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"restart:with(plots):with(geometry):" }}{PARA 201 "> " 0 "" {MPLTEXT 1 205 89 "plur:= (a,b,c,d,e,f) -> [ (a+b)/(a+b+c+d+e+ f), (e+f)/(a+b+c+d+e+f), (c+d)/(a+b+c+d+e+f)]:" }}{PARA 201 "> " 0 "" {MPLTEXT 1 205 114 "aplur:= (a,b,c,d,e,f) -> [ (a+b+c+f)/(2*(a+b+c+d+e +f)), (e+f+a+d)/(2*(a+b+c+d+e+f)), (c+d+b+e)/(2*(a+b+c+d+e+f))]:" }} {PARA 201 "> " 0 "" {MPLTEXT 1 205 81 "prdown := (a,b,c) -> [ -a/sqrt( 2) + b/sqrt(2), -a/sqrt(6)-b/sqrt(6)+sqrt(2/3)*c]:" }}{PARA 201 "> " 0 "" {MPLTEXT 1 205 104 "prup := (x,y) -> [-1/2*sqrt(2)*x-1/6*sqrt(6)*y +1/3, 1/2*sqrt(2)*x-1/6*sqrt(6)*y+1/3, 1/3+1/3*sqrt(6)*y]:" }}{PARA 202 "> " 0 "" }{PARA 201 "> " 0 "" {MPLTEXT 1 205 158 "tri:=spacecurve (\{[ [1,0,0],[0,1,0],[0,0,1],[1,0,0]], [ [1,0,0],[0,1/2,1/2]], [ [0,1, 0],[1/2,0,1/2]], [ [0,0,1],[1/2,1/2,0]]\},color=black,scaling=constrai ned):" }}{PARA 201 "> " 0 "" {MPLTEXT 1 205 128 "procline:=(a,b,c,d,e, f) -> spacecurve(\{[ plur(a,b,c,d,e,f), aplur(a,b,c,d,e,f)]\}, color=b lue,thickness=2, axes=none,style=line):" }}{PARA 201 "> " 0 "" {MPLTEXT 1 205 150 "procpoints:=(a,b,c,d,e,f) -> spacecurve(\{[ plur(a ,b,c,d,e,f), aplur(a,b,c,d,e,f)]\}, color=green, axes=none,style=point , symbolsize=15, symbol=CIRCLE):" }}{PARA 201 "> " 0 "" {MPLTEXT 1 205 115 "normalize := pnt -> ( pnt[1]/(pnt[1]+pnt[2]+pnt[3]), pnt[2]/( pnt[1]+pnt[2]+pnt[3]), pnt[3]/(pnt[1]+pnt[2]+pnt[3])):" }}{PARA 201 "> " 0 "" {MPLTEXT 1 205 77 "apvertices := proc(a,b,c,d,e,f) local A,B,C ,D,E,F,G,H, prof, i, po, apo,CH,L;" }{MPLTEXT 1 205 25 "\n prof:=(a ,b,c,d,e,f);" }{MPLTEXT 1 205 26 "\n po:= [a+b, e+f, c+d];" } {MPLTEXT 1 205 39 "\n apo:= [a+b+c+f, e+f+a+d, c+d+b+e];" } {MPLTEXT 1 205 1 "\n" }{MPLTEXT 1 205 56 "\n point(A, prdown(normal ize([po[1],po[2],po[3]]) ));" }{MPLTEXT 1 205 56 "\n point(B, prdo wn(normalize([po[1],po[2],apo[3]]) ));" }{MPLTEXT 1 205 56 "\n poin t(C, prdown(normalize([po[1],apo[2],po[3]]) ));" }{MPLTEXT 1 205 57 " \n point(D, prdown(normalize([po[1],apo[2],apo[3]]) ));" }{MPLTEXT 1 205 56 "\n point(E, prdown(normalize([apo[1],po[2],po[3]]) ));" } {MPLTEXT 1 205 57 "\n point(F, prdown(normalize([apo[1],po[2],apo[3 ]]) ));" }{MPLTEXT 1 205 57 "\n point(G, prdown(normalize([apo[1],a po[2],po[3]]) ));" }{MPLTEXT 1 205 58 "\n point(H, prdown(normalize ([apo[1],apo[2],apo[3]]) ));" }{MPLTEXT 1 205 5 "\n " }{MPLTEXT 1 205 39 "\n CH:=convexhull(\{A,B,C,D,E,F,G,H\});" }{MPLTEXT 1 205 12 "\n L:=[]: " }{MPLTEXT 1 205 33 "\n for i from 1 to nops(CH) \+ do " }{MPLTEXT 1 205 51 "\n L:=[op(L), prup(op(coordinates(CH[ i])))]:" }{MPLTEXT 1 205 14 "\n od: " }{MPLTEXT 1 205 21 "\n \+ L:=[op(L),L[1]]:" }{MPLTEXT 1 205 6 "\n " }{MPLTEXT 1 205 47 "\n return(spacecurve(L,color=red,axes=none));" }{MPLTEXT 1 205 10 "\n end proc:" }{MPLTEXT 1 205 1 "\n" }}{PARA 202 "> " 0 "" }{PARA 201 "> \+ " 0 "" {MPLTEXT 1 205 119 "plotprofile := (a,b,c,d,e,f) -> display(tri , procline(a,b,c,d,e,f), procpoints(a,b,c,d,e,f), apvertices(a,b,c,d,e ,f) ):" }}}}{PARA 203 "" 0 "" }{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 205 25 "plotprofile(3,6,2,4,8,0);" }}}{EXCHG {PARA 201 "> " 0 "" }} {PARA 204 "" 0 "" }}{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }