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0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 329 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 330 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 331 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 332 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 333 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 334 "" 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 335 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 336 "" 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 337 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 338 "" 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 339 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 340 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 341 "" 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Tim es" 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 "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 }{PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "Times" 1 10 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 12 0 0 0 1 2 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" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 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 30 "Mozi az arkhim\351d\351sz i kock\341r\363l\n" }{TEXT 323 12 "K\351sz\355tette: " }{TEXT 324 18 " dr. Szilassi Lajos" }{TEXT 325 62 "\n SZTE JGYTF Mate matika Tansz\351k\nE-mail: " }{TEXT 326 26 "szilassi@jgytf.u-szeg ed.hu" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Miut\341n meghat\341roztuk az arkhim\351d\351szi \+ kocka " }{TEXT 264 9 "(4,3,3,3)" }{TEXT -1 236 " cs\372csainak a koord in\341t\341it, bemutatjuk, hogy a kocka \351s okta\351der szimmetriacs oportj\341hoz tartoz\363 arkhim\351deszi (f\351lig szab\341lyos) poli \351derek mik\351nt sz\341rmaztathat\363k egym\341sb\363l.\nUgyanezt a sz\341rmaztat\341st elv\351gez\374k a nagy-rombikockaokta\351derb\365 l " }{TEXT 265 6 "(8,6,4" }{TEXT 266 1 ")" }{TEXT -1 16 " kiindulva i s.\n" }}{PARA 0 "" 0 "" {TEXT -1 25 "Azt vigzsg\341ljuk, hogy az " } {TEXT 256 5 " f(x)" }{TEXT -1 2 ", " }{TEXT 257 4 "g(x)" }{TEXT -1 6 " ill. " }{TEXT 258 4 "h(x)" }{TEXT -1 26 " f\374ggv\351nyek ment\351n \+ halad\363 " }{TEXT 259 5 "(x,y)" }{TEXT -1 173 " \351rt\351kp\341rok m ik\351nt alak\355tj\341k ki az arkhim\351d\351szi kock\341t m\341s f \351lig szab\341lyos poli\351derr\351, majd ugyanezt a vizsg\341latot \+ elv\351gezz\374k a nagy-rombikockaokta\351derrel \351s a -line\341ris - " }{TEXT 260 6 " ff(x)" }{TEXT -1 2 ", " }{TEXT 261 5 "gg(x)" } {TEXT -1 6 " ill. " }{TEXT 262 5 "hh(x)" }{TEXT -1 18 " f\374ggv\351ny ekkel is." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "restart;\nwith (plots):with(plottools):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 329 11 "Alap adatok:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "f := x -> -1/2* x-5+1/2*sqrt(x^2+60*x+100);\ng := x -> -10*(x-10)/(x+10);\nh := x -> \+ 2*sqrt(-25+5*x);\nk := x -> 5+x^2/20;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 330 1 "h" }{TEXT -1 4 " \351s " }{TEXT 331 1 "k " }{TEXT -1 16 " egym\341s inverze." }{TEXT 332 2 " k" }{TEXT -1 63 "- ra a \"balos\" arkhim\351deszi kocka el\365\341ll\355t\341s\341ra lesz sz\374ks\351g\374nk." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "ff := x -> (sqrt(2)-1)*x;\ngg:= x -> (10-x)*sqrt(2)/2;\nhh:= x -> 2*x- 10;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 275 "x := 5+1/5*(5/3*(26+6*sqrt(33))^(1/3)\n -40/3*1/((26+6*sqrt(33) )^(1/3))-5/3)^2;\ny := 10/3*( (26+6*sqrt(33))^(2/3)-8\n -(26 +6*sqrt(33))^(1/3))/((26+6*sqrt(33))^(1/3));\nx0:= evalf(x): y0:=evalf (y):\nx1:=10*sqrt(2)-10;\nx2:=10*(3+sqrt(2))/7; y2:=(sqrt(2)-1)*x2;" } {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 333 41 "A poli\351derek \+ gr\341fjait el\365\341ll\355t\363 m\341trixok." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Az \351lv\341zas locka:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 604 "K :=[[[ 10, 10, 10],[-10, 10, 10]],\n [[-10, 1 0, 10],[-10,-10, 10]],\n [[-10,-10, 10],[ 10,-10, 10]],\n [[ 1 0,-10, 10],[ 10, 10, 10]],\n [[ 10, 10,-10],[-10, 10,-10]],\n \+ [[-10, 10,-10],[-10,-10,-10]],\n [[-10,-10,-10],[ 10,-10,-10]],\n \+ [[ 10,-10,-10],[ 10, 10,-10]],\n [[ 10, 10, 10],[ 10, 10,-10]] ,\n [[ 10,-10, 10],[ 10,-10,-10]],\n [[-10,-10, 10],[-10,-10,- 10]],\n [[-10, 10, 10],[-10, 10,-10]]]:\nKL:=[[[ 10, 0 , 0],[ 10, 10, 0]],\n [[ 10, 0, 0],[ 10, 0, 10]],\n [[ 10, 0, 0],[ 10, 10, 10]],\n [[9.9, 0, 0],[9.9, 10, 0],[9.9,10,10],[9.9, 0 , 10]]]:\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "A \"jobbos\" arkhim \351d\351szi kocka" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1839 "R : =(x,y) ->[\n[[ x, y, 10],[ -y, x, 10],[ -x, -y, 10],[ y, -x, 10]] ,\n[[ -x,-10, -y],[ -y,-10, x],[ x,-10, y],[ y,-10, -x]],\n[[ -y, \+ -x,-10],[ x, -y,-10],[ y, x,-10],[ -x, y,-10]],\n[[-10, -y, -x],[- 10, x, -y],[-10, y, x],[-10, -x, y]], \n[[ 10, x, y],[ 10, -y, \+ x],[ 10, -x, -y],[ 10, y, -x]],\n[[ y, 10, x],[ x, 10, -y],[ -y, 1 0, -x],[ -x, 10, y]],\n[[ x, y, 10],[ 10, x, y],[ y, 10, x]],\n [[ -x, 10, y],[ -y, x, 10],[-10, y, x]],\n[[ y,-10, -x],[ x, -y, -10],[ 10, -x, -y]], \n[[ -y, -x,-10],[-10, -y, -x],[ -x,-10, -y]],\n[ [ y, -x, 10],[ 10, -y, x],[ x,-10, y]],\n[[-10, -x, y],[ -y,-10, \+ x],[ -x, -y, 10]], \n[[ 10, y, -x],[ x, 10, -y],[ y, x,-10]], \n[ [ -y, 10, -x],[ -x, y,-10],[-10, x, -y]],\n\n[[ x, y, 10],[ -y, x , 10],[ y, 10, x]],\n[[ y, 10, x],[ -x, 10, y],[ -y, x, 10]], \n \n[[-10, y, x],[-10, -x, y],[ -x, -y, 10]], \n[[ -y, x, 10],[ -x, \+ -y, 10],[-10, y, x]],\n\n[[ -x, -y, 10],[ y, -x, 10],[ -y,-10, x]] , \n[[ -y,-10, x],[ x,-10, y],[ y, -x, 10]],\n\n[[ y, -x, 10],[ \+ x, y, 10],[ 10, -y, x]], \n[[ 10, x, y],[ 10, -y, x],[ x, y, 10 ]], \n\n[[ -y, -x,-10],[ x, -y,-10],[ y,-10, -x]],\n[[ y,-10, -x],[ -x,-10, -y],[ -y, -x,-10]], \n\n[[ x, -y,-10],[ y, x,-10],[ 10, y , -x]],\n[[ 10, -x, -y],[ 10, y, -x],[ x, -y,-10]], \n\n[[ -x, y,-1 0],[ -y, -x,-10],[-10, -y, -x]],\n[[-10, -y, -x],[-10, x, -y],[ -x, \+ y,-10]],\n \n[[ y, x,-10],[ -x, y,-10],[ -y, 10, -x]],\n[[ x, 10, \+ -y],[ -y, 10, -x],[ y, x,-10]], \n\n[[-10, x, -y],[-10, y, x],[ - x, 10, y]],\n[[ -y, 10, -x],[ -x, 10, y],[-10, x, -y]],\n\n[[-10, - y, -x],[-10, -x, y],[ -x,-10, -y]], \n[[ -x,-10, -y],[ -y,-10, x],[- 10, -x, y]],\n\n[[ x,-10, y],[ y,-10, -x],[ 10, -x, -y]],\n[[ 10, \+ -y, x],[ 10, -x, -y],[ x,-10, y]],\n\n[[ 10, y, -x],[ 10, x, y], [ x, 10, -y]],\n[[ y, 10, x],[ x, 10, -y],[ 10, x, y]] \n ]:\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "A \"balos\" arkhim\351d\351szi \+ kocka" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1840 "L :=(x,y) ->[\n [[ x, y, 10],[ -y, x, 10],[ -x, -y, 10],[ y, -x, 10]],\n[[ -x,-10, -y],[ -y,-10, x],[ x,-10, y],[ y,-10, -x]],\n[[ -y, -x,-10],[ x, -y,-10],[ y, x,-10],[ -x, y,-10]],\n[[-10, -y, -x],[-10, x, -y],[ -10, y, x],[-10, -x, y]], \n[[ 10, x, y],[ 10, -y, x],[ 10, -x, \+ -y],[ 10, y, -x]],\n[[ y, 10, x],[ x, 10, -y],[ -y, 10, -x],[ -x, \+ 10, y]],\n[[ x, y, 10],[ 10, x, y],[ y, 10, x]],\n[[ -x, 10, y ],[ -y, x, 10],[-10, y, x]],\n[[ y,-10, -x],[ x, -y,-10],[ 10, -x , -y]], \n[[ -y, -x,-10],[-10, -y, -x],[ -x,-10, -y]],\n[[ y, -x, 10] ,[ 10, -y, x],[ x,-10, y]],\n[[-10, -x, y],[ -y,-10, x],[ -x, -y, 10]], \n[[ 10, y, -x],[ x, 10, -y],[ y, x,-10]], \n[[ -y, 10, -x] ,[ -x, y,-10],[-10, x, -y]],\n\n[[ x, y, 10],[ -x, 10, y] , [ y, 10, x]],\n[[ -x, 10, y],[ -y, x, 10] , [ x, y, 10]], \n\n[[-y, \+ x, 10],[-10, -x, y],[ -x, -y, 10]], \n[[-10, -x, y],[ -y, x, 10],[ -10, y, x]],\n\n[[ -x, -y, 10],[ x, -10,y],[ -y,-10, x]], \n[[ x,- 10, y],[ y, -x, 10],[ -x, -y, 10]],\n\n[[ y, -x, 10],[ 10, x, y],[ 10, -y, x]], \n[[ 10, x, y],[ x, y, 10],[ y, -x, 10]], \n\n[[ \+ x, -y,-10],[ -x, -10,-y],[ y,-10, -x]],\n[[ -x,-10, -y],[ -y, -x,-10] ,[ x,-y, -10]], \n\n[[ y, x,-10],[ 10, -x, -y],[ 10, y, -x]],\n[[ \+ 10, -x, -y],[ x, -y,-10],[ y, x, -10]], \n\n[[ -y, -x,-10],[ -10, x ,-y],[-10, -y, -x]],\n[[-10, x, -y],[ -x, y,-10],[-y, -x, -10]],\n \+ \n[[ -x, y,-10],[ x, 10, -y],[ -y, 10, -x]],\n[[ x, 10, -y],[ y, \+ x,-10],[ -x, y, -10]], \n\n[[-10, y, x],[ -y, 10, -x],[ -x, 10, y]] ,\n[[ -y, 10, -x],[-10, x, -y],[-10, y, x]],\n\n[[-10, -y, -x],[ -y ,-10, x],[ -x,-10, -y]], \n[[ -y,-10, x],[-10, -x, y],[-10, -y, -x] ],\n\n[[ y,-10, -x],[ 10, -x, -y],[ 10, -y, x]],\n[[ 10, -y, x],[ y , -10, -x],[ x,-10, y]],\n\n[[ 10, y, -x],[ y, 10, x],[ x, 10, - y]],\n[[ y, 10, x],[ 10, x, y],[ 10, y, -x]] \n ]:\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "A nagy rombikubokta\351der" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2208 "G :=(x,y) ->[\n [[ x, y, 10],[ y, x, 10],[ -y, x, 10],[ -x, y, 10],\n [ -x, -y, 10],[ -y, -x, 1 0],[ y, -x, 10],[ x, -y, 10]],\n [[ x, 10, y],[ y, 10, x],[ -y, \+ 10, x],[ -x, 10, y],\n [ -x, 10,-y],[ -y, 10, -x],[ y, 10, -x],[ \+ x, 10, -y]],\n [[ 10, x, y],[ 10, y, x],[ 10, -y, x],[ 10, -x, \+ y],\n [ 10, -x, -y],[ 10, -y, -x],[ 10, y, -x],[ 10, x, -y]],\n [[ \+ x, y,-10],[ y, x,-10],[ -y, x,-10],[ -x, y,-10],\n [ -x, -y,-10 ],[ -y, -x,-10],[ y, -x,-10],[ x, -y,-10]],\n [[ x,-10, y],[ y,-1 0, x],[ -y,-10, x],[ -x,-10, y],\n [ -x,-10, -y],[ -y,-10, -x],[ \+ y,-10, -x],[ x,-10, -y]],\n [[-10, x, y],[-10, y, x],[-10, -y, x ],[-10, -x, y],\n [-10, -x, -y],[-10, -y, -x],[-10, y, -x],[-10, x , -y]],\n [[ y, x, 10],[ x, y, 10],\n [ 10, y, x],[ 10, x, y], \n [ x, 10, y],[ y, 10, x]], \n [[ y, -x, 10],[ x,-y, 10],\n [ \+ 10, -y, x],[ 10,-x, y],\n [ x,-10, y],[ y,-10, x]], \n [[ -y, -x , 10],[ -x,-y, 10],\n [-10, -y, x],[ -10,-x, y],\n [ -x,-10, y], [ -y,-10, x]], \n [[ -y, x, 10],[ -x, y, 10],\n [ -10, y, x],[-10 , x, y],\n [ -x, 10, y],[ -y, 10, x]], \n [[ -y, -x,-10],[ -x, -y ,-10],\n [-10, -y, -x],[-10, -x, -y],\n [ -x,-10, -y],[ -y,-10, -x]] , \n [[ -y, x,-10],[ -x, y,-10],\n [-10, y, -x],[-10, x, -y],\n \+ [ -x, 10, -y],[ -y, 10, -x]], \n [[ y, x,-10],[ x, y,-10],\n [ 10 , y, -x],[ 10, x, -y],\n [ x, 10, -y],[ y, 10, -x]], \n [[ y, -x ,-10],[ x, -y,-10],\n [ 10, -y, -x],[ 10, -x, -y],\n [ x,-10, -y], [ y,-10, -x]],\n [[ y, x, 10],[ y, 10, x],[ -y, 10, x],[ -y, x, 10]], \n [[ -x, y, 10],[ -x, -y, 10],[-10, -y, x],[-10, y, x]],\n [[ -y, -x, 10],[ y, -x, 10],[ y,-10, x],[ -y,-10, x]], \n [[ x, \+ -y, 10],[ x, y, 10],[ 10, y, x],[ 10, -y, x]], \n [[ y, x,-10], [ -y, x,-10],[ -y, 10, -x],[ y, 10, -x]],\n [[ -x, y,-10],[ -x, -y, -10],[-10, -y, -x],[-10, y, -x]],\n [[-10, x, -y],[-10, x, y],[ -x , 10, y],[ -x, 10, -y]],\n [[-10, -x, -y],[-10, -x, y],[ -x,-10, y] ,[ -x,-10, -y]], \n [[ x,-10, y],[ x,-10, -y],[ 10, -x, -y],[ 10, - x, y]],\n [[ y,-10, -x],[ -y,-10, -x],[ -y, -x,-10],[ y, -x,-10]], \+ \n [[ 10, y, -x],[ 10, -y, -x],[ x, -y,-10],[ x, y,-10]], \n [[ 10, x, y],[ 10, x, -y],[ x, 10, -y],[ x, 10, y]] ]:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "Az \341talak\355t\341sok sorrendje " }}{EXCHG {PARA 0 "" 0 "" {TEXT 290 103 "Nr. Jel C\355m \+ x y n\351v " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{TEXT 291 106 "1 . P1 (4,4,4) 10 \+ 10 kocka" }}{PARA 0 "" 0 "" {TEXT -1 110 " \+ 2. H12 10. - >.x0 \+ h(x) \n " }{TEXT 272 6 "HH18 " } {TEXT -1 38 " " }{TEXT 268 31 "10 -> x2 hh(x)" }{TEXT -1 3 " \n " }{TEXT 292 120 "3. \+ P2 (4,3,3,3) x0 \+ y0 arkhim\351d\351szi kiocka\n" }{TEXT 267 0 " " }{TEXT -1 8 " " }{TEXT 293 1 " " }{TEXT 273 2 "P8" }{TEXT 294 10 " " }{TEXT 270 15 " (8,6,4) " }{TEXT 295 19 " \+ " }{TEXT 269 70 "x2 y2 \+ nagy rombikubokta\351der" }{TEXT -1 90 "\n 4. H23 \+ x0. - > .5 h(x ) " }}{PARA 0 "" 0 "" {TEXT -1 9 " " }{TEXT 274 4 "HH83" } {TEXT -1 32 " " }{TEXT 271 42 " \+ x2 -> 5 hh(x)" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 296 138 "5. P3 (6,6,3) \+ 5 0 arkh im\351d\351szi csonk\355tott okta\351der\n" }{TEXT -1 84 " 6. U34 \+ 5. - > 10 \+ 0" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 297 115 "7. P4 \+ (4,3,4,3) 10 0 \+ kubokta\351der" }}{PARA 0 "" 0 "" {TEXT -1 87 " 8. \+ G42 10. - >.x0 \+ g(x)" }}{PARA 0 "" 0 "" {TEXT -1 8 " " }{TEXT 276 4 "GG4 2" }{TEXT -1 29 " " }{TEXT 275 46 " \+ 10 -> x2 gg(x)" }{TEXT -1 1 " " }}{PARA 256 " " 0 "" {TEXT -1 122 " 9. P2 (4,3,3,3) \+ x0 y0 arkhim\351d\351 szi kocka" }}{PARA 256 "" 0 "" {TEXT 277 0 "" }{TEXT -1 9 " " }{TEXT 280 2 "P8" }{TEXT -1 5 " " }{TEXT 279 20 " (8,6, 4) " }{TEXT -1 19 " " }{TEXT 278 73 " x2 \+ y2 nagy rombikubokta\351der" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "10. G25 \+ x0. - >.x1 g(x)" }}{PARA 0 "" 0 "" {TEXT -1 9 " " }{TEXT 282 4 "GG85" }{TEXT -1 30 " \+ " }{TEXT 281 43 " x2 -> x1 \+ gg(x)" }}{PARA 0 "" 0 "" {TEXT 298 120 "11. P5 \+ (4,4,4,3) x1 x1 \+ rombikubokta\351der" }}{PARA 0 "" 0 "" {TEXT -1 84 "12. \+ V56 x1 - >. 0 \+ x" }}{PARA 0 "" 0 "" {TEXT 299 116 "13. P6 ( 3,3,3,3) 0 0 \+ okta\351der" }}{PARA 0 "" 0 "" {TEXT -1 88 "14. F62 \+ 0. - > .x0 f( x)" }}{PARA 0 "" 0 "" {TEXT -1 9 " " }{TEXT 284 4 "FF68" } {TEXT -1 32 " " }{TEXT 283 45 " \+ 0 - > x2 ff(x)" }{TEXT -1 1 "\n" }{TEXT 300 124 "14. P2 (4,3,3,3) x0 \+ y0 arkhim\351d\351szi kocka" }} {PARA 256 "" 0 "" {TEXT -1 8 " " }{TEXT 287 2 "P8" }{TEXT -1 19 " " }{TEXT 286 9 " (8,6,4) " }{TEXT -1 20 " \+ " }{TEXT 285 72 " x2 y2 \+ nagy rombikubokta\351der" }}{PARA 0 "" 0 "" {TEXT -1 87 "1 5, F27 x0. - >.10 \+ f(x)" }}{PARA 0 "" 0 "" {TEXT -1 9 " " }{TEXT 289 4 "FF87" }{TEXT -1 33 " " }{TEXT 288 43 " x2 -> 10 ff(x)" }{TEXT -1 1 "\n" } {TEXT 301 137 "16. P7 (8,8,3) \+ 10 x1 arkhim\351d\351sz i csonk\355tott kocka" }}{PARA 0 "" 0 "" {TEXT -1 217 "17. R71 \+ 10 \+ x1 ->.10\n \+ " } {TEXT 302 5 "kocka" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "Tervek" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "pont:= (x,y)-> disk([x,y], 0 .2, color=yellow):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "A - mozg \363 " }{TEXT 263 7 "P(x, y)" }{TEXT -1 57 " pont \351rtelmez\351si ta rtom\341nya (10 oldalhossz\372s\341g\372 n\351gyzet)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "Ne:=rectangle([0,10],[10,0], color=cyan,s tyle=patchnogrid):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "A mozg\341s t le\355r\363 f\374ggv\351nyek \351s feliratuk." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 305 "Fv:=plot(f(t),t=0..12,linestyle=16,color=red) :\nFt:=textplot([11.5,f(11.5)+1,\"y=f(x)\"],color=red):\nGv:=plot(g(t) ,t=x1..12,linestyle=16,color=magenta):\nGt:=textplot([11.5,g(11.5)+1, \"y=g(x)\"],color=magenta):\nHv:=plot(h(t),t=0..12,linestyle=16,color= blue):\nHt:=textplot([11.5,h(11.5)+1,\"y=h(x)\"],color=blue):\n" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "A mozg\341s egyenes szakaszai (min dk\351t mozg\341sn\341l ugyanaz)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "UL:=line([5,0],[10,0],color=gold,linestyle=16):\nVL: =line([x1,x1],[0,0],color=brown,linestyle=16):\nRL:=line([10,x1],[10,1 0],color=maroon,linestyle=16):\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 303 31 "A nagy rombikubokta\351der mozg\341sa" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 152 "FF:=line([ 0, 0],[10,x1],color=red,linestyle=16): \nGG:=line([10, 0],[x1,x1],color=magenta,linestyle=16):\nHH:=line([5,0 ],[10,10],color=blue,linestyle=16):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Az arkhim\351d\351szi polidereket meghat\341roz\363 helyek:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 143 "SP1:=pont(10,10):\nSP2:=po nt(x0,y0):\nSP8:=pont(x2,y2):\nSP3:=pont( 5, 0):\nSP4:=pont(10, 0):\nS P5:=pont(x1,x1):\nSP6:=pont( 0, 0):\nSP7:=pont(10,x1):" }}}{SECT 1 {PARA 20 "" 0 "" {TEXT -1 14 "Megjelen\355t\351sek" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 116 "display(SP1,SP2,SP3,SP4,SP5,SP6,SP7,Ne,\n \+ Fv,Ft,Gv,Gt,Hv,Ht,\n UL,VL,RL, scaling=constrained,axes=n one);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "di splay(SP1,SP8,SP3,SP4,SP5,SP6,SP7,Ne,\n FF,GG,HH,\n UL,V L,RL, scaling=constrained,axes=none);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "display(SP1,SP2,SP3,SP4,SP5,SP6,SP7,SP8, Ne,\n Fv,Ft,Gv,Gt,Hv,Ht,FF,GG,HH,\n UL,VL,RL, scaling=co nstrained,axes=none);" }{TEXT -1 0 "" }}}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 5 "Mozi1" }} {EXCHG {PARA 0 "" 0 "" {TEXT 305 2 "n:" }{TEXT -1 37 " a mozg\341s fin oms\341ga (A k\351pek sz\341ma " }{TEXT 304 10 "17*(n+1) " }{TEXT -1 6 "lesz!)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "n:=12:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 331 "p1 :=polygonplot3d(R(10,10) ): \np2 :=polygonplot3d(R(x0,y0)):\np3 :=polygonplot3d(R( 5, 0)):\np3b :=polygonplot3d(G( 5, 0)):\np4 :=polygonplot3d(R(10, 0)):\np5 :=polygo nplot3d(R(x1,x1)):\np5b:=polygonplot3d(G(x1,x1)):\np6 :=polygonplot3d( G( 0, 0)):\np7 :=polygonplot3d(R(10,x1)):\np7b:=polygonplot3d(G(10,x1) ):\np8 :=polygonplot3d(G(x1,x1)):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 505 "for i from 0 to n do \nx:=10-i*(10-x0)/n: h12[i]:=p olygonplot3d(R(x,h(x))):\n g42[i]:=polygonplot3d(R( x,g(x))):\nx:=x0-i*(x0-5)/n: h23[i]:=polygonplot3d(R(x,h(x))):\nx:=5 +i*5/n: u34[i]:=polygonplot3d(G(x,0)):\nx:=x0+i*(x1-x0)/n; \+ g25[i]:=polygonplot3d(R(x,g(x))):\nx:=x1-i*x1/n; v56[i]:=polygon plot3d(G(x,x)):\nx:=i*x0/n; f62[i]:=polygonplot3d(R(x,f(x))): \nx:=x0+i*(10-x0)/n; f27[i]:=polygonplot3d(R(x,f(x))):\nx:=x1+i*(10-x 1)/n; r71[i]:=polygonplot3d(G(10,x)):\nod:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 988 "P1:=display3d([seq(p1,i=0..n)],insequence=true) :\nP2:=display3d([seq(p2,i=0..n)],insequence=true):\nP3:=display3d([se q(p3,i=0..n/2)],insequence=true):\nP3b:=display3d([seq(p3b,i=0..n)],in sequence=true):\nP4:=display3d([seq(p4,i=0..n)],insequence=true):\nP5: =display3d([seq(p5,i=0..n/2)],insequence=true):\nP5b:=display3d([seq(p 5b,i=0..n)],insequence=true):\nP6:=display3d([seq(p6,i=0..n)],insequen ce=true):\nP7:=display3d([seq(p7,i=0..n/2)],insequence=true):\nP7b:=di splay3d([seq(p7b,i=0..n)],insequence=true):\n\nH12:=display3d([seq(h12 [i],i=0..n)],insequence=true):\nH23:=display3d([seq(h23[i],i=0..n)],in sequence=true):\nU34:=display3d([seq(u34[i],i=0..n)],insequence=true): \nG42:=display3d([seq(g42[i],i=0..n)],insequence=true):\nG25:=display3 d([seq(g25[i],i=0..n)],insequence=true):\nV56:=display3d([seq(v56[i],i =0..n)],insequence=true):\nF62:=display3d([seq(f62[i],i=0..n)],inseque nce=true):\nF27:=display3d([seq(f27[i],i=0..n)],insequence=true):\nR71 :=display3d([seq(r71[i],i=0..n)],insequence=true):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "mozi1:=display3d(P1,H12,P2,H23,P3,P3b,U34, P4,G42,P2,G25,P5,P5b,V56,P6,F62,P2,F27,P7,P7b,R71,insequence=true, ori entation=[70,80],scaling=CONSTRAINED):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "mozi1b:=display3d(P2,H23,P3,P3b,U34,P4,G42,P2,G25,P5 ,P5b,V56,P6,F62,P2,F27,P7,P7b,R71,P1,H12,\ninsequence=true, orientatio n=[70,80],scaling=CONSTRAINED):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 261 "K1:=display3d(\n polygonplot3d(K),\n polygonplot3d(KL,c olor=cyan),\n spacecurve([10,t,f(t)],t=0..10,color=red, linestyle=1 6),\n spacecurve([10,t,g(t)],t=0..10,color=magenta, linestyle=16), \n spacecurve([10,t,h(t)],t=5..10,color=blue, linestyle=16)\n):\n" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 15 "Megjelen\355t\351sek:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "mozi1;" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "mozi1b;" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "display3d(K1,mozi1b,insequen ce=false);" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 5 "Mozi2" }}{EXCHG {PARA 0 "" 0 "" {TEXT 307 2 "n:" }{TEXT -1 37 " a mozg\341s finoms\341ga (A k\351pek sz\341 ma " }{TEXT 306 10 "17*(n+1) " }{TEXT -1 6 "lesz!)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "n:=20:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 300 "p1 :=polygonplot3d(G(10,10)): \np2 :=polygonplot3d(G (x2,y2)):\np3 :=polygonplot3d(G( 5, 0)):\np4 :=polygonplot3d(G(10, 0)) :\np5 :=polygonplot3d(G(x1,x1)):\np5b:=polygonplot3d(G(x1,x1)):\np6 := polygonplot3d(G( 0, 0)):\np7 :=polygonplot3d(G(10,x1)):\np7b:=polygonp lot3d(G(10,x1)):\np8 :=polygonplot3d(G(x1,x1)):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 509 "for i from 0 to n do \nx:=10-i*(10-x2)/n: h1 2[i]:=polygonplot3d(G(x,hh(x))):\n g42[i]:=polygonp lot3d(G(x,gg(x))):\nx:=x2-i*(x2-5)/n: h23[i]:=polygonplot3d(G(x,hh(x ))):\nx:=5+i*5/n: u34[i]:=polygonplot3d(G(x,0)):\nx:=x2+i*(x1- x2)/n; g25[i]:=polygonplot3d(G(x,gg(x))):\nx:=x1-i*x1/n; v56[i] :=polygonplot3d(G(x,x)):\nx:=i*x2/n; f62[i]:=polygonplot3d(G(x ,ff(x))):\nx:=x2+i*(10-x2)/n; f27[i]:=polygonplot3d(G(x,ff(x))):\nx:= x1+i*(10-x1)/n; r71[i]:=polygonplot3d(G(10,x)):\nod:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 829 "P1:=display3d([seq(p1,i=0..n)],ins equence=true):\nP2:=display3d([seq(p2,i=0..n)],insequence=true):\nP3:= display3d([seq(p3,i=0..n)],insequence=true):\nP4:=display3d([seq(p4,i= 0..n)],insequence=true):\nP5:=display3d([seq(p5,i=0..n)],insequence=tr ue):\nP6:=display3d([seq(p6,i=0..n)],insequence=true):\nP7:=display3d( [seq(p7,i=0..n)],insequence=true):\n\nH12:=display3d([seq(h12[i],i=0.. n)],insequence=true):\nH23:=display3d([seq(h23[i],i=0..n)],insequence= true):\nU34:=display3d([seq(u34[i],i=0..n)],insequence=true):\nG42:=di splay3d([seq(g42[i],i=0..n)],insequence=true):\nG25:=display3d([seq(g2 5[i],i=0..n)],insequence=true):\nV56:=display3d([seq(v56[i],i=0..n)],i nsequence=true):\nF62:=display3d([seq(f62[i],i=0..n)],insequence=true) :\nF27:=display3d([seq(f27[i],i=0..n)],insequence=true):\nR71:=display 3d([seq(r71[i],i=0..n)],insequence=true):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 138 "mozi2:=display3d(P1,H12,P2,H23,P3,U34,P4,G42,P2,G2 5,P5,V56,P6,F62,P2,F27,P7,R71,insequence=true, orientation=[70,80],sca ling=CONSTRAINED):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "mozi 2b:=display3d(P2,H23,P3,U34,P4,G42,P2,G25,P5,V56,P6,F62,P2,F27,P7,R71, P1,H12,insequence=true, orientation=[70,80],scaling=CONSTRAINED):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 264 "K2:=display3d(\n polygon plot3d(K),\n polygonplot3d(KL,color=cyan),\n spacecurve([10,t,ff (t)],t=0..10,color=red, linestyle=16),\n spacecurve([10,t,gg(t)],t= 0..10,color=magenta, linestyle=16),\n spacecurve([10,t,hh(t)],t=5.. 10,color=blue, linestyle=16)\n):\n" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 15 "Megjelen\355t\351sek:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "mozi2;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " mozi2b;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "d isplay3d(K2,mozi2,insequence=false);" }{TEXT -1 0 "" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 5 "Mozi3" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 132 "Olyan \372tvonalat tervez\374nk, amely minden kock\341b\363l sz\341rmaztathat\363 f\351l ig szab\341lyos (\351s szab\341lyos) poli\351dert pontosan egyszer tar talmaz." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 19 "M\373veletek sorrendj e" }}{EXCHG {PARA 0 "" 0 "" {TEXT 308 102 "Nr. Jel C \355m x y \+ n\351v " }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{TEXT 309 106 "1. \+ P1 (4,4,4) 10 \+ 10 kocka" }}{PARA 0 "" 0 "" {TEXT -1 92 " 2. \+ R17 10 \+ 10 ->.x1" }}{PARA 0 "" 0 "" {TEXT 310 120 " 3. P7 \+ (8,8,3) 10 x1 \+ cson\355tott kocka" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{TEXT 317 82 " 4. FF78 \+ 10 - > x2 ff(x)" }}{PARA 256 "" 0 "" {TEXT 316 126 " 5. P8 (8,6,4) \+ x2 y2 nagy rombikubokta \351der" }}{PARA 0 "" 0 "" {TEXT -1 6 " 6. " }{TEXT 318 2 " " } {TEXT 319 76 "GG84 x2 -> \+ 10 gg(x)" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 311 116 " 7. P4 (4,3,4,3) 10 \+ 0 kubokta\351der" }}{PARA 0 "" 0 "" {TEXT -1 87 " 8. U43 \+ 10 - > 5 0\n " }{TEXT 312 128 " 9. P3 \+ (6,6,3) 5 0 \+ csonk\355rott okta\351der\n " }{TEXT -1 86 "10. U36 5 - > 0 \+ 0\n " }{TEXT 320 117 "11. P6 (3,3,3,3) \+ 0 0 okta \351der" }}{PARA 0 "" 0 "" {TEXT -1 89 "12, F62 \+ 0. - >.x0 f(x)\n" }{TEXT 313 126 "13. P2 (4,3,3,3) x0 \+ y0 jobbos arkhim\351d\351szi kocka \n" }{TEXT -1 85 "10. G25 \+ x0. - >. x1 g(x)" }}{PARA 0 "" 0 "" {TEXT 314 120 "15 . P5 (4,4,4,3) x1 \+ x1 rombikubokta\351der" }{TEXT -1 86 "\n1 0. G25 x1. - >. y0 \+ g(x)" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 315 125 "17. \+ P9 (4,3,3,3) y0 \+ x0 balos arkhim\351d\351szi kocka\n" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "Tervek" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 485 "SP9:=pont(y0,x0):\nut2:=line([10,1 0],[10,x1],linestyle=16,color=red):\nut4:=line([10,x1],[x2,y2],linesty le=16,color=pink):\nut6:=line([x2,y2],[10,0],linestyle=16,color=gold): \nut8:=line([10, 0],[ 5,0],linestyle=16,color=blue):\nut10:=line([5, 0 ],[ 0,0],linestyle=16,color=orange):\nut12:=plot(f(t),t=0..x0,linestyl e=16,color=blue):\nut14:=plot(g(t),t=x1..x0,linestyle=16,color=magenta ):\nut16:=plot(g(t),t=y0..x1,linestyle=16,color=brown):\nut18:=plot(k( t),t=y0..10,linestyle=16,color=yellow):\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 140 "display(SP1,SP2,SP3,SP4,SP5,SP6,SP7,SP8,SP9,Ne,\n \+ ut2, ut4, ut6, ut8,ut10,\n ut12,ut14,ut16,ut18,scaling=co nstrained,axes=none);\n" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 15 "A harmadik mozi" }}{EXCHG {PARA 0 "" 0 "" {TEXT 322 2 "n:" } {TEXT -1 37 " a mozg\341s finoms\341ga (A k\351pek sz\341ma " } {TEXT 321 10 "17*(n+1) " }{TEXT -1 6 "lesz!)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "n:=14:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 330 "p1 :=polygonplot3d(G(10,10)): \np2 :=polygonplot3d(R(x0,y0)):\np3 :=polygonplot3d(G( 5, 0)):\np4 :=polygonplot3d(R(10, 0)):\np5a :=poly gonplot3d(R(x1,x1)):\np5:=polygonplot3d(G(x1,x1)):\np5b:=polygonplot3d (L(x1,x1)):\np6 :=polygonplot3d(G( 0, 0)):\np7 :=polygonplot3d(G(10,x1 )):\np8 :=polygonplot3d(G(x2,y2)):\np9 :=polygonplot3d(L(y0,x0)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 505 "for i from 0 to n do \nx:=1 0-i*(10-x1)/n: u17[i]:=polygonplot3d(G(10,x)):\nx:=10-i*(10-x2)/n: u 78[i]:=polygonplot3d(G(x,ff(x))):\nx:=x2+i*(10-x2)/n: u84[i]:=polygon plot3d(G(x,gg(x))):\nx:=10-i*5/n; u43[i]:=polygonplot3d(G(x,0)) :\nx:= 5-i*5/n; u36[i]:=polygonplot3d(G(x,0)):\nx:=i*x0/n; \+ u62[i]:=polygonplot3d(R(x,f(x))):\nx:=x0-i*(x0-x1)/n; u25[i]:=po lygonplot3d(R(x,g(x))):\nx:=x1-i*(x1-y0)/n; u59[i]:=polygonplot3d(L(x ,g(x))):\nx:=y0+i*(10-y0)/n; u91[i]:=polygonplot3d(L(x,k(x))):\nod:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 546 "P1:=display3d([seq(p1,i= 0..n)],insequence=true):\nP2:=display3d([seq(p2,i=0..n)],insequence=tr ue):\nP3:=display3d([seq(p3,i=0..n)],insequence=true):\nP4:=display3d( [seq(p4,i=0..n)],insequence=true):\nP5a:=display3d([seq(p5a,i=0..n/2)] ,insequence=true):\nP5:=display3d([seq(p5,i=0..n)],insequence=true):\n P5b:=display3d([seq(p5b,i=0..n/2)],insequence=true):\nP6:=display3d([s eq(p6,i=0..n)],insequence=true):\nP7:=display3d([seq(p7,i=0..n)],inseq uence=true):\nP8:=display3d([seq(p8,i=0..n)],insequence=true):\nP9:=di splay3d([seq(p9,i=0..n)],insequence=true):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 485 "U17:=display3d([seq(u17[i],i=0..n)],insequence=tru e):\nU78:=display3d([seq(u78[i],i=0..n)],insequence=true):\nU84:=displ ay3d([seq(u84[i],i=0..n)],insequence=true):\nU43:=display3d([seq(u43[i ],i=0..n)],insequence=true):\nU36:=display3d([seq(u36[i],i=0..n)],inse quence=true):\nU62:=display3d([seq(u62[i],i=0..n)],insequence=true):\n U25:=display3d([seq(u25[i],i=0..n)],insequence=true):\nU59:=display3d( [seq(u59[i],i=0..n)],insequence=true):\nU91:=display3d([seq(u91[i],i=0 ..n)],insequence=true):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "mozi3:=display3d(\nP1,U17,P7,U78,P8,U84,P4,U43,P3,U36,P6,U62,\nP2,U25 ,P5a,P5,P5b,U59,P9,U91,insequence=true, orientation=[70,80]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "mozi3b:=display3d(\nP8,U84, P4,U43,P3,U36,P6,U62,\nP2,U25,P5a,P5,P5b,U59,P9,U91,P1,U17,P7,U78,inse quence=true, orientation=[70,80],scaling=CONSTRAINED):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 516 "K3:=display3d(\n polygonplot3d( K),\n polygonplot3d(KL,color=cyan),\n spacecurve([10,t,f(t)],t=0 ..10,color=red, linestyle=16),\n spacecurve([10,t,k(t)],t=0..10,col or=yellow, linestyle=16),\n spacecurve([10,t,g(t)],t=0..10,color=ma genta, linestyle=16),\n spacecurve([10,t,h(t)],t=5..10,color=blue, \+ linestyle=16),\n spacecurve([10,t,ff(t)],t=0..10,color=red, linesty le=16),\n spacecurve([10,t,gg(t)],t=0..10,color=magenta, linestyle= 16),\n spacecurve([10,t,hh(t)],t=5..10,color=blue, linestyle=16)\n) :\n" }}}{SECT 1 {PARA 20 "" 0 "" {TEXT -1 15 "Megjelen\355t\351sek:" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "mozi3;" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "mozi3b;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "display3d(K3,mozi3,insequence=false,scaling=c onstrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 "N\351vvel ell\341tott mozi" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "V\341lasszuk ki, hogy magyar, vagy angol nevekkel l\341ss uk el a poli\351dereket." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 20 "Magy ar elnevez\351sek\n" }{TEXT 334 14 "Az elnevez\351sek" }{TEXT 340 1 " " }{TEXT 335 16 "dr. G\351vay G\341bor " }{TEXT 341 59 "egyetemi adju nktust\363l - SZTE Bolyaii Int\351zet - sz\341rmaznak. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 382 "n:=24:\nTF:=[TIMES,BOLD,14]:\nN0:= ` `:\nN1:=`Kocka: (4,4,4)`:\nN2:=`(Jobbos) arkhim\351d\351szi kocka : (4,3,3,3,3)`:\nN3:=`Arkhim\351d\351szi csonk\355tott okta\351der: (6 ,6,4)`:\nN4:=`Kubokta\351der: (4,3,4,3)`:\nN5:=`Rombikubokta\351der: ( 4,4,4,3)`:\nN6:=`Okta\351der: (3,3,3,3)`:\nN7:=`Arkhim\351d\351szi cso nk\355tott kocka: (8,8,3)`:\nN8:=`Nagy rombikubokta\351der: (8,6,4)`: \nN9:=`(Balos) arkhim\351deszi kocka: (4,3,3,3,3)`:\n" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 18 "Angol elnevez\351sek\n" }{TEXT 336 27 "Az elnevez\351sek (p\351 ld\341ul) a " }{TEXT 337 4 "POLY" }{TEXT 338 31 " nev\373 c\351lprogra m elnevez\351sei: " }{TEXT 339 19 "http:\\\\www.peda.com" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 358 "n:=24:\nTF:=[TIMES,BOLD,16]:\nN0:= ` `:\nN1:=`Cube: (4,4,4)`:\nN2:=`(Right-handed) Snub Cube: (4,3,3,3 ,3)`:\nN3:=`Tuncated Octahedron: (6,6,4)`:\nN4:=`Cuboctahedron: (4,3,4 ,3)`:\nN5:=`Rhombicuboctahedron: (4,4,4,3)`:\nN6:=`Octahedron: (3,3,3, 3)`:\nN7:=`Tuncated Cube: (8,8,3)`:\nN8:=`Great Rhombicuboctahedron:: \+ (8,6,4)`:\nN9:=`(Left-handed) Snub Cube: (4,3,3,3,3)`:\n" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 573 "p1 :=polygonplot3d(G(10,10),titlefont=TF,title=N1): \+ \np2 :=polygonplot3d(R(x0,y0),titlefont=TF,title=N2):\np3 :=polygonplo t3d(G( 5, 0),titlefont=TF,title=N3):\np4 :=polygonplot3d(R(10, 0),titl efont=TF,title=N4):\np5a :=polygonplot3d(R(x1,x1),titlefont=TF,title=N 0):\np5:=polygonplot3d(G(x1,x1),titlefont=TF,title=N5):\np5b:=polygonp lot3d(L(x1,x1),titlefont=TF,title=N0):\np6 :=polygonplot3d(G( 0, 0),ti tlefont=TF,title=N6):\np7 :=polygonplot3d(G(10,x1),titlefont=TF,title= N7):\np8 :=polygonplot3d(G(x2,y2),titlefont=TF,title=N8):\np9 :=polygo nplot3d(L(y0,x0),titlefont=TF,title=N9):\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 713 "for i from 0 to n do \nx:=10-i*(10-x1)/n: u17[i]: =polygonplot3d(G(10,x)\n,titlefont=TF,title=N0):\nx:=10-i*(10-x2)/n: \+ u78[i]:=polygonplot3d(G(x,ff(x))\n,titlefont=TF,title=N0):\nx:=x2+i*(1 0-x2)/n: u84[i]:=polygonplot3d(G(x,gg(x))\n,titlefont=TF,title=N0):\n x:=10-i*5/n; u43[i]:=polygonplot3d(G(x,0)\n,titlefont=TF,title= N0):\nx:= 5-i*5/n; u36[i]:=polygonplot3d(G(x,0)\n,titlefont=TF, title=N0):\nx:=i*x0/n; u62[i]:=polygonplot3d(R(x,f(x))\n,titl efont=TF,title=N0):\nx:=x0-i*(x0-x1)/n; u25[i]:=polygonplot3d(R(x,g(x ))\n,titlefont=TF,title=N0):\nx:=x1-i*(x1-y0)/n; u59[i]:=polygonplot3 d(L(x,g(x))\n,titlefont=TF,title=N0):\nx:=y0+i*(10-y0)/n; u91[i]:=pol ygonplot3d(L(x,k(x))\n,titlefont=TF,title=N0):\nod:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 548 "P1:=display3d([seq(p1,i=0..n)],ins equence=true):\nP2:=display3d([seq(p2,i=0..n)],insequence=true):\nP3:= display3d([seq(p3,i=0..n)],insequence=true):\nP4:=display3d([seq(p4,i= 0..n)],insequence=true):\nP5a:=display3d([seq(p5a,i=0..n/2)],insequenc e=true):\nP5:=display3d([seq(p5,i=0..n)],insequence=true):\nP5b:=displ ay3d([seq(p5b,i=0..n/2)],insequence=true):\nP6:=display3d([seq(p6,i=0. .n)],insequence=true):\nP7:=display3d([seq(p7,i=0..n)],insequence=true ):\nP8:=display3d([seq(p8,i=0..n)],insequence=true):\nP9:=display3d([s eq(p9,i=0..n)],insequence=true):\n\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 485 "U17:=display3d([seq(u17[i],i=0..n)],insequence=true) :\nU78:=display3d([seq(u78[i],i=0..n)],insequence=true):\nU84:=display 3d([seq(u84[i],i=0..n)],insequence=true):\nU43:=display3d([seq(u43[i], i=0..n)],insequence=true):\nU36:=display3d([seq(u36[i],i=0..n)],insequ ence=true):\nU62:=display3d([seq(u62[i],i=0..n)],insequence=true):\nU2 5:=display3d([seq(u25[i],i=0..n)],insequence=true):\nU59:=display3d([s eq(u59[i],i=0..n)],insequence=true):\nU91:=display3d([seq(u91[i],i=0.. n)],insequence=true):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "m ozi4:=display3d(\nP1,U17,P7,U78,P8,U84,P4,U43,P3,U36,P6,U62,\nP2,U25,P 5a,P5,P5b,U59,P9,U91,insequence=true, orientation=[30,60],scaling=CONS TRAINED):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "mozi4b:=displ ay3d(\nP8,U84,P4,U43,P3,U36,P6,U62,\nP2,U25,P5a,P5,P5b,U59,P9,U91,P1,U 17,P7,U78,insequence=true, orientation=[70,80],scaling=CONSTRAINED):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "mozi4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "mozi4b;" }{TEXT -1 0 "" }}}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 6 "Egy \374tt" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 318 "A:=array(1..3,1.. 3):\nA[1,1]:=polygonplot3d(G(10,10)):\nA[1,2]:=polygonplot3d(G(10,x1)) :\nA[1,3]:=polygonplot3d(G(x2,y2)):\nA[2,1]:=polygonplot3d(G(10, 0)): \nA[2,2]:=polygonplot3d(G( 5, 0)):\nA[2,3]:=polygonplot3d(G( 0, 0)):\n A[3,1]:=polygonplot3d(L(x0,y0)):\nA[3,2]:=polygonplot3d(G(x1,x1)):\nA[ 3,3]:=polygonplot3d(R(y0,x0)):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "display3d(A,scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 362 "display3d(\{translate(A[1,1], 25,0, 25),\n translate(A[1,2], 0, 0, 25),\n translate(A[1,3],- 25,0, 25),\n translate(A[2,1], 25,0, 0),\n A[2,2] ,\n translate(A[2,3],-25,0, 0),\n translate(A[3,1 ],-25,0,-25),\n translate(A[3,2], 0,0,-25),\n tra nslate(A[3,3], 25,0,-25)\n\n\},scaling=constrained);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "replot(% , view=[-36..36, 0.1..12, -36..36], style=PATCH);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "Eg y \"mell\351kterm\351k\"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 733 "H :=(x,y) ->[\n[[ x, y, 10],[ -y, x, 10],[ -x, -y, 10],[ y, -x, \+ 10]],\n[[ -x,-10, -y],[ -y,-10, x],[ x,-10, y],[ y,-10, -x]],\n[[ \+ -y, -x,-10],[ x, -y,-10],[ y, x,-10],[ -x, y,-10]],\n[[-10, -y, -x ],[-10, x, -y],[-10, y, x],[-10, -x, y]], \n[[ 10, x, y],[ 10, - y, x],[ 10, -x, -y],[ 10, y, -x]],\n[[ y, 10, x],[ x, 10, -y],[ - y, 10, -x],[ -x, 10, y]],\n[[ x, y, 10],[ 10, x, y],[ y, 10, x] ],\n[[ -x, 10, y],[ -y, x, 10],[-10, y, x]],\n[[ y,-10, -x],[ x, -y,-10],[ 10, -x, -y]], \n[[ -y, -x,-10],[-10, -y, -x],[ -x,-10, -y]] ,\n[[ y, -x, 10],[ 10, -y, x],[ x,-10, y]],\n[[-10, -x, y],[ -y,- 10, x],[ -x, -y, 10]], \n[[ 10, y, -x],[ x, 10, -y],[ y, x,-10]], \n[[ -y, 10, -x],[ -x, y,-10],[-10, x, -y]]]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "n:=20:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "display3d(seq(polygonplot3d(H(10*i/n,g(10*i/n))),i=0..n),\nins equence=true,scaling=constrained);" }{TEXT -1 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "0" 0 }{VIEWOPTS 1 1 1 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }