// fltk 7Fl_Tile 32 63 1061 63 25 [ // fltk N4xcas23Comment_Multiline_InputE 32 63 1061 62 25 Les niveaux 1 a 15 definissent la figure, y compris l'affichage de la longueur MN=sqrt(L).ŁA partir du niveau 16, on cherche le minimum de L analytiquement. , // fltk N4xcas10Log_OutputE 32 125 1061 1 25 ] , // fltk 7Fl_Tile 32 128 1061 531 25 [ // fltk N4xcas6FigureE 32 128 1061 530 25 // fltk N4xcas12History_PackE 34 -986 334 1644 25 [ // fltk 7Fl_Tile 62 -986 306 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -986 306 35 25 A:=point([2,0,0]); , // fltk N4xcas10Log_OutputE 62 -951 306 1 25 , // fltk N4xcas10Gen_OutputE 62 -950 306 32 14 pnt(pnt[[2,0,0],0,"A"]) ] , // fltk 7Fl_Tile 62 -916 306 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -916 306 35 25 B:=point([2,1,0]); , // fltk N4xcas10Log_OutputE 62 -881 306 1 25 , // fltk N4xcas10Gen_OutputE 62 -880 306 32 14 pnt(pnt[[2,1,0],0,"B"]) ] , // fltk 7Fl_Tile 62 -846 306 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -846 306 35 25 C:=point([-1,2,0]); , // fltk N4xcas10Log_OutputE 62 -811 306 1 25 , // fltk N4xcas10Gen_OutputE 62 -810 306 32 14 pnt(pnt[[-1,2,0],0,"C"]) ] , // fltk 7Fl_Tile 62 -776 306 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -776 306 35 25 O:=point([-1,0,2]); , // fltk N4xcas10Log_OutputE 62 -741 306 1 25 , // fltk N4xcas10Gen_OutputE 62 -740 306 32 14 pnt(pnt[[-1,0,2],0,"O"]) ] , // fltk 7Fl_Tile 62 -706 306 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -706 306 35 25 pyramide(O,A,B,C,affichage=vert+rempli); , // fltk N4xcas10Log_OutputE 62 -671 306 1 25 , // fltk 9Fl_Scroll 62 -670 306 59 14 [ // fltk N4xcas10Gen_OutputE 62 -670 1206 32 14 pnt(pnt[[[[-1,0,2],[2,0,0],[2,1,0]],[[-1,0,2],[2,1,0],[-1,2,0]],[[-1,0,2],[2,0,0],[-1,2,0]],[[2,0,0],[2,1,0],[-1,2,0]]],1073741826]) , // fltk 12Fl_Scrollbar 62 279 290 25 14 [] , // fltk 12Fl_Scrollbar 352 247 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 -609 306 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -609 306 35 25 droite(A,C,affichage=line_width_3+rouge) , // fltk N4xcas10Log_OutputE 62 -574 306 1 25 , // fltk 9Fl_Scroll 62 -573 306 59 14 [ // fltk N4xcas10Gen_OutputE 62 -573 387 32 14 pnt(pnt[line[[2,0,0],[-1,2,0]],131073]) , // fltk 12Fl_Scrollbar 62 279 290 25 14 [] , // fltk 12Fl_Scrollbar 352 247 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 -512 306 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -512 306 35 25 I:=milieu(A,B); , // fltk N4xcas10Log_OutputE 62 -477 306 1 25 , // fltk N4xcas10Gen_OutputE 62 -476 306 32 14 pnt(pnt[[2,1/2,0],0,"I"]) ] , // fltk 7Fl_Tile 62 -442 306 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -442 306 35 25 assume(t=[1.32,-1.0,2.0]) , // fltk N4xcas10Log_OutputE 62 -407 306 1 25 , // fltk N4xcas10Gen_OutputE 62 -406 306 32 14 parameter(t,-1.0,2.0,1.32) ] , // fltk 7Fl_Tile 62 -372 306 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -372 306 35 25 M:=element(droite(A,C),t); , // fltk N4xcas10Log_OutputE 62 -337 306 1 25 , // fltk 9Fl_Scroll 62 -336 306 59 14 [ // fltk N4xcas10Gen_OutputE 62 -336 729 32 14 pnt(pnt[[-1+t+2*t,2*(1-t),0],[0,[pnt(pnt[line[[2,0,0],[-1,2,0]],0]),t]],"M"]) , // fltk 12Fl_Scrollbar 62 279 290 25 14 [] , // fltk 12Fl_Scrollbar 352 247 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 -275 306 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -275 306 35 25 IM:=droite(I,M,affichage=hidden_name+bleu+line_width_3) , // fltk N4xcas10Log_OutputE 62 -240 306 1 25 , // fltk 9Fl_Scroll 62 -239 306 59 14 [ // fltk N4xcas10Gen_OutputE 62 -239 640 32 14 pnt(pnt[line[[2,1/2,0],[-1+t+2*t,2*(1-t),0]],-2147352572,"IM"]) , // fltk 12Fl_Scrollbar 62 279 290 25 14 [] , // fltk 12Fl_Scrollbar 352 247 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 -178 306 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -178 306 35 25 P:=orthogonal(I,IM,affichage=hidden_name); , // fltk N4xcas10Log_OutputE 62 -143 306 1 25 , // fltk 9Fl_Scroll 62 -142 306 59 14 [ // fltk N4xcas10Gen_OutputE 62 -142 775 32 14 pnt(pnt[hyperplan([[-1+t+2*t-2,2*(1-t)-1/2,0],[2,1/2,0]]),-2147483648,"P"]) , // fltk 12Fl_Scrollbar 62 279 290 25 14 [] , // fltk 12Fl_Scrollbar 352 247 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 -81 306 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 -81 306 35 25 OB:=droite(O,B,affichage=line_width_3+hidden_name) , // fltk N4xcas10Log_OutputE 62 -46 306 1 25 , // fltk 9Fl_Scroll 62 -45 306 59 14 [ // fltk N4xcas10Gen_OutputE 62 -45 504 32 14 pnt(pnt[line[[-1,0,2],[2,1,0]],-2147352576,"OB"]) , // fltk 12Fl_Scrollbar 62 279 290 25 14 [] , // fltk 12Fl_Scrollbar 352 247 16 43 14 [] ] ] , // fltk 7Fl_Tile 62 16 306 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 16 306 35 25 N:=inter_unique(P,OB); , // fltk N4xcas10Log_OutputE 62 51 306 1 25 , // fltk N4xcas10Gen_OutputE 62 52 306 32 14 Too large for display ] , // fltk 7Fl_Tile 62 86 306 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 86 306 35 25 L:=normal(longueur2(M,N)) , // fltk N4xcas10Log_OutputE 62 121 306 1 25 , // fltk 9Fl_Scroll 62 122 306 59 14 [ // fltk N4xcas10Gen_OutputE 62 122 733 32 14 (5096*t^4-20328*t^3+30686*t^2-20730*t+5283)/(392*t^2-840*t+450) , // fltk 12Fl_Scrollbar 62 156 306 25 14 [] , // fltk 12Fl_Scrollbar 368 122 16 34 14 [] ] ] , // fltk 7Fl_Tile 62 183 306 101 25 [ // fltk N4xcas19Multiline_Input_tabE 62 183 306 41 25 legende(O," MN="+evalf(sqrt(L))) , // fltk N4xcas10Log_OutputE 62 224 306 1 25 , // fltk 9Fl_Scroll 62 225 306 59 14 [ // fltk N4xcas10Gen_OutputE 62 225 473 32 14 pnt(pnt[[-1,0,2],63," MN=2.07392486078"]) , // fltk 12Fl_Scrollbar 62 259 306 25 14 [] , // fltk 12Fl_Scrollbar 368 225 16 34 14 [] ] ] , // fltk 7Fl_Tile 62 286 306 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 286 306 35 25 dL:=factor(diff(L,t)); , // fltk N4xcas10Log_OutputE 62 321 306 1 25 , // fltk 9Fl_Scroll 62 322 306 59 14 [ // fltk N4xcas10Gen_OutputE 62 322 701 32 14 (71344*t^4-295176*t^3+457380*t^2-315180*t+81513)/(14*t-15)^3 , // fltk 12Fl_Scrollbar 62 356 306 25 14 [] , // fltk 12Fl_Scrollbar 368 322 16 34 14 [] ] ] , // fltk 7Fl_Tile 62 383 306 95 25 [ // fltk N4xcas19Multiline_Input_tabE 62 383 306 35 25 sol:=proot(numer(dL),t); , // fltk N4xcas10Log_OutputE 62 418 306 1 25 , // fltk 9Fl_Scroll 62 419 306 59 14 [ // fltk N4xcas10Gen_OutputE 62 419 1127 32 14 [0.867558904443,0.986646833315+0.205660150628*i,0.986646833315-0.205660150628*i,1.29651006629] , // fltk 12Fl_Scrollbar 62 453 306 25 14 [] , // fltk 12Fl_Scrollbar 368 419 16 34 14 [] ] ] , // fltk 7Fl_Tile 62 480 306 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 480 306 35 25 subst(sqrt(L),t,sol[0]) , // fltk N4xcas10Log_OutputE 62 515 306 1 25 , // fltk N4xcas10Gen_OutputE 62 516 306 32 14 0.689762632051 ] , // fltk 7Fl_Tile 62 550 306 68 25 [ // fltk N4xcas19Multiline_Input_tabE 62 550 306 35 25 subst(sqrt(L),t,sol[3]) , // fltk N4xcas10Log_OutputE 62 585 306 1 25 , // fltk N4xcas10Gen_OutputE 62 586 306 32 14 2.06572876676 ] , // fltk 7Fl_Tile 62 620 306 36 25 [ // fltk N4xcas19Multiline_Input_tabE 62 620 306 35 25 , // fltk N4xcas10Log_OutputE 62 655 306 1 25 ] ] // fltk N4xcas5Geo3dE 386 159 587 499 25 -1.4995,3.4989,-0.9997,3.9988,[pnt(pnt[[2,0,0],0,"A"]),pnt(pnt[[2,1,0],0,"B"]),pnt(pnt[[-1,2,0],0,"C"]),pnt(pnt[[-1,0,2],0,"O"]),pnt(pnt[[[[-1,0,2],[2,0,0],[2,1,0]],[[-1,0,2],[2,1,0],[-1,2,0]],[[-1,0,2],[2,0,0],[-1,2,0]],[[2,0,0],[2,1,0],[-1,2,0]]],1073741826]),pnt(pnt[line[[2,0,0],[-1,2,0]],131073]),pnt(pnt[[2,1/2,0],0,"I"]),parameter(t,-1.0,2.0,1.32),pnt(pnt[[-1+t+2*t,2*(1-t),0],[0,[pnt(pnt[line[[2,0,0],[-1,2,0]],0]),t]],"M"]),pnt(pnt[line[[2,1/2,0],[-1+t+2*t,2*(1-t),0]],-2147352572,"IM"]),pnt(pnt[hyperplan([[-1+t+2*t-2,2*(1-t)-1/2,0],[2,1/2,0]]),-2147483648,"P"]),pnt(pnt[line[[-1,0,2],[2,1,0]],-2147352576,"OB"]),pnt(pnt[[-1+3*(3*(-1+t+2*t-2)+1/2*(2*(1-t)-1/2))/(7*t-15/2),(3*(-1+t+2*t-2)+1/2*(2*(1-t)-1/2))/(7*t-15/2),2-2*(3*(-1+t+2*t-2)+1/2*(2*(1-t)-1/2))/(7*t-15/2)],0,"N"]),(5096*t^4-20328*t^3+30686*t^2-20730*t+5283)/(392*t^2-840*t+450),pnt(pnt[[-1,0,2],63," MN=2.07392486078"]),(71344*t^4-295176*t^3+457380*t^2-315180*t+81513)/(14*t-15)^3,[0.867558904443,0.986646833315+0.205660150628*i,0.986646833315-0.205660150628*i,1.29651006629],0.689762632051,2.06572876676],-1.4995,3.4989,0.29699,-0.3033,-0.45767,-0.78124,0.5,0.5,0,2097152,1,2.5,0 , // fltk N4xcas10Log_OutputE 32 658 1061 1 25 ] , // fltk 7Fl_Tile 32 661 1061 36 25 [ // fltk N4xcas23Comment_Multiline_InputE 32 661 1061 35 25 On represente la longueur en fonction de t, avec OM=t*OA+(1-t)*OC (egalite de vecteurs) , // fltk N4xcas10Log_OutputE 32 696 1061 1 25 ] , // fltk 7Fl_Tile 32 699 1061 389 25 [ // fltk N4xcas19Multiline_Input_tabE 32 699 1061 35 25 plot(sqrt(L),t=-1..3) , // fltk N4xcas10Log_OutputE 32 734 1061 1 25 , // fltk 7Fl_Tile 32 735 1061 353 25 [ // fltk N4xcas7Graph2dE 32 735 911 353 25 -1,3,0,7.5,[pnt(pnt[curve(group[pnt[t+(i)*sqrt((5096*t^4-20328*t^3+30686*t^2-20730*t+5283)/(392*t^2-840*t+450)),t,-1.0,3.0],group[-1.0+6.98746116664*(i),-0.99+6.95165036447*(i),-0.98+6.91584179716*(i),-0.97+6.88003549539*(i),-0.96+6.84423149044*(i),-0.95+6.80842981414*(i),-0.94+6.77263049892*(i),-0.93+6.73683357781*(i),-0.92+6.70103908447*(i),-0.91+6.66524705317*(i),-0.9+6.62945751886*(i),-0.89+6.59367051711*(i),-0.88+6.55788608422*(i),-0.87+6.52210425714*(i),-0.86+6.48632507357*(i),-0.85+6.4505485719*(i),-0.84+6.4147747913*(i),-0.83+6.37900377169*(i),-0.82+6.34323555377*(i),-0.81+6.30747017906*(i),-0.8+6.27170768989*(i),-0.79+6.23594812944*(i),-0.78+6.20019154174*(i),-0.77+6.16443797174*(i),-0.76+6.12868746525*(i),-0.75+6.09294006906*(i),-0.74+6.05719583088*(i),-0.73+6.02145479944*(i),-0.72+5.98571702443*(i),-0.71+5.9499825566*(i),-0.7+5.91425144776*(i),-0.69+5.87852375079*(i),-0.68+5.84279951971*(i),-0.67+5.80707880966*(i),-0.66+5.77136167696*(i),-0.65+5.73564817916*(i),-0.64+5.69993837503*(i),-0.63+5.6642323246*(i),-0.62+5.62853008925*(i),-0.61+5.59283173166*(i),-0.6+5.55713731591*(i),-0.59+5.52144690751*(i),-0.58+5.48576057342*(i),-0.57+5.45007838208*(i),-0.56+5.4144004035*(i),-0.55+5.37872670927*(i),-0.54+5.3430573726*(i),-0.53+5.30739246839*(i),-0.52+5.27173207326*(i),-0.51+5.23607626561*(i),-0.5+5.20042512566*(i),-0.49+5.16477873553*(i),-0.48+5.12913717926*(i),-0.47+5.0935005429*(i),-0.46+5.05786891454*(i),-0.45+5.02224238441*(i),-0.44+4.9866210449*(i),-0.43+4.95100499066*(i),-0.42+4.91539431867*(i),-0.41+4.87978912826*(i),-0.4+4.84418952127*(i),-0.39+4.80859560206*(i),-0.38+4.77300747761*(i),-0.37+4.7374252576*(i),-0.36+4.70184905452*(i),-0.35+4.66627898374*(i),-0.34+4.63071516357*(i),-0.33+4.59515771544*(i),-0.32+4.55960676392*(i),-0.31+4.52406243688*(i),-0.3+4.48852486556*(i),-0.29+4.45299418471*(i),-0.28+4.41747053271*(i),-0.27+4.38195405166*(i),-0.26+4.34644488755*(i),-0.25+4.31094319038*(i),-0.24+4.27544911428*(i),-0.23+4.23996281769*(i),-0.22+4.20448446349*(i),-0.21+4.16901421915*(i),-0.2+4.13355225694*(i),-0.19+4.09809875403*(i),-0.18+4.06265389275*(i),-0.17+4.02721786073*(i),-0.16+3.99179085111*(i),-0.15+3.95637306275*(i),-0.14+3.92096470044*(i),-0.13+3.88556597514*(i),-0.12+3.85017710421*(i),-0.11+3.81479831164*(i),-0.1+3.77942982836*(i),-0.09+3.74407189245*(i),-0.08+3.7087247495*(i),-0.07+3.67338865283*(i),-0.06+3.63806386388*(i),-0.05+3.60275065251*(i),-0.04+3.56744929735*(i),-0.03+3.53216008618*(i),-0.02+3.4968833163*(i),-0.01+3.46161929497*(i),7.52869988574e-16+3.4263683398*(i),0.01+3.39113077927*(i),0.02+3.35590695312*(i),0.03+3.32069721296*(i),0.04+3.28550192273*(i),0.05+3.25032145929*(i),0.06+3.21515621305*(i),0.07+3.18000658855*(i),0.08+3.14487300522*(i),0.09+3.10975589801*(i),0.1+3.0746557182*(i),0.11+3.03957293422*(i),0.12+3.00450803247*(i),0.13+2.96946151828*(i),0.14+2.93443391689*(i),0.15+2.89942577445*(i),0.16+2.86443765918*(i),0.17+2.82947016258*(i),0.18+2.79452390066*(i),0.19+2.75959951535*(i),0.2+2.72469767597*(i),0.21+2.6898190808*(i),0.22+2.65496445883*(i),0.23+2.62013457153*(i),0.24+2.58533021491*(i),0.25+2.55055222161*(i),0.26+2.51580146327*(i),0.27+2.48107885301*(i),0.28+2.44638534822*(i),0.29+2.4117219535*(i),0.3+2.37708972392*(i),0.31+2.34248976858*(i),0.32+2.30792325448*(i),0.33+2.27339141082*(i),0.34+2.23889553362*(i),0.35+2.20443699089*(i),0.36+2.17001722836*(i),0.37+2.13563777569*(i),0.38+2.10130025348*(i),0.39+2.06700638101*(i),0.4+2.03275798483*(i),0.41+1.9985570084*(i),0.42+1.96440552284*(i),0.43+1.93030573903*(i),0.44+1.89626002118*(i),0.45+1.8622709022*(i),0.46+1.82834110104*(i),0.47+1.79447354238*(i),0.48+1.76067137908*(i),0.49+1.72693801773*(i),0.5+1.69327714802*(i),0.51+1.65969277635*(i),0.52+1.62618926469*(i),0.53+1.59277137539*(i),0.54+1.55944432324*(i),0.55+1.52621383603*(i),0.56+1.49308622527*(i),0.57+1.46006846903*(i),0.58+1.42716830943*(i),0.59+1.39439436758*(i),0.6+1.3617562797*(i),0.61+1.32926485891*(i),0.62+1.29693228815*(i),0.63+1.26477235099*(i),0.64+1.23280070888*(i),0.65+1.20103523525*(i),0.66+1.1694964194*(i),0.67+1.13820785664*(i),0.68+1.1071968446*(i),0.69+1.07649511124*(i),0.7+1.04613970579*(i),0.71+1.01617409166*(i),0.72+0.986649489912*(i),0.73+0.957626532543*(i),0.74+0.92917729839*(i),0.75+0.901387818866*(i),0.76+0.874361156522*(i),0.77+0.848221174221*(i),0.78+0.823117123688*(i),0.79+0.799229183974*(i),0.8+0.776775064858*(i),0.81+0.756017746202*(i),0.82+0.737274338637*(i),0.83+0.720925913304*(i),0.84+0.707427961695*(i),0.85+0.697320947371*(i),0.86+0.691240297063*(i),0.87+0.689925334332*(i),0.88+0.694227351131*(i),0.89+0.705118514708*(i),0.9+0.723705741306*(i),0.91+0.751256847534*(i),0.92+0.789249771073*(i),0.93+0.8394591923*(i),0.94+0.904099255136*(i),0.95+0.986048876853*(i),0.96+1.08920252028*(i),0.97+1.2190236206*(i),0.98+1.38344875899*(i),0.99+1.59444091401*(i),1+1.87082869339*(i),1.01+2.24390089766*(i),1.02+2.7695125925*(i),1.03+3.55771167553*(i),1.04+4.8589159761*(i),1.05+7.3913801147*(i),1.06+14.3878612031*(i),1.07+119.602272978*(i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, // fltk 7Fl_Tile 943 735 150 353 25 [ // fltk N4xcas14Mouse_PositionE 943 735 150 50 25 [] , // fltk 8Fl_Group 943 785 150 140 25 [ // fltk 9Fl_Button 943 785 50 28 25 [] , // fltk 9Fl_Button 993 785 50 28 25 [] , // fltk 9Fl_Button 1043 785 50 28 25 [] , // fltk 9Fl_Button 943 813 50 28 25 [] , // fltk 9Fl_Button 993 813 50 28 25 [] , // fltk 9Fl_Button 1043 813 50 28 25 [] , // fltk 9Fl_Button 943 841 50 28 25 [] , // fltk 9Fl_Button 993 841 50 28 25 [] , // fltk 9Fl_Button 1043 841 50 28 25 [] , // fltk 9Fl_Button 943 869 50 28 25 [] , // fltk 9Fl_Button 993 869 50 28 25 [] , // fltk 9Fl_Button 1043 869 50 28 25 [] , // fltk 9Fl_Button 943 897 50 28 25 [] , // fltk 11Fl_Menu_Bar 993 897 100 28 25 [] ] , // fltk 8Fl_Group 943 925 150 163 25 [ ] ] ] ] , // fltk 7Fl_Tile 32 1090 1061 36 25 [ // fltk N4xcas19Multiline_Input_tabE 32 1090 1061 35 25 , // fltk N4xcas10Log_OutputE 32 1125 1061 1 25 ]