{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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Out put" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}} {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 50 "choquet.mws 3 juin 04 09h25 v ersion 03 06 04 10h00" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(linalg):\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warni ng, the protected names norm and trace have been redefined and unprote cted\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "cercle1:=matrix(3 ,1,[R*cos(theta), R* sin(theta),0]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(cercle1G-%'matrixG6#7%7#*&%\"RG\"\"\"-%$cosG6#%&thetaGF,7#*&F +F,-%$sinGF/F,7#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 124 "Po ur avoir une repr\351sentation rationnelle et un calcul alg\351brique \+ ult\351rieur on exprimera cela en fonction de t=tan(theta/2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 220 "P:=matrix(3,3,[u/sqrt(u^2+v ^2+1),v/sqrt(u^2+v^2),u/(sqrt(u^2+v^2+1)*sqrt(u^2+v^2)),v/sqrt(u^2+v^2 +1),-u/sqrt(u^2+v^2),-v/(sqrt(u^2+v^2+1)*sqrt(u^2+v^2)),-1/sqrt(u^2+v^ 2+1),0,-(u^2+v^2)/(sqrt(u^2+v^2+1)*sqrt(u^2+v^2))]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG-%'matrixG6#7%7%*&%\"uG\"\"\",(*$)F+\"\"#F,F ,*$)%\"vGF0F,F,F,F,#!\"\"F0*&F3F,,&F.F,F1F,F4*(F+F,F-F4F7F47%*&F3F,F-F 4,$*&F+F,F7F4F5,$*(F3F,F-F4F7F4F57%,$*&F,F,*$F-#F,F0F5F5\"\"!,$*&F7#F, F0F-F4F5" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 227 "Le plan du seco nd cercle est ux+vy-z+h=0 ; la sph\350re porteuse \351tant x^2+(y-b)^2 +(z-c)^2=r^2 ; le rayon r2 de ce cercle est racine de r^2-H^2 o\371 H \+ est la distance du centre de la sph\350re au plan soit H=(vb-c+h)/sqrt (u^2+v^2+1) ; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "H:=(v*b-c +h)/sqrt(u^2+v^2+1);r2:=sqrt(r^2-H^2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"HG*&,(*&%\"vG\"\"\"%\"bGF)F)%\"cG!\"\"%\"hGF)F),(*$)%\"uG\" \"#F)F)*$)F(F2F)F)F)F)#F,F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r2G* $,&*$)%\"rG\"\"#\"\"\"F+*&,(*&%\"vGF+%\"bGF+F+%\"cG!\"\"%\"hGF+F*,(*$) %\"uGF*F+F+*$)F/F*F+F+F+F+F2F2#F+F*" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 143 "Une repr\351sentation param\351trique de ce second \+ cercle dans le rep\350re d'origine O'=(0,b,c) d'axe O'Z normale de O' \+ men\351e au plan ux+vy-z+h=0 est :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "X:=r2*cos(phi);Y:=r2*sin(phi);Z:=H;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG*&,&*$)%\"rG\"\"#\"\"\"F+*&,(*&%\"vGF+%\"bGF +F+%\"cG!\"\"%\"hGF+F*,(*$)%\"uGF*F+F+*$)F/F*F+F+F+F+F2F2#F+F*-%$cosG6 #%$phiGF+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"YG*&,&*$)%\"rG\"\"#\" \"\"F+*&,(*&%\"vGF+%\"bGF+F+%\"cG!\"\"%\"hGF+F*,(*$)%\"uGF*F+F+*$)F/F* F+F+F+F+F2F2#F+F*-%$sinG6#%$phiGF+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"ZG*&,(*&%\"vG\"\"\"%\"bGF)F)%\"cG!\"\"%\"hGF)F),(*$)%\"uG\"\"#F)F) *$)F(F2F)F)F)F)#F,F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 122 "Pour avoir une repr\351sent ation rationnelle et un calcul alg\351brique ult\351rieur on exprimera cela en fonction de s=tan(phi/2);" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 27 "cercle2 avec l'origine O' :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "cercle2:=multiply(P,matrix(3,1,[X,Y,Z]));\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%(cercle2G-%'matrixG6#7%7#,(**%\"uG\" \"\",(*$)F,\"\"#F-F-*$)%\"vGF1F-F-F-F-#!\"\"F1,&*$)%\"rGF1F-F-*&,(*&F4 F-%\"bGF-F-%\"cGF6%\"hGF-F1F.F6F6#F-F1-%$cosG6#%$phiGF-F-**F4F-,&F/F-F 2F-F5F7FA-%$sinGFDF-F-**F,F-F.F6FGF5F " 0 "" {MPLTEXT 1 0 46 "cerc le2:=matadd(matrix(3,1,[0,b,c]),cercle2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(cercle2G-%'matrixG6#7%7#,(**%\"uG\"\"\",(*$)F,\"\"#F -F-*$)%\"vGF1F-F-F-F-#!\"\"F1,&*$)%\"rGF1F-F-*&,(*&F4F-%\"bGF-F-%\"cGF 6%\"hGF-F1F.F6F6#F-F1-%$cosG6#%$phiGF-F-**F4F-,&F/F-F2F-F5F7FA-%$sinGF DF-F-**F,F-F.F6FGF5FF-**F4F-F.F5F7FAFBF-F-**F,F-FGF5F7FAFHF -F6**F4F-F.F6FGF5F " 0 "" {MPLTEXT 1 0 51 "tangente1:=matrix(3,1,[-sin( theta),cos(theta),0]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*tangent e1G-%'matrixG6#7%7#,$-%$sinG6#%&thetaG!\"\"7#-%$cosGF-7#\"\"!" }}} {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 23 "tangente au cercle 2 : " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "tangente2:=multiply(P,matrix (3,1,[-sin(phi),cos(phi),0]));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% *tangente2G-%'matrixG6#7%7#,&*(%\"uG\"\"\",(*$)F,\"\"#F-F-*$)%\"vGF1F- F-F-F-#!\"\"F1-%$sinG6#%$phiGF-F6*(F4F-,&F/F-F2F-F5-%$cosGF9F-F-7#,&*( F4F-F.F5F7F-F6*(F,F-F " 0 "" {MPLTEXT 1 0 43 "AB:=matadd(cercle2,scalarmul(cercle1,-1));\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ABG-%'matrixG6#7%7#,***%\"uG\"\"\", (*$)F,\"\"#F-F-*$)%\"vGF1F-F-F-F-#!\"\"F1,&*$)%\"rGF1F-F-*&,(*&F4F-%\" bGF-F-%\"cGF6%\"hGF-F1F.F6F6#F-F1-%$cosG6#%$phiGF-F-**F4F-,&F/F-F2F-F5 F7FA-%$sinGFDF-F-**F,F-F.F6FGF5FF -**F4F-F.F5F7FAFBF-F-**F,F-FGF5F7FAFHF-F6**F4F-F.F6FGF5F \+ " 0 "" {MPLTEXT 1 0 63 "ABv:=convert(AB,vector);tangente1v:=convert(ta ngente1,vector);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$ABvG-%'vector G6#7%,***%\"uG\"\"\",(*$)F+\"\"#F,F,*$)%\"vGF0F,F,F,F,#!\"\"F0,&*$)%\" rGF0F,F,*&,(*&F3F,%\"bGF,F,%\"cGF5%\"hGF,F0F-F5F5#F,F0-%$cosG6#%$phiGF ,F,**F3F,,&F.F,F1F,F4F6F@-%$sinGFCF,F,**F+F,F-F5FFF4F;F,F,*&%\"RGF,-FB 6#%&thetaGF,F5,,F=F,**F3F,F-F4F6F@FAF,F,**F+F,FFF4F6F@FGF,F5**F3F,F-F5 FFF4F;F,F5*&FKF,-FHFMF,F5,(F>F,*(F-F4F6F@FAF,F5*(FFF@F-F5F;F,F5" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%+tangente1vG-%'vectorG6#7%,$-%$sinG6 #%&thetaG!\"\"-%$cosGF,\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "condition1:=dotprod(ABv,tangente1v)=0;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+condition1G/,&**,:**)%\"uG\"\"$\"\"\"*&,4*&)%\"rG\" \"#F-)F+F3F-F-*&F1F-)%\"vGF3F-F-*$F1F-F-*&F6F-)%\"bGF3F-!\"\"**F3F-F7F -F;F-%\"cGF-F-**F3F-F7F-F;F-%\"hGF-F<*$)F>F3F-F<*(F3F-F>F-F@F-F-*$)F@F 3F-FF-F<*(F+F-FFFIF@F-F-*,%\"RGF--FK6#%&thetaGF-FFFIFNFIF4F-F<*,Fen F-FfnF-FFFIFNFIF6F-F<**FenF-FfnF-FFFIFNFIFF-F<*(F7F-FFFIF@F-F-*,FenF--FSFgnF-FFFIFNFIF4F-F -*,FenF-FapF-FFFIFNFIF6F-F-**FenF-FapF-FFFIFNFIF-F-FFF[oFNF]o-FKF_oF-F <\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "condition2:=dotpr od(ABv,convert(tangente2,vector))=0;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+condition2G/,(**,:**)%\"uG\"\"$\"\"\"*&,4*&)%\"rG\"\"#F-)F+F3 F-F-*&F1F-)%\"vGF3F-F-*$F1F-F-*&F6F-)%\"bGF3F-!\"\"**F3F-F7F-F;F-%\"cG F-F-**F3F-F7F-F;F-%\"hGF-F<*$)F>F3F-F<*(F3F-F>F-F@F-F-*$)F@F3F-FF-F <*(F+F-FFFIF@F-F-*,%\"RGF--FK6#%&thetaGF-FFFIFNFIF4F-F<*,FenF-FfnF-FFF IFNFIF6F-F<**FenF-FfnF-FFFIFNFIFF-F<*(F7F-FFFIF@ F-F-*,FenF--FSFgnF-FFFIFNFIF4F-F-*,FenF-FdpF-FFFIFNFIF6F-F-**FenF-FdpF -FFFIFNFIF-F-FFF[oFNF]o-F_o6#*(,&*(F7F-FRF-FNFIF-*(F+F-FJF-FFFIF-F-FNF ]oFFF]oF-F-*(,4*(F>F-FFFIF4F-F-*(F>F-FFFIF6F-F-*&F>F-FFFIF-*(F.FIFJF-F 4F-F<*(F.FIFJF-F6F-F<*&F.FIFJF-F<**FNFIFFFIF7F-F;F-F<*(FNFIFFFIF>F-F-* (FNFIFFFIF@F-F " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 404 "Le but est d'obtenir un e \351quation en t au moins du quatri\350me degr\351, de fa\347on \340 compl\351ter (en permettant une construction) ce qui a \351t\351 prou v\351 th\351oriquement par diverses m\351thodes, pour r\351pondre \340 ma question Q38 dans la RMS, r\351ponse qui va \351tre publi\351e par Tissier dans une prochaine RMS. Ainsi cela confortera qu'il y a au mo ins quatre couples de points des deux cercles, dont la distance est ex tr\351male. " }}}}{MARK "26 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }