{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 } {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 "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 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 Outpu t" -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 Plot" -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 {SECT 0 {PARA 3 "" 0 "" {TEXT -1 6 "Macros" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "with(geom3d):with(plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 195 "p olyedre:=proc(pts,faces) local i,j,nb_faces, nb_sommets; nb_faces:=nop s(faces); nb_sommets:=nops(faces[1]); polygonplot3d([seq([seq(pts[face s[i][j]],j=1..nb_sommets)],i=1..nb_faces)]); end proc:" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 76 "my_mod:=proc(i,m) local j; j:=i mod m; if j=0 \+ then m else j end if end proc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 206 " centres:=proc(pts,faces) local i,j,k,nb_sommets,nb_faces; nb_faces:=no ps(faces); nb_sommets:=nops(faces[1]); [seq([seq(sum(pts[faces[i][k]][ j],k=1..nb_sommets)/nb_sommets,j=1..3)],i=1..nb_faces)]; end proc:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "centre:=proc(pts) centres(pts,[[seq (i,i=1..nops(pts))]]) end proc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "r_circonscrit:=proc(pts) local g,p; point(g,op(centre(pts))); point(p ,op(pts[1])); distance(g,p); end proc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 205 "r_inscrit:=proc(pts,faces) local g,p,q,r,P; point(g,op(centre (pts))); point(p,op(pts[faces[1][1]])); point(q,op(pts[faces[1][2]])); point(r,op(pts[faces[1][3]])); plane(P,[p,q,r]); distance(g,P); end p roc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "Kepler:=proc(n) local pts, faces; pts:=pts||n; faces:=faces||n; simplify(convert(r_circonscrit(pt s)/r_inscrit(pts,faces),radical)) end proc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "Plan\350tes := ['Mercure', 'V\351nus', 'Terre', 'Mar s', 'C\351r\350s', \"Ast\351ro\357des 2\", 'Jupiter', 'Saturne', 'Chir on', 'Uranus', 'Neptune', 'Pluton']:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "Distances:=[0.39,0.72,1,1.52,2.9,3.9,5.2,9.54,13.7,19.18,30.1,39 .5]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "Plan\350tes := ['Mercure', 'V\351nus', 'Terre', 'Mars', 'C\351r\350s', 'Jupiter', 'Saturne', 'Ur anus', 'Neptune', 'Pluton']:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "Dis tances:=[0.39,0.72,1,1.52,2.9,5.2,9.54,19.18,30.1,39.5]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "setoptions(labels=[\"\",\"Distance au Soleil \+ en U.A.\"]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 237 "MC:=proc(p,d,t) lo cal i,lbl,nb; global Plan\350tes, Distances; nb:=nops(p); lbl:=[seq(i= Plan\350tes[p[i]],i=1..nb)]; plot([[seq([i,d[i]],i=1..nb)],[seq([i,D istances[p[i]]],i=1..nb)]],0..nb,xtickmarks=lbl,legend=[t,\"Observatio ns\"]); end proc:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "Titius:=proc( m) local n,pl,d_Titius; pl:=[seq(n,n=1..m)]: d_Titius:=map(x->0.39+0.2 9*2^(x-2),pl): MC(pl,d_Titius,\"Loi de Titius-Bode\"); end proc:" }} {PARA 7 "" 1 "" {TEXT -1 43 "Warning, the name polar has been redefine d\n" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 12 "Le T\351tr a\350dre" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "On prend deux points A et B au hasard dans l'espace." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "point(a,0,0,0): point(b,1,0,0):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 159 "L'ensemble des points \351quidistants de A et B forme le plan d'\351quation x=1/2. Et, parmi ceux-ci, ceux qui sont \340 une d istance AB de A et de B forment un cercle." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 83 "x:='x': y:='y': z:='z': X:='X': Y:='Y': Z:='Z': poi nt(c,[x,y,z]): point(d,[X,Y,Z]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "plan_mediateur := solve(distance(a,c)=distance(b,c)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/plan_mediateurG<%/%\"xG#\"\"\" \"\"#/%\"yGF,/%\"zGF." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "ce rcle := solve(\{distance(a,b)=distance(a,c),distance(a,b)=distance(b,c )\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cercleG<%/%\"xG#\"\"\"\"\" #/%\"zGF,/%\"yG,$*&F(F)-%'RootOfG6$,(*$)%#_ZGF*F)F)\"\"$!\"\"*&\"\"%F) )F,F*F)F)/%&labelG%$_L1GF)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 154 " On choisit deux points C et D sur ce cercle, \340 une distance de AB l 'un de l'autre et on a ainsi quatre points \351quidistants, formant un t\351tra\350dre r\351gulier." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "eq_d:=subs(\{x=X,y=Y,z=Z\},cercle): assign(cercle); assign(eq_d) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "sols:=solve(\{distanc e(c,d)=distance(a,b)\}); z:=3^(1/2)/2: Z:=3^(1/2)/6: y:=simplify(conve rt(y,radical)): Y:=simplify(convert(Y,radical)):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solsG6&<$/%\"ZG,&*&\"\"$!\"\"%\"zG\"\"\"F.*&F+F,,&\" \"'F.*&\"\")F.)F-\"\"#F.F,#F.F5F./F-F-<$/F(,&*&F+F,F-F.F.*&F+F,F0F6F,F 7<$/F-,$*&F1F,F+F6F./F(,$*&F5F,F+F6F.<$/F-,$*&F1F,F+F6F,/F(,$*&F5F,F+F 6F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "x,y,z; X,Y,Z;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%#\"\"\"\"\"#\"\"!,$*&F%!\"\"\"\"$F#F$ " }}{PARA 11 "" 1 "" {XPPMATH 20 "6%#\"\"\"\"\"#,$*(\"\"$!\"\"F%F#F(F# F$,$*&\"\"'F)F(F#F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "pts 4:=[[0,0,0],[1,0,0],[x,y,z],[X,Y,Z]]: faces4:=[[1,2,4],[1,3,4],[2,3,4] ,[1,2,3]]: polyedre(pts4,faces4);" }}{PARA 13 "" 1 "" {GLPLOT3D 485 485 485 {PLOTDATA 3 "6#-%)POLYGONSG6&7%7%$\"\"!F)F(F(7%$\"\"\"F)F(F(7% $\"+++++]!#5$\"+4e'\\;)F0$\"+Z8v')GF07%F'7%F.F($\"+SSDg')F0F-7%F*F6F-7 %F'F*F6" 1 2 0 1 10 0 2 1 1 1 2 1.000000 45.000000 45.000000 0 0 "Curv e 1" }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 7 "Le Cube" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "On prend simplement les points de l'espace dont toutes les coordonn\351es sont de valeur absolue 1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "pts6:=[seq(seq(seq([(-1)^i,(-1)^j,(-1)^k] ,k=1..2),j=1..2),i=1..2)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%pts6G 7*7%!\"\"F'F'7%F'F'\"\"\"7%F'F)F'7%F'F)F)7%F)F'F'7%F)F'F)7%F)F)F'7%F)F )F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Les faces sont obtenues en fixant l'une des coordonn\351es." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "faces6:=[[1,2,4,3],[5,6,8,7],[1,2,6,5],[3,4,8,7],[1,3 ,7,5],[2,4,8,6]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'faces6G7(7&\" \"\"\"\"#\"\"%\"\"$7&\"\"&\"\"'\"\")\"\"(7&F'F(F-F,7&F*F)F.F/7&F'F*F/F ,7&F(F)F.F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "polyedre(pts 6,faces6);" }}{PARA 13 "" 1 "" {GLPLOT3D 485 485 485 {PLOTDATA 3 "6#-% )POLYGONSG6(7&7%$!\"\"\"\"!F(F(7%F(F($\"\"\"F*7%F(F,F,7%F(F,F(7&7%F,F( F(7%F,F(F,7%F,F,F,7%F,F,F(7&F'F+F2F17&F/F.F3F47&F'F/F4F17&F+F.F3F2" 1 2 0 1 10 0 2 1 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 10 "L'octa\350dre" }}{EXCHG {PARA 0 " " 0 "" {TEXT -1 122 "On prend les centres des faces d'un cube ! Les fa ces sont les triangles obtenus avec trois points non oppos\351s deux \+ \340 deux." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "pts8:=centres (pts6,faces6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%pts8G7(7%!\"\"\" \"!F(7%\"\"\"F(F(7%F(F'F(7%F(F*F(7%F(F(F'7%F(F(F*" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 233 "faces8:=NULL: for i to nops(pts8)-2 do for \+ j from i+1 to nops(pts8)-1 do for k from j+1 to nops(pts8) do l:=[i,j, k]; if product(sum(pts8[l[n]][m],n=1..3),m=1..3)<>0 then faces8:=faces 8,l end if end do end do end do; faces8:=[faces8];" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%'faces8G7*7%\"\"\"\"\"$\"\"&7%F'F(\"\"'7%F'\"\"%F)7 %F'F-F+7%\"\"#F(F)7%F0F(F+7%F0F-F)7%F0F-F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "polyedre(pts8,faces8);" }}{PARA 13 "" 1 "" {GLPLOT3D 485 485 485 {PLOTDATA 3 "6#-%)POLYGONSG6*7%7%$!\"\"\"\"!$F*F *F+7%F+F(F+7%F+F+F(7%F'F,7%F+F+$\"\"\"F*7%F'7%F+F0F+F-7%F'F3F/7%7%F0F+ F+F,F-7%F6F,F/7%F6F3F-7%F6F3F/" 1 2 0 1 10 0 2 1 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "Le dod\351ca\350dre" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 131 "On \+ part d'un pentagone r\351gulier dans le plan z=0 et d'un pentagone r \351gulier dans le plan z=h obtenu en d\351calant le premier de pi/5. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 125 "penta1:=[seq([cos(2*i* Pi/5),sin(2*i*Pi/5),0],i=0..4)]: h:='h': penta2:=[seq([cos((2*i+1)*Pi/ 5),sin((2*i+1)*Pi/5),h],i=0..4)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "polygonplot3d([penta1,subs(h=1/2,penta2)],scaling=CON STRAINED);" }}{PARA 13 "" 1 "" {GLPLOT3D 485 485 485 {PLOTDATA 3 "6$-% )POLYGONSG6$7'7%$\"\"\"\"\"!$F*F*F+7%$\"+Q*p,4$!#5$\"+l^c5&*F/F+7%$!+V *p,4)F/$\"+CD&y(eF/F+7%F3$!+CD&y(eF/F+7%F-$!+l^c5&*F/F+7'7%$\"+V*p,4)F /F5$\"+++++]F/7%$!+Q*p,4$F/F0FA7%$!\"\"F*F+FA7%FDF;FA7%F?F8FA-%(SCALIN GG6#%,CONSTRAINEDG" 1 2 0 1 10 0 2 1 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 151 "On ch oisit h de sorte la distance d'un sommet du premier polygone au sommet le plus proche du second soit exactement la longueur d'un c\364t\351 \+ du polygone," }}{PARA 0 "" 0 "" {TEXT -1 90 "de sorte \340 obtenir des faces qui soient des triangles \351quilat\351raux. On trouve h=1 (ou \+ -1)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "point(a,op(penta1[1 ])): point(b,op(penta1[2])): point(c,op(penta2[1])):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "sols:=solve(distance(a,b)=distance(a,c),h );h:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solsG6$\"\"\"!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG\"\"\"" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 292 "Soit O1 et O2 les centres des deux pentagones et O leu r milieu. Tous les points des deux pentagones sont \351quidistants de \+ O, disons \340 la distance d. La sph\350re de centre O et de rayon d r ecoupe la droite (O1O2) en deux points D1 et D2 qui, avec les dix poin ts pr\351c\351dents, forment un dod\351ca\350dre." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 114 "z:='z': point(O,0,0,h/2): point(d,[0,0,z]): sols:=solve(distance(O,a)=distance(O,d),z): sols:=min(sols),max(sols) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solsG6$,&#\"\"\"\"\"#F(*&F)!\" \"\"\"&F'F+,&F'F(*&F)F+F,F'F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "pts12:=[op(penta1),op(penta2),seq([0,0,sols[i]],i=1..2)]: simpli fy(convert(pts12,radical));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7.7%\" \"\"\"\"!F&7%,&#F%\"\"%!\"\"*&F*F+\"\"&#F%\"\"#F%,$*(F*F+F/F.,&F-F%*$F -F.F%F.F%F&7%,&#F%F*F+*&F*F+F-F.F+,$*(F*F+F/F.,&F-F%F3F+F.F%F&7%F5,$*( F*F+F/F.F:F.F+F&7%F(,$*(F*F+F/F.F2F.F+F&7%,&#F%F*F%*&F*F+F-F.F%F8F%7%, &*&F*F+F-F.F+FCF%F0F%7%F+F&F%7%FFF?F%7%FBF " 0 "" {MPLTEXT 1 0 122 "faces12:=[seq(op([[i,m y_mod(i+1,5),i+5],[i,my_mod(i+1,5),11], [i,i+5,5+my_mod(i-1,5)],[i+5,5 +my_mod(i-1,5),12]]),i=1..5)];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(f aces12G767%\"\"\"\"\"#\"\"'7%F'F(\"#67%F'F)\"#57%F)F-\"#77%F(\"\"$\"\" (7%F(F1F+7%F(F2F)7%F2F)F/7%F1\"\"%\"\")7%F1F7F+7%F1F8F27%F8F2F/7%F7\" \"&\"\"*7%F7F=F+7%F7F>F87%F>F8F/7%F=F'F-7%F=F'F+7%F=F-F>7%F-F>F/" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "polyedre(pts12,faces12);" }} {PARA 13 "" 1 "" {GLPLOT3D 485 485 485 {PLOTDATA 3 "6#-%)POLYGONSG667% 7%$\"\"\"\"\"!$F*F*F+7%$\"+Q*p,4$!#5$\"+l^c5&*F/F+7%$\"+V*p,4)F/$\"+CD &y(eF/F(7%F'F,7%F+F+$!+!))R.='F/7%F'F27%F3$!+CD&y(eF/F(7%F2F<7%F+F+$\" +))R.=;!\"*7%F,7%$!+V*p,4)F/F5F+7%$!+Q*p,4$F/F0F(7%F,FEF87%F,FHF27%FHF 2F@7%FE7%FFF=F+7%$!\"\"F*F+F(7%FEFOF87%FEFPFH7%FPFHF@7%FO7%F-$!+l^c5&* F/F+7%FIFXF(7%FOFWF87%FOFZFP7%FZFPF@7%FWF'F<7%FWF'F87%FWF " 0 "" {MPLTEXT 1 0 64 "pts20:=centres (pts12,faces12): simplify(convert(pts20,radical));" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#767%,&#\"\"\"\"\"$F'*&\"\"'!\"\"\"\"&#F'\"\"#F',&*(\" #7F+F.F-,&F,F'*$F,F-F'F-F'*(F1F+F.F-,&F,F'F3F+F-F'F&7%,&#F'\"\"%F'*&F1 F+F,F-F',$*(F1F+F.F-F2F-F',&#F'F*F'*&F*F+F,F-F+7%,&F-F'*&F*F+F,F-F'\" \"!#F.F(7%,&F>F'*&F*F+F,F-F'FC,&#F,F*F'*&F*F+F,F-F'7%,&#F'F1F+*&F1F+F, F-F+,&*(F*F+F.F-F2F-F'*(F1F+F.F-F5F-F'F&7%#F+F*F/F=7%,&#F'F1F'*&F1F+F, F-F'FOFD7%F>F/FH7%,&#F'F.F+*&F*F+F,F-F+FCF&7%,&#F'F*F+*&F*F+F,F-F+FCF= 7%,&#F'F(F+*&F*F+F,F-F+F/FD7%,&#F'F9F+*&F1F+F,F-F+F;FH7%FL,&*(F1F+F.F- F5F-F+*(F*F+F.F-F2F-F+F&7%FS,&*(F1F+F.F-F5F-F+*(F1F+F.F-F2F-F+F=7%F\\o FhoFD7%F`o,$*(F1F+F.F-F2F-F+FH7%F%FhoF&7%F7F]pF=7%FUFdoFD7%F>FhoFH" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 189 "faces20:=[[1,2,18,17,3],[5 ,7,1,2,6],[6,5,11,9,10],[9,10,14,13,15],[13,14,18,17,19],[1,3,4,8,7], \+ [5,7,8,12,11],[9,11,12,16,15],[13,15,16,20,19],[4,3,17,19,20],[2,6,10, 14,18],[4,8,12,16,20]];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(faces20G 7.7'\"\"\"\"\"#\"#=\"#<\"\"$7'\"\"&\"\"(F'F(\"\"'7'F/F-\"#6\"\"*\"#57' F2F3\"#9\"#8\"#:7'F6F5F)F*\"#>7'F'F+\"\"%\"\")F.7'F-F.F<\"#7F17'F2F1F> \"#;F77'F6F7F@\"#?F97'F;F+F*F9FB7'F(F/F3F5F)7'F;FF@FB" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "polyedre(pts20,faces20);" }}{PARA 13 "" 1 "" {GLPLOT3D 485 485 485 {PLOTDATA 3 "6#-%)POLYGONSG6.7'7%$\"+ $H8,1(!#5$\"+iDZH^F*$\"+LLLLLF*7%$\"+z**QjVF*$\"+)Q)=qJF*$!+&H8,1#F*7% F0$!+)Q)=qJF*F47%F($!+iDZH^F*F-7%$\"+i*zns)F*$\"\"!F@$\"+nmmmmF*7'7%$! +9Ls'p#F*$\"+^4m*H)F*F-7%$\"+9Ls'p#F*FGFAF'F/7%$!+ommm;F*F+F47'FLFD7%$ !+$H8,1(F*F+FA7%$!+i*zns)F*F?F-7%$!+HmW$R&F*F?F47'FSFV7%FMF:F47%FE$!+^ 4m*H)F*F-7%FQF:FA7'FenFZF6F97%FJFfnFA7'F'F<7%$\"+HmW$R&F*F?$\"+I8,17! \"*7%$\"+ommm;F*F+F_oFI7'FDFIFbo7%$!+z**QjVF*F2F_oFP7'FSFPFfo7%FgoF7F_ oFhn7'FenFhnFjo7%FcoF:F_oFjn7'F\\oF " 0 "" {MPLTEXT 1 0 17 "n:=[4,6,8,12,20]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "rapports:=map(Kepler,n);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)rapportsG7'\"\"$*$F&#\"\"\"\"\"#F',$*,F*F)\"\"&F(,* \"#qF)*&\"#?F)F-F(!\"\"*(F-F),&F-F)*$F-F(F)F(,&F-F)F5F2F(F2**F*F)F4F(F 6F(F-F(F)F(F*F(,**&F-F)F4F(F2*&F-F)F6F(F2*&F6F(F-F(F)*&F4F(F-F(F2F2F2, $*.F*F),(\"#:F)*&\"\"%F)F-F(F)*&F4F(F6F(F)F(,&\"#DF)*&\"#5F)F-F(F)F(F* F(F4#F2F*,&F@F)*&\"\"(F)F-F(F)F2F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "r:=evalf(rapports);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"rG7'$\"\"$\"\"!$\"+330K " 0 "" {MPLTEXT 1 0 91 "T:=1: V:=T/r[5] : Me:=V/r[3]: Ma:=T*r[4]: J:=Ma*r[1]: S:=J*r[2]: d_Kepler:=[Me,V,T,Ma ,J,S];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)d_KeplerG7($\"+N(Rze%!#5$ \"+DZaYzF(\"\"\"$\"+r&3%e7!\"*$\"+8dAvPF.$\"+ZF))QlF." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Ceci est \340 comparer aux observations : " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "MC([1,2,3,4,6,7],d_Kepl er,\"Kepler\"); " }}{PARA 13 "" 1 "" {GLPLOT2D 485 485 485 {PLOTDATA 2 "6'-%'CURVESG6%7(7$$\"\"\"\"\"!$\"31+++N(Rze%!#=7$$\"\"#F*$\"3')**** *\\sWl%zF-7$$\"\"$F*F(7$$\"\"%F*$\"3#******4d3%e7!#<7$$\"\"&F*$\"3?+++ 8dAvPF;7$$\"\"'F*$\"3s*****pu#))QlF;-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*F M-%'LEGENDG6#Q'Kepler6\"-F$6%7(7$F($\"39+++++++RF-7$F/$\"3u*********** **>(F-F37$F7$\"3-++++++?:F;7$F=$\"3;+++++++_F;7$FB$\"3:************R&* F;-FG6&FIFMFJFM-FO6#Q-ObservationsFR-%*AXESTICKSG6$7(/F)%(MercureG/F0% &V|dynusG/F5%&TerreG/F8%%MarsG/F>%(JupiterG/FC%(SaturneG%(DEFAULTG-%+A XESLABELSG6$Q!FRQ;Distance~au~Soleil~en~U.A.FR-%%VIEWG6$;FMFBFdp" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Kepler" "Observat ions" }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 40 "Le Myst\350re du Monde selon Titius et Bode" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "Pla netes_connues:=[1,2,3,4,6,7]: Planetes_supposees:=[seq(n,n=1..7)]:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 460 "plot([seq([n, Distances[Pl anetes_connues[n]]], n=1..6)], 0..6, labels=[\"Plan\350tes connues\", \"Distance en U.A.\"]); plot([[seq([n, log(Distances[Planetes_connues[ n]])],n=1..4)],[seq([n, log(Distances[Planetes_connues[n]])],n=5..6)]] , 0..6, axes=FRAME,labels=[\"Plan\350tes connues\",\"log(distance)\"], colour=[red,red]); plot([seq([n, log(Distances[Planetes_supposees[n]]) ],n=1..7)], 0..7, axes=FRAME, labels=[\"Plan\350tes en incluant la pla n\350te suppos\351e\",\"log(distance)\"]);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7(7$$\"\"\"\"\"!$\"39 +++++++R!#=7$$\"\"#F*$\"3u*************>(F-7$$\"\"$F*F(7$$\"\"%F*$\"3- ++++++?:!#<7$$\"\"&F*$\"3;+++++++_F;7$$\"\"'F*$\"3:************R&*F;-% 'COLOURG6&%$RGBG$\"#5!\"\"$F*F*FM-%+AXESLABELSG6%Q1Plan|cytes~connues6 \"Q1Distance~en~U.A.FR-%%FONTG6#%(DEFAULTG-%%VIEWG6$;FMFBFW" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}{PARA 13 "" 1 "" {GLPLOT2D 485 485 485 {PLOTDATA 2 "6'-%'CURVESG6$7&7$$\"\"\"\" \"!$!3T+++*R&3;%*!#=7$$\"\"#F*$!35+++q1/&G$F-7$$\"\"$F*$F*F*7$$\"\"%F* $\"3!)******[L5(=%F--%'COLOURG6&%$RGBG$\"*++++\"!\")F6F6-F$6$7$7$$\"\" &F*$\"3-+++E'e'[;!#<7$$\"\"'F*$\"39+++&[$\\bAFKF<-%+AXESLABELSG6%Q1Pla n|cytes~connues6\"Q.log(distance)FU-%%FONTG6#%(DEFAULTG-%*AXESSTYLEG6# %&FRAMEG-%%VIEWG6$;F6FMFZ" 1 2 0 1 10 0 2 9 1 3 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}{PARA 13 "" 1 "" {GLPLOT2D 485 485 485 {PLOTDATA 2 "6&-%'CURVESG6$7)7$$\"\"\"\"\"!$!3T+++*R&3;%*!#=7$ $\"\"#F*$!35+++q1/&G$F-7$$\"\"$F*$F*F*7$$\"\"%F*$\"3!)******[L5(=%F-7$ $\"\"&F*$\"3'******pt5Z1\"!#<7$$\"\"'F*$\"3-+++E'e'[;FA7$$\"\"(F*$\"39 +++&[$\\bAFA-%'COLOURG6&%$RGBG$\"#5!\"\"F6F6-%+AXESLABELSG6%QIPlan|cyt es~en~incluant~la~plan|cyte~suppos|dye6\"Q.log(distance)FW-%%FONTG6#%( DEFAULTG-%*AXESSTYLEG6#%&FRAMEG-%%VIEWG6$;F6FHFfn" 1 2 0 1 10 0 2 9 1 3 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "Comparons le r\351sultat obtenu en utilisant la \"lo i\" de Titius-Bode et les observations :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Titius(8); Titius(10);" }}{PARA 13 "" 1 "" {GLPLOT2D 485 485 485 {PLOTDATA 2 "6'-%'CURVESG6%7*7$$\"\"\"\"\"!$\"3K++++++]`!# =7$$\"\"#F*$\"3[+++++++oF-7$$\"\"$F*$\"3u*************p*F-7$$\"\"%F*$ \"3/++++++]:!#<7$$\"\"&F*$\"3'*************4FF=7$$\"\"'F*$\"3D++++++I] F=7$$\"\"(F*$\"3#*************p'*F=7$$\"\")F*$\"3%************\\*=!#;- %'COLOURG6&%$RGBG$\"#5!\"\"$F*F*FZ-%'LEGENDG6#Q3Loi~de~Titius-Bode6\"- F$6%7*7$F($\"39+++++++RF-7$F/$\"3u*************>(F-7$F4F(7$F9$\"3-++++ ++?:F=7$F?$\"3!***************GF=7$FD$\"3;+++++++_F=7$FI$\"3:********* ***R&*F=7$FN$\"3(************z\">FR-FT6&FVFZFWFZ-Ffn6#Q-ObservationsFi n-%*AXESTICKSG6$7*/F)%(MercureG/F0%&V|dynusG/F5%&TerreG/F:%%MarsG/F@%& C|dyr|cysG/FE%(JupiterG/FJ%(SaturneG/FO%'UranusG%(DEFAULTG-%+AXESLABEL SG6$Q!FinQ;Distance~au~Soleil~en~U.A.Fin-%%VIEWG6$;FZFNF\\r" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Loi de Titius-Bode" " Observations" }}}{PARA 13 "" 1 "" {GLPLOT2D 485 485 485 {PLOTDATA 2 "6 '-%'CURVESG6%7,7$$\"\"\"\"\"!$\"3K++++++]`!#=7$$\"\"#F*$\"3[+++++++oF- 7$$\"\"$F*$\"3u*************p*F-7$$\"\"%F*$\"3/++++++]:!#<7$$\"\"&F*$ \"3'*************4FF=7$$\"\"'F*$\"3D++++++I]F=7$$\"\"(F*$\"3#********* ****p'*F=7$$\"\")F*$\"3%************\\*=!#;7$$\"\"*F*$\"3!)*********** 4v$FR7$$\"#5F*$\"3c***********HY(FR-%'COLOURG6&%$RGBG$FZ!\"\"$F*F*F]o- %'LEGENDG6#Q3Loi~de~Titius-Bode6\"-F$6%7,7$F($\"39+++++++RF-7$F/$\"3u* ************>(F-7$F4F(7$F9$\"3-++++++?:F=7$F?$\"3!***************GF=7$ FD$\"3;+++++++_F=7$FI$\"3:************R&*F=7$FN$\"3(************z\">FR 7$FT$\"39++++++5IFR7$FY$\"3+++++++]RFR-Fhn6&FjnF]oF[oF]o-F_o6#Q-Observ ationsFbo-%*AXESTICKSG6$7,/F)%(MercureG/F0%&V|dynusG/F5%&TerreG/F:%%Ma rsG/F@%&C|dyr|cysG/FE%(JupiterG/FJ%(SaturneG/FO%'UranusG/FU%(NeptuneG/ FZ%'PlutonG%(DEFAULTG-%+AXESLABELSG6$Q!FboQ;Distance~au~Soleil~en~U.A. Fbo-%%VIEWG6$;F]oFYF_s" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Loi de Titius-Bode" "Observations" }}}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "7 2 2 0" 2 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }