:F,F,F:F./%#y1G*(FNF,,&F-F,FBF,F,FBF./%#c4G*&FJF.,&F- F,FJF,F,/%#y4G*(FNF,FJF.FenF,/%#c3G*&FOF,F2F./%#c2G*&FSF,F:F./%#c1G*&F WF,FBF." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "# L\366sung Eckpunkte Parallelogram m" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "Q1s:=subs(sol,Q1);\nQ2 s:=subs(sol,Q2);\nQ3s:=subs(sol,Q3);\nQ4s:=subs(sol,Q4);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$Q1sG7%*&,(*&%#X1G\"\"\"%\"hGF*!\"\"*&%\"aGF*F +F*F**&F.F*%#Z1GF*F*F*F0F,*(%\"bGF*,&F+F*F0F*F*F0F,,$F+F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Q2sG7%*&,(*&%#X2G\"\"\"%\"hGF*!\"\"*&%\"aGF* F+F*F**&F.F*%#Z2GF*F*F*F0F,*(%\"bGF*,&F+F*F0F*F*F0F,,$F+F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Q3sG7%*&,(*&%#X3G\"\"\"%\"hGF*!\"\"*&%\"a GF*F+F*F**&F.F*%#Z3GF*F*F*F0F,*(%\"bGF*,&F+F*F0F*F*F0F,,$F+F," }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Q4sG7%*&,(*&%#X4G\"\"\"%\"hGF*!\"\" *&%\"aGF*F+F*F**&F.F*%#Z4GF*F*F*F0F,*(%\"bGF*F0F,,&F+F*F0F*F*,$F+F," } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "Q1xy:=[Q1s[1],Q1s[2]];\nQ2 xy:=[Q2s[1],Q2s[2]];\nQ3xy:=[Q3s[1],Q3s[2]];\nQ4xy:=[Q4s[1],Q4s[2]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Q1xyG7$*&,(*&%#X1G\"\"\"%\"hGF*! \"\"*&%\"aGF*F+F*F**&F.F*%#Z1GF*F*F*F0F,*(%\"bGF*,&F+F*F0F*F*F0F," }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Q2xyG7$*&,(*&%#X2G\"\"\"%\"hGF*!\" \"*&%\"aGF*F+F*F**&F.F*%#Z2GF*F*F*F0F,*(%\"bGF*,&F+F*F0F*F*F0F," }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Q3xyG7$*&,(*&%#X3G\"\"\"%\"hGF*!\" \"*&%\"aGF*F+F*F**&F.F*%#Z3GF*F*F*F0F,*(%\"bGF*,&F+F*F0F*F*F0F," }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Q4xyG7$*&,(*&%#X4G\"\"\"%\"hGF*!\" \"*&%\"aGF*F+F*F**&F.F*%#Z4GF*F*F*F0F,*(%\"bGF*F0F,,&F+F*F0F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "# Bedingungen Quadrat" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "winkelbed:=innerprod(Q2xy-Q 1xy,Q4xy-Q1xy);\nseitenlaengebed:=innerprod(Q2xy-Q1xy,Q2xy-Q1xy)-inner prod(Q4xy-Q1xy,Q4xy-Q1xy);\n\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*w inkelbedG*,%\"hG\"\"#,H*(%#Z2G\"\"\")%#X1GF'F+%#Z4GF+F+*,F'F+F*F+F-F+% \"aGF+F.F+!\"\"**F*F+F-F+%#Z1GF+%#X4GF+F1**F*F+F-F+F0F+F3F+F+*()F0F'F+ F*F+F.F+F+**F0F+F*F+F3F+F4F+F+*(F7F+F*F+F3F+F1**F3F+%#X2GF+F.F+F-F+F1* *F3F+F;F+F0F+F.F+F+*()F3F'F+F;F+F4F+F+*(F>F+F;F+F0F+F1**F0F+F3F+F.F+F- F+F+*(F7F+F3F+F.F+F1*(F0F+F>F+F4F+F1*&F7F+F>F+F+*()%\"bGF'F+F*F+F.F+F+ *(FEF+F3F+F*F+F1*(FEF+F3F+F.F+F1*&FEF+F>F+F+F+F3!\"#F*F1F.F1" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%0seitenlaengebedG,&**%\"hG\"\"#,<*&)%#Z2GF (\"\"\")%#X1GF(F-F-**F(F-F+F-F/F-%\"aGF-!\"\"*,F(F-F,F-F/F-%#Z1GF-%#X2 GF-F2*,F(F-F,F-F/F-F1F-F4F-F-*&)F1F(F-F+F-F-*,F(F-F1F-F,F-F4F-F5F-F-** F(F-F8F-F,F-F4F-F2*&)F4F(F-)F5F(F-F-**F(F-F " 0 "" {MPLTEXT 1 0 48 "s olab:=solve(\{winkelbed,seitenlaengebed\},\{b,a\});" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>%&solabG6$<$/%\"aG,$*&,0**\"\"#\"\"\"%#X1GF.)%#Z2GF- F.)%#Z4GF-F.!\"\"**F/F.%#Z1GF.F0F.F3F.F.**F/F.F6F.F2F.F1F.F.*()F6F-F.F 0F.%#X4GF.F4**F6F.F0F.F3F.F:F.F.**F6F.F2F.F1F.%#X2GF.F.*(F9F.F2F.F=F.F 4F.,,*&F9F.F0F.F.*&F9F.F2F.F.**F-F.F6F.F0F.F3F.F4**F-F.F6F.F2F.F1F.F4* (F-F.F0F.F2F.F.F4F4/%\"bG*,F3F.F6F.F1F.,.*&F1F.F:F.F4*&F6F.F:F.F.*&F=F .F6F.F4*&F3F.F=F.F.*&F1F.F/F.F.*&F3F.F/F.F4F.F?F4<$F'/FF,$FGF4" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 16 "# L\366sung Quadrat" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "Q1s:=subs(solab[2],Q1s);\nQ2s:=subs(solab[2],Q2s);\nQ 3s:=subs(solab[2],Q3s);\nQ4s:=subs(solab[2],Q4s);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$Q1sG7%*&,(*&%#X1G\"\"\"%\"hGF*!\"\"*(,0**\"\"#F*F)F* )%#Z2GF0F*)%#Z4GF0F*F,**F)F*%#Z1GF*F1F*F4F*F***F)F*F6F*F3F*F2F*F**()F6 F0F*F1F*%#X4GF*F,**F6F*F1F*F4F*F:F*F***F6F*F3F*F2F*%#X2GF*F**(F9F*F3F* F=F*F,F*,,*&F9F*F1F*F**&F9F*F3F*F***F0F*F6F*F1F*F4F*F,**F0F*F6F*F3F*F2 F*F,*(F0F*F1F*F3F*F*F,F+F*F,*(F.F*F?F,F6F*F,F*F6F,,$*,F4F*F2F*,.*&F2F* F:F*F,*&F6F*F:F*F**&F=F*F6F*F,*&F4F*F=F*F**&F2F*F)F*F**&F4F*F)F*F,F*F? F,,&F+F*F6F*F*F,,$F+F," }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$Q2sG7%*&, (*&%#X2G\"\"\"%\"hGF*!\"\"*(,0**\"\"#F*%#X1GF*)%#Z2GF0F*)%#Z4GF0F*F,** F1F*%#Z1GF*F2F*F5F*F***F1F*F7F*F4F*F3F*F**()F7F0F*F2F*%#X4GF*F,**F7F*F 2F*F5F*F;F*F***F7F*F4F*F3F*F)F*F**(F:F*F4F*F)F*F,F*,,*&F:F*F2F*F**&F:F *F4F*F***F0F*F7F*F2F*F5F*F,**F0F*F7F*F4F*F3F*F,*(F0F*F2F*F4F*F*F,F+F*F ,*(F.F*F?F,F3F*F,F*F3F,,$*,F5F*F7F*,.*&F3F*F;F*F,*&F7F*F;F*F**&F)F*F7F *F,*&F5F*F)F*F**&F3F*F1F*F**&F5F*F1F*F,F*F?F,,&F+F*F3F*F*F,,$F+F," }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%$Q3sG7%*&,(*&%#X3G\"\"\"%\"hGF*!\"\" *(,0**\"\"#F*%#X1GF*)%#Z2GF0F*)%#Z4GF0F*F,**F1F*%#Z1GF*F2F*F5F*F***F1F *F7F*F4F*F3F*F**()F7F0F*F2F*%#X4GF*F,**F7F*F2F*F5F*F;F*F***F7F*F4F*F3F *%#X2GF*F**(F:F*F4F*F>F*F,F*,,*&F:F*F2F*F**&F:F*F4F*F***F0F*F7F*F2F*F5 F*F,**F0F*F7F*F4F*F3F*F,*(F0F*F2F*F4F*F*F,F+F*F,*(F.F*F@F,%#Z3GF*F,F*F GF,,$*0F5F*F7F*F3F*,.*&F3F*F;F*F,*&F7F*F;F*F**&F>F*F7F*F,*&F5F*F>F*F** &F3F*F1F*F**&F5F*F1F*F,F*F@F,,&F+F*FGF*F*FGF,F,,$F+F," }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$Q4sG7%*&,(*&%#X4G\"\"\"%\"hGF*!\"\"*(,0**\"\"#F *%#X1GF*)%#Z2GF0F*)%#Z4GF0F*F,**F1F*%#Z1GF*F2F*F5F*F***F1F*F7F*F4F*F3F *F**()F7F0F*F2F*F)F*F,**F7F*F2F*F5F*F)F*F***F7F*F4F*F3F*%#X2GF*F**(F:F *F4F*F=F*F,F*,,*&F:F*F2F*F**&F:F*F4F*F***F0F*F7F*F2F*F5F*F,**F0F*F7F*F 4F*F3F*F,*(F0F*F2F*F4F*F*F,F+F*F,*(F.F*F?F,F5F*F,F*F5F,,$*,F7F*F3F*,.* &F3F*F)F*F,*&F7F*F)F*F**&F=F*F7F*F,*&F5F*F=F*F**&F3F*F1F*F**&F5F*F1F*F ,F*F?F,,&F+F*F5F*F*F,,$F+F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 23 "agen:=subs(solab[2],a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%agenG,$*&,0**\"\"#\"\"\"%#X1GF*)%#Z2GF)F*)%#Z4GF)F*! \"\"**F+F*%#Z1GF*F,F*F/F*F***F+F*F2F*F.F*F-F*F**()F2F)F*F,F*%#X4GF*F0* *F2F*F,F*F/F*F6F*F***F2F*F.F*F-F*%#X2GF*F**(F5F*F.F*F9F*F0F*,,*&F5F*F, F*F**&F5F*F.F*F***F)F*F2F*F,F*F/F*F0**F)F*F2F*F.F*F-F*F0*(F)F*F,F*F.F* F*F0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "# Augenabstand" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "bgen:=subs(solab[2],b);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%bgenG,$*,%#Z4G\"\"\"%#Z1GF(%#Z2GF( ,.*&F*F(%#X4GF(!\"\"*&F)F(F-F(F(*&%#X2GF(F)F(F.*&F'F(F1F(F(*&F*F(%#X1G F(F(*&F'F(F4F(F.F(,,*&)F)\"\"#F()F*F9F(F(*&F8F()F'F9F(F(**F9F(F)F(F:F( F'F(F.**F9F(F)F(F \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 131 "# Beispiel \n# (wie in der Aufgabe, aber h=30 statt 150 fuer besseren Plot, beachte Aufpunkt \n# Augenabstand haeng en nicht von h ab)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "slist:=\{X1=0,Z1=-8,X3=-8,Z3 =-24,X2=2,Z2=-9,X4=-10,Z4=-18,h=30\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&slistG<+/%#X4G!#5/%#X2G\"\"#/%#Z4G!#=/%#X1G\"\"!/%#Z1G!\")/%#X3G F4/%#Z3G!#C/%#Z2G!\"*/%\"hG\"#I" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "# Aufpunkt" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "[subs(slist,agen)*1.0,0,0]; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"+xI#p2(!\"*\"\"!F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "# Augenabstand" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "subs(slist,bgen)*1.0;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$!+:YQ:Y!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "P1p:=subs(slist,P1y);\nP2p:= subs(slist,P2y);\nP3p:=subs(slist,P3y);\nP4p:=subs(slist,P4y);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$P1pG7%\"\"!F&!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$P2pG7%\"\"#\"\"!!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$P3pG7%!\")\"\"!!#C" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$P4pG7%!#5\"\"!!#=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "# Das urspruegliche Viereck" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "polygonplot([[P1p[1],P1p[3]],[P2p[1],P2p[3]],[P3p[1],P3p[3]],[P4p[ 1],P4p[3]]],scaling=constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 256 487 487 {PLOTDATA 2 "6$-%)POLYGONSG6#7&7$$\"\"!F)$!\")F)7$$\"\"#F)$!\" *F)7$F*$!#CF)7$$!#5F)$!#=F)-%(SCALINGG6#%,CONSTRAINEDG" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "# Das Quadrat" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 87 "Q1p:=subs(slist,Q1s);\nQ2p:=subs(slist,Q2s);\nQ3p:= subs(slist,Q3s);\nQ4p:=subs(slist,Q4s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Q1pG7%#!$`#\"#8#\"$l\"F(!#I" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$Q2pG7%#!$G\"\"#8#\"$S\"F(!#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %$Q3pG7%#!$`\"\"#8#\"#:F(!#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Q4p G7%#!$y#\"#8#\"#SF(!#I" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "p olygonplot([[Q1p[1],Q1p[2]],[Q2p[1],Q2p[2]],[Q3p[1],Q3p[2]],[Q4p[1],Q4 p[2]]],scaling=constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 379 414 414 {PLOTDATA 2 "6$-%)POLYGONSG6#7&7$$!+YQ:Y>!\")$\"+p2Bp7F*7$$!+YQ:Y) *!\"*$\"+xI#p2\"F*7$$!+xI#p<\"F*$\"+ah%Q:\"F07$$!+Q:YQ@F*$\"+xI#p2$F0- %(SCALINGG6#%,CONSTRAINEDG" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 119 "sl1:=expand(Q1p*t+(1-t)*P1p):\nsl2:=expand(Q2 p*t+(1-t)*P2p):\nsl3:=expand(Q3p*t+(1-t)*P3p):\nsl4:=expand(Q4p*t+(1-t )*P4p):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 176 "SP1:=spacecurve (sl1,t=-10..10,thickness=3):\nSP2:=spacecurve(sl2,t=-10..10,thickness= 3):\nSP3:=spacecurve(sl3,t=-10..10,thickness=3):\nSP4:=spacecurve(sl4, t=-10..10,thickness=3):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 109 "Qu1:=polygonplot3d([Q1p,Q2p,Q3p,Q4p],axes=box ed):\nQu2:=polygonplot3d([P1p,P2p,P3p,P4p],axes=boxed,color=red):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 18 "h1:=subs(slist,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h1G\"#I" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "display(S P1,SP2,SP3,SP4,Qu1,Qu2,axes=normal,view=[-h1..h1,-h1..h1,-h1..10],scal ing=constrained,orientation=[97,61]);" }}{PARA 13 "" 1 "" {GLPLOT3D 1264 808 808 {PLOTDATA 3 "6,-%'CURVESG6$7T7%$\"+YQ:Y>!\"($!+p2Bp7F*$\" $7#\"\"!7%$\"+&**=n'=F*$!+KaU<7F*$\"+#3/-.#F*7%$\"+XTG(y\"F*$!+%4?c;\" F*$\"+j\"3/%>F*7%$\"+%H\\yq\"F*$!+dZ\"Q6\"F*$\"+XAh]=F*7%$\"+VWTG;F*$! 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