{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 10 0 0 0 0 0 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 1 10 0 0 0 0 0 2 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 262 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "T imes" 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 "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Ti mes" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 14 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 "Normal" -1 257 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 }} {SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 44 "H\341romsz\366glap\372 to roidok n\351gysz\366gekb\365l k\351pezve" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart;with(plots):" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 "A t\363rusz alapadatai:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "d:=10: # gy\373r\373 sugara\nr:=5: # keresztmetsz et sugara\nszin:=[red,green,coral, blue,yellow,magenta,cyan]:" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "1. eset: " }{TEXT 257 60 "A h\341romsz\366geknek vannak a \+ forg\341stengelyre mer\365leges oldalai." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "p:=7: # gy\373r\373 egy sor\341ban l\351v\365 lapj ainak sz\341ma\nq:=5: # keresztmetszet lapjainak sz\341ma: 2*q\nf:=2 *Pi/p: df:=f/2: # df:=0:\ng:= Pi/q: dg:=g/2: # dg:=0: " }}} {EXCHG {PARA 257 "" 0 "" {TEXT -1 182 "# df b\341rmi lehet de df = f/2 esetben kapunk egyenl\365sz\341r\372 h\341romsz\366geket;\n dg ugya ncsak b\341rmi lehet, de csak dg = 0\351s dg =g/2 esetben lesz a tor oid szimmetrikus a forg\341ss\355kj\341ra." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 211 "for i from 0 to p do\n for j from 0 to 2*q do \n fm:=i*f-j*df:\n gm:=j*g+dg:\n n[i,j]:=[evalhf((d+r*cos(gm) )*cos(fm)),\n evalhf((d+r*cos(gm))*sin(fm)),\n \+ evalhf(r*sin(gm))]:\n od;\nod;" }{TEXT -1 41 "( A 0. \351s a p. ill. 2*q. pont egybeesik.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 171 " haromszog:=polygonplot3d([seq(seq([[n[i,j],n[i+1,j],n[i+1,j+1]],\n \+ [n[i,j],n[i+1,j+1],n[i,j+1]]],\n i=0..p-1),j= 0..2*q-1)],scaling= constrained):" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "haromszog;" }{TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 262 27 "Kontroll rajz tubeplottal:\n" }{TEXT 258 0 "" }{TEXT 259 51 "\311rdekes megeml\355teni, hogy a tubeplot utas\355t \341s csak " }{TEXT 260 4 "p>4-" }{TEXT 261 28 " esetben ad helyes ra jzot. " }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "tu beplot([d*sin(s),d*cos(s),0],s=0..2*Pi,radius=r,grid=[p+1,2*q+1],grids tyle=triangular,scaling=constrained); " }{TEXT -1 44 "# A k\351t rajz \+ (fg=0 ^ dg=0) esetben azonos." }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 46 "H\351t egybe v\341g\363, p\341ronk\351nt szomsz\351dos tartom\341ny " }{TEXT 263 29 "( Az 1. eset speci\341lis esete)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a:=1: " }{TEXT -1 0 "" }{MPLTEXT 1 0 50 " # a:=2: , 3,4 ...stb. finomabb\341 teszi a rajzot\n" }{TEXT -1 0 "" }{MPLTEXT 1 0 138 "p:=14*a: # gy\373r\373 egy sor\341ban l\351v\365 lapjainak sz \341ma\nq:= 5*a: # keresztmetszet lapjainak sz\341ma: 2*q\nf:=2*Pi/p: df:=f/2:\ng:= Pi/q: dg:=g/2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 211 "for i from 0 to p do\n for j from 0 to 2*q do\n fm:=i*f- j*df:\n gm:=j*g+dg:\n n[i,j]:=[evalhf((d+r*cos(gm))*cos(fm)),\n \+ evalhf((d+r*cos(gm))*sin(fm)),\n evalhf(r*sin( gm))]:\n od;\nod;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 295 "for s from 1 to 7 do\ntartomany:=[seq(seq([[n[i,j],n[i+1,j],n[i+1,j+1]],\n \+ [n[i,j],n[i+1,j+1],n[i,j+1]]],\n i=2*a*(s-1)..2*a* s-1),j=0..2*q-1)]:\nt[s]:=polygonplot3d(tartomany,color=szin[s],scalin g=constrained):\nod:\nharomszog:=display3d(seq(t[i],i=1..7),insequence = false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "haromszog;" }{TEXT -1 0 "" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 46 "H\351t egybev\341g\363, p\341ronk\351nt szomsz\351dos tar tom\341ny " }{TEXT 264 29 "( Egy tartom\341ny 4 lapb\363l \341ll)" } {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 451 "f:=Pi/7:\nf or i from 0 to 6 do\n A[i]:=[d*sin(2*i*f),d*cos(2*i*f),r];\n B[i]:=[ d*sin(2*i*f+f),d*cos(2*i*f+f),-r];\nod:\nP:=[seq(polygonplot3d([\n \+ [A[i mod 7],A[(i+1) mod 7],B[i mod 7]]\n ,[A[i mod 7],A[(i+1) mod 7] ,B[(i+2) mod 7]]\n ,[A[(i+1) mod 7],B[(i+2) mod 7],B[(i+3) mod 7]]\n ,[B[(i+2) mod 7],B[(i+3) mod 7],A[(i+3) mod 7]]\n ],color=szin[ i]),i=1..7)]:\nharomszog:=display(seq(P[i],i=1..7),\n insequ ence=false,scaling=constrained):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "haromszog;" }{TEXT -1 0 "" } }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 8 "2.eset: " }{TEXT 256 56 "A h\341romsz\366geknek vannak \+ a forg\341stengelyt metsz\365 oldalai." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "p:=3: # gy\373r\373 egy sor\341ban l\351v\365 lapj ainak sz\341ma: 2*p\nq:=5: # keresztmetszet lapjainak sz\341ma\nf:= \+ Pi/p: \ng:=2*Pi/q: dg:=2*g/2: # dg:=0: " }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 108 "# dg b\341rmi lehet, 0 \351s g k\366z\366tt, de csak \+ dg =g/2 esetben lesz a toroid szimmetrikus a forg\341ss\355kj\341 ra." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 208 "for i from 0 to 2*p do\n for j from 0 to q do\n fm:=i*f:\n gm:=j*g-i*dg:\n n[i ,j]:=[evalhf((d+r*cos(gm))*cos(fm)),\n evalhf((d+r*cos(gm) )*sin(fm)),\n evalhf(r*sin(gm))]:\n od;\nod;" }{TEXT -1 43 "# ( A 0. \351s a 2*p. ill. q. pont egybeesik.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 171 "haromszog:=polygonplot3d([seq(seq([[n[i,j] ,n[i+1,j],n[i+1,j+1]],\n [n[i,j],n[i+1,j+1],n[i,j+1 ]]],\n i=0..2*p-1),j=0..q-1)],scaling= constrained):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "haromszog;" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 21 "Kontroll tubeplottal:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "tubeplot([d*sin(s),d*cos(s),0],s=0..2*Pi,radius=r,gr id=[2*p+1,q+1],gridstyle=triangular,scaling=constrained);" }{TEXT -1 36 " # A k\351t rajz dg=0 esetben azonos." }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "VRML f \341jl" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "with(plottools):\n vrml(haromszog, `Heawood4.wrl`,\n background_color=COLOR(RGB,0,1,1 ));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}}{MARK "0" 0 } {VIEWOPTS 1 1 1 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }