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{TEXT -1 50 "Warning, the name changecoords has been redefined \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "a=sqrt(p^2+q^2),b=sqr t(q^2+r^2),c=sqrt(p^2+r^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%/%\"aG* $,&*$)%\"pG\"\"#\"\"\"F+*$)%\"qGF*F+F+#F+F*/%\"bG*$,&F,F+*$)%\"rGF*F+F +F//%\"cG*$,&F'F+F4F+F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 " p:=sqrt(b^2+c^2-a^2):q:=sqrt(a^2+c^2-b^2):r:=sqrt(a^2+b^2-c^2):pp:=(a+ b+c)/2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "r2:=simplify((pp -a)*(pp-b)*(pp-c)/pp);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r2G,$*,\" \"%!\"\",(%\"aGF(%\"bG\"\"\"%\"cGF,F,,(F*F,F+F(F-F,F,,(F*F(F+F(F-F,F,, (F*F,F+F,F-F,F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f:=x/p +y/q+z/r;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,(*&%\"xG\"\"\",(*$ )%\"bG\"\"#F(F(*$)%\"cGF-F(F(*$)%\"aGF-F(!\"\"#F4F-F(*&%\"yGF(,(F1F(F. 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the name changecoords ha s been redefined\n" }}}{PARA 13 "" 1 "" {TEXT -1 5 "resta" }{MPLTEXT 1 0 0 "" }{TEXT -1 3 "rt:" }}{EXCHG {PARA 7 "" 1 "" {TEXT -1 50 "Warni ng, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 51 "a:=sqrt(p^2+q^2):b:=sqrt(q^2+r^2):c:=sqrt(p^2+ r^2):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "pp:=(a+b+c)/2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "r2:=simplify((pp-a)*(pp-b)*(pp-c)/pp);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#r2G,$*,\"\"%!\"\",(*$,&*$)%\"pG\"\"#\"\"\"F0* $)%\"qGF/F0F0#F0F/F(*$,&F1F0*$)%\"rGF/F0F0F4F0*$,&F,F0F7F0F4F0F0,(F*F( F5F0F:F(F0,(F*F0F5F0F:F(F0,(F*F0F5F0F:F0F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "A:=numer(expand(r2))-denom(expand(r2))/2+(p^2+q ^2)^(1/2)*(q^2+r^2)^(1/2)*(p^2+r^2)^(1/2);B:=(p^2+q^2)^(1/2)*(q^2+r^2) ^(1/2)*(p^2+r^2)^(1/2);eq3:=A^2=B^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"AG,.*&)%\"qG\"\"#\"\"\",&*$)%\"pGF)F*F**$)%\"rGF)F*F*#F*F)F**&,& *$F'F*F*F/F*F2F-F*F**&,&F,F*F5F*F2F0F*F**$F7F2!\"\"*$F4F2F9*$F+F2F9" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG*(,&*$)%\"pG\"\"#\"\"\"F+*$)%\" qGF*F+F+#F+F*,&F,F+*$)%\"rGF*F+F+F/,&F'F+F1F+F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq3G/*$),.*&)%\"qG\"\"#\"\"\",&*$)%\"pGF,F-F-*$)%\"r GF,F-F-#F-F,F-*&,&*$F*F-F-F2F-F5F0F-F-*&,&F/F-F8F-F5F3F-F-*$F:F5!\"\"* $F7F5F<*$F.F5F " 0 "" {MPLTEXT 1 0 15 "f:=x/p+y/q+z/r;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"fG,(*&%\"xG\"\"\"%\"pG!\"\"F(*&%\"yGF(%\"qGF*F(*&%\"zGF(%\"rGF*F(" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "eq1:=diff(r2,p)*diff(f,q)- diff(r2,q)*diff(f,p):eq2:=diff(r2,q)*diff(f,r)-diff(r2,r)*diff(f,q):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "sol:=solve(\{f=1,eq1,eq2 \},\{x,y,z\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assign(so l);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#,$**\"\"#!\"\"%\"pG\"\"$,L**F%\"\"\"),&*$)%\"qGF%F+F+ *$)%\"rGF%F+F+#F(F%F+,&*$)F'F%F+F+F.F+#F+F%,&F6F+F1F+F8F+**F%F+F/F+F-F 8F2F+F&**F(F+F/F+F5F8F2F+F+*&)F9F4F+F2F+F&*&)F5F4F+F/F+F&*&F?F+F2F+F&* &F,F+F/F+F&*&F5F8)F0\"\"%F+F+*(F%F+F5F8)F3FDF+F+*(F/F+F5F8F7F+F+*(F5F8 F2F+F7F+F+**F(F+F9F8F2F+F/F+F+*&F-F8FCF+F+*&F9F8FFF+F+*&F,F+F2F+F&*(F% F+F,F+F7F+F&*(F7F+F9F8F/F+F+*(F%F+F9F8FCF+F+*(F9F8F2F+F7F+F+*&F-F8FFF+ F+*&F/F+F=F+F&F+,do*&)F'FDF+F,F+F&*&FCF+F=F+F&*(F2F+F5F8FCF+F+*(F2F+F? F+F7F+F&*(F2F+F=F+F7F+F&*(F2F+F=F+F/F+F&*(F2F+F-F8FCF+F+*(F2F+F9F8FUF+ F+*(F2F+F?F+F/F+F&*(F2F+F,F+F7F+F&*(FFF+F-F8F7F+F+*(FFF+F-F8F/F+F+*(FF F+F9F8F7F+F+*(FFF+F9F8F/F+F+*(F2F+F5F8FUF+F+*(F2F+F,F+F/F+F&*(FFF+F5F8 F7F+F+*(FFF+F5F8F/F+F+*(F/F+F-F8FUF+F+*(F7F+F,F+F/F+F&*(F7F+F5F8FCF+F+ *(F7F+F9F8FCF+F+*(F7F+F=F+F/F+F&*(FUF+F5F8F/F+F+*(F7F+F-F8FCF+F+*(FUF+ F9F8F/F+F+*(F7F+F?F+F/F+F&**F7F+F,F+F5F8F9F8F+*,F%F+F2F+F-F8F/F+F7F+F+ *,F%F+F2F+F9F8F/F+F7F+F+*,F%F+F2F+F5F8F/F+F7F+F+**F/F+F=F+F5F8F-F8F+*( F2F+F-F8FUF+F+*(F2F+F9F8FCF+F+*&FFF+F?F+F&**F2F+F?F+F-F8F9F8F+F&F+" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 179 "fonc:=proc(p,q)\nfsolve((q ^2*(p^2+r^2)^(1/2)+(q^2+r^2)^(1/2)*p^2+(p^2+q^2)^(1/2)*r^2-(p^2+q^2)^( 1/2)-(q^2+r^2)^(1/2)-(p^2+r^2)^(1/2))^2 = (p^2+q^2)*(q^2+r^2)*(p^2+r^2 ),r=0..5)\nend;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%foncGf*6$%\"pG% \"qG6\"F)F)-%'fsolveG6$/*$),.*&)9%\"\"#\"\"\",&*$)9$F4F5F5*$)%\"rGF4F5 F5#F5F4F5*&,&*$F2F5F5F:F5F=F8F5F5*&,&F7F5F@F5F=F;F5F5*$FBF=!\"\"*$F?F= FD*$F6F=FDF4F5*(FBF5F?F5F6F5/F<;\"\"!\"\"&F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "fonc(1,1/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+)fw\"Q!)!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot( fonc(1,x),'x'=1/2..1);" }}{PARA 8 "" 1 "" {TEXT -1 70 "Error, (in fsol ve) \{q, p\} are in the equation, and are not solved for\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot3d(fonc(p,q),p=1/2..1,q=1/2..1) ;" }}{PARA 8 "" 1 "" {TEXT -1 70 "Error, (in fsolve) \{q, p\} are in t he equation, and are not solved for\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "p:=1/2:q:=1 /2:rr:=fsolve(eq3,r=0..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#rrG$ \"+xwU&R\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 8 "" 1 "" {TEXT -1 78 "Error, (in plot3d/expression) bad range argumen ts: 1/2 = 0 .. 1, 1/2 = 0 .. 1\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "r:='r':;rr:=solve(eq3,r):" }}}{EXCHG {PARA 0 "> " 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 99 "eq:=\{f=1,r2=1,diff(r2,a)*diff(f,b)-diff(r2,b)*diff (f,a),diff(r2,b)*diff(f,c)-diff(r2,c)*diff(f,b)\}:" }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "eliminate(eq,\{a,b,c\});" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 425 "restart:\na:=1:\np:=a*cos(v)*cos(u); q:=a*cos(v)* sin(u); r:=a*sin(v);\nABC:=[[p,0,0],[0,q,0],[0,0,r]];\nplan:=x/p+y/q+z /r-1; \nprintf(\" 9 fois la distance du cdg du triangle ABC \340 l'ori gine : p^2+q^2+r^2 =%a\\n\",simplify(p^2+q^2+r^2));\nsys:=simplify(\{p lan,diff(plan,u),diff(plan,v)\}):\nenveloppe:=subs(op(subs(cos(u)^2=1- sin(u)^2,cos(v)^2=1-sin(v)^2,\n simplify(solve( sys,\{x,y,z\}))))\n ,[x,y,z]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 366 "with(plots):\nABC:=[[p,0,0],[0,q,0],[0,0,r]]:\nn:=8: \nale:=rand(0..100)/100:\n# i=0..4*n),j=-n..n) # pour tout avoir\n# \+ i=1..n),j=1..n) # pour un huiti\350me \ndisplay([seq(seq(polygonpl ot3d(subs(u=i*Pi/2/n,v=j*Pi/2/n,ABC), color=COLOR(RGB,ale(),ale(),ale ())),i=1..n),j=1..n)],scaling=constrained,orientation=[-20,50],lightmo del=light2);\n\n#,style=wireframe,thickness=2" }{TEXT -1 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefin ed\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG*&-%$cosG6#%\"vG\"\"\"-F '6#%\"uGF*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG*&-%$cosG6#%\"vG\" \"\"-%$sinG6#%\"uGF*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG-%$sinG6 #%\"vG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ABCG7%7%*&-%$cosG6#%\"vG \"\"\"-F)6#%\"uGF,\"\"!F07%F0*&F(F,-%$sinGF.F,F07%F0F0-F4F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%planG,**(%\"xG\"\"\"-%$cosG6#%\"vG!\"\"-F *6#%\"uGF-F(*(%\"yGF(F)F--%$sinGF/F-F(*&%\"zGF(-F4F+F-F(F(F-" }}{PARA 6 "" 1 "" {TEXT -1 71 " 9 fois la distance du cdg du triangle ABC \340 l'origine : p^2+q^2+r^2 =1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*enve loppeG7%*&)-%$cosG6#%\"uG\"\"$\"\"\")-F)6#%\"vGF,F-*&)-%$sinGF*F,F-F.F -*$)-F5F0F,F-" }}{PARA 13 "" 1 "" {GLPLOT3D 496 496 496 {PLOTDATA 3 "6 _o-%)POLYGONSG6$7%7%$\"+iwR>'*!#5$\"\"!F,F+7%F+$\"+jrT8>F*F+7%F+F+$\"+ @K!4&>F*-%&COLORG6&%$RGBG$\"+++++**F*$\"+++++PF*$\"+++++oF*-F$6$7%7%$ \"+jWFh!*F*F+F+7%F+$\"+wFI`PF*F+F0-F46&F6$\"+++++EF*$\"+++++&*F*$\"+++ ++;F*-F$6$7%7%$\"+o:$\\:)F*F+F+7%F+$\"+p5&*[aF*F+F0-F46&F6$\"\"\"F,$\" +++++*)F*$\"+++++LF*-F$6$7%7%$\"+E#*>NpF*F+F+7%F+$\"+G#*>NpF*F+F0-F46& F6$\"+++++F*F+F+7%F+F( F+F0-F46&F6Fbq$\"+++++8F*$\"+++++\\F*-F$6$7%7%$!+oPi6?!#>F+F+7%F+$\"+/ G&y!)*F*F+F0-F46&F6$\"+++++YF*$\"+++++q!#6$\"+++++XF*-F$6$7%F@7%F+$\"+ c&*R-=F*F+7%F+F+$\"+DV$o#QF*-F46&F6$\"+++++VF*$\"+++++!)Fcs$\"+++++wF* -F$6$7%7%$\"+1R`N&)F*F+F+7%F+$\"+2R`NNF*F+F\\t-F46&F6$\"+++++eF*$\"+++ ++:F*F+-F$6$7%7%$\"+nvx\"o(F*F+F+7%F+$\"+s'*zK^F*F+F\\t-F46&F6$\"+++++ pF*Fet$\"+++++QF*-F$6$7%7%$\"+C[\"G`'F*F+F+7%F+$\"+D[\"G`'F*F+F\\t-F46 &F6$\"+++++\"*F*$FbsF*$\"+++++mF*-F$6$7%7%$\"+q'*zK^F*F+F+7%F+$\"+ovx 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