{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 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 " " {TEXT -1 567 "Dateiname: tangkegl.mws\nDateigr\366\337e: 760 KB\nNam e: Daniel Weihing\nSchule: Isolde-Kurz-Gymnasium\nKlasse: 13\nDatum: 2 3.3.99\nKategorie: Geometrie / Anwendungen \nThema: Tangentialkegel mi t geom3d\nStichw\366rter: Tangentialkegel, Tangenten, Kugel, geom3d, t ubeplot\nKurzbeschreibung: Ebene in der Tangentialkegel die Kugel ber \374hrt mit Tangentengleichung berechnen. Lot zur Ebene und durch Mitt elpunkt der Kugel und gegebenen Punkt. Abstand zwischen Lotfu\337punkt und Punkt. Mit tubeplot l\344\337t sich Kegel darstellen, hierzu ist \+ Einheitsvektor und tan n\366tig um Radius zu berechnen. " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "Update auf Maple8: 8.6.2004 Michael Klumpp" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "restart:with(plots):with(linalg):with(ge om3d):\nopt:=view=[-10..10,-10..10,-10..10],orientation=[50,-50]:\n" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "point(M,1,2,3);\nr:=5;\npo int(P,-3,-2,-5);coordinates(P);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "sphere(K,[M,r]);\nKplot:=draw(K,style=wireframe,opt) :\nPplot:=display(draw(P,symbol=circle,opt),color=red):\ndisplay(Kplot ,Pplot);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "Ebene:=evalm( ([x,y,z]-coordinates(M))&*(coordinates(P)-coordinates(M))=r^2);\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Ebene := 11-4*x-4*y-8*z = 0; \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "plane(E,Ebene,[x,y,z ]);\nEplot:=draw(E,style=patchnogrid,color=green,opt):\ndisplay(Pplot, Kplot,Eplot);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "n:=Norma lVector(E);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "line(N,[M, vector(n)]);\nNplot:=draw(N,color=blue,thickness=3):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "display(Eplot,Nplot);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "intersection(Ms,N,E);\nMsplot:=dis play(draw(Ms,symbol=circle),color=black):\ndisplay(Eplot,Nplot,Msplot, Kplot,Pplot);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "d:=dista nce(M,Ms);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "rs:=sqrt(r^ 2-d^2);\n" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 40 "Parameterdarstellun g des Schnittkreises:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "u:= [ux,uy,uz]:\nv:=[vx,vy,vz]:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "skp:=innerprod(u,n)=0:\nux,uy:=1,0:uz:=solve(skp,uz):\nu0:=evalm (u/norm(u,2));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "v:=conv ert(crossprod(n,u),list):\nv0:=evalm(v/norm(v,2));\n\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "SK:=evalm(coordinates(Ms)+u0*rs*cos (alpha)+v0*rs*sin(alpha));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "SKplot:=spacecurve(\{SK\},alpha=-Pi..Pi,color=gold,thickness=3): SKplot;\n" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "us:=coordinates(Ms)-coordinates(P); \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "us0:=evalm(us/norm(us ,2));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "d1:=distance(Ms, P);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "alpha:=evalf(arcta n(rs/d1));\n'alpha'=evalf(alpha*180/Pi);\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 168 "Keplot:=tubeplot(evalm(coordinates(P)+evalm(t*us0) ),t=0..d1,radius=t*tan(alpha),style=patchnogrid,color=yellow):\ndispla y(Keplot,Kplot,SKplot,Eplot,Nplot,Msplot,Pplot);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }