Dandelinsche Kugeln im Kegel

Prof. Dr. Dörte Haftendorn Nov. 06, http://haftendorn.uni-lueneburg.de

alpha:=PI/4:betta:=PI/3: m:=2:

d:=2*m*sin(alpha)/(sin(betta)-sin(alpha)):

R:=(m+d)*sin(alpha):

keg:=plot::Surface([h*tan(alpha)*cos(t),h*tan(alpha)*sin(t),-h],

            t=0..2*PI,h=0..m+R/tan(betta)

    ,Color=[1,0,0,0.5],FillColorType=Flat, Mesh=[30,30]):

eb:=plot::Implicit3d(-cos(betta)*x+sin(betta)*z=-m*(sin(alpha)+sin(betta)),

      x=-R..R,y=-R/2..R/2,z=-m-R/tan(betta)..0,

      FillColorType=Flat,FillColor=[1,0.5,0,1]):

ko:=plot::Sphere(m*sin(alpha),[0,0,-m]):

ku:=plot::Surface([R*cos(t)*cos(phi),R*sin(t)*cos(phi),-(m+d)+R*sin(phi)],

               t=0..2*PI,phi=PI/4..PI/2, FillColor=[0,0,1,0.8]):

nv:=plot::Arrow3d([-5*cos(betta),0,5*sin(betta)]):

line:=plot::Line3d([m*sin(alpha)*cos(t),m*sin(alpha)*sin(t),-m],

        [(m+d)*sin(alpha)*cos(t),(m+d)*sin(alpha)*sin(t),-(m+d)],

        LineWidth=0.8,LineColor=[0,1,0],t=0..2*PI):

 

plot(keg, eb,ko,ku,nv, Scaling=Constrained)

MuPAD graphics

uf1:=m*sin(alpha)*cos(betta):

vf1 :=m*(1+sin(alpha)*sin(betta)) :

uf2:=(m+d)*sin(alpha)*cos(betta):

vf2 :=(m+d)*(1-sin(alpha)*sin(betta)) :

 

F1g:=plot::Point3d([uf1,0,-vf1], PointSize=40,

PointColor=RGB::Black):

F2g:=plot::Point3d([-uf2,0,-vf2], PointSize=40,

PointColor=RGB::Black):

Wo schneidet die grüne Gerade die Ebene?

hz:=(cos(betta)*tan(alpha)*cos(t)+ sin(betta))^(-1)*m*(sin(alpha)+sin(betta))

math

lineM1:=plot::Line3d([m*cos(alpha)*sin(alpha)*cos(t),

           m*cos(alpha)*sin(alpha)*sin(t),-m*cos(alpha)*cos(alpha)],

        [hz*tan(alpha)*cos(t),hz*tan(alpha)*sin(t),-hz],

        LineWidth=0.8,LineColor=[0,1,0],t=0..2*PI):

 

lineM2:=plot::Line3d([(m+d)*cos(alpha)*sin(alpha)*cos(t),

        (m+d)*cos(alpha)*sin(alpha)*sin(t),-(m+d)*cos(alpha)*cos(alpha)],

        [hz*tan(alpha)*cos(t),hz*tan(alpha)*sin(t),-hz],

        LineWidth=0.8,LineColor=[0,1,1],t=0..2*PI):

 

lineF1:=plot::Line3d([uf1,0,-vf1],

        [hz*tan(alpha)*cos(t),hz*tan(alpha)*sin(t),-hz],

        LineWidth=0.8,LineColor=[0,1,0],t=0..2*PI):

lineF2:=plot::Line3d([-uf2,0,-vf2],

        [hz*tan(alpha)*cos(t),hz*tan(alpha)*sin(t),-hz],

        LineWidth=0.8,LineColor=[0,1,1],t=0..2*PI):

kro:=plot::Circle3d(m*cos(alpha)*sin(alpha),

          [0,0,-m*cos(alpha)*cos(alpha)],[0,0,1]):

kru:=plot::Circle3d((m+d)*cos(alpha)*sin(alpha),

          [0,0,-(m+d)*cos(alpha)*cos(alpha)],[0,0,1]):

kotr:=plot::Sphere(m*sin(alpha),[0,0,-m],FillColor=[1,0.5,0,0.85]):

kutr:=plot::Surface([R*cos(t)*cos(phi),R*sin(t)*cos(phi),-(m+d)+R*sin(phi)],

               t=0..2*PI,phi=PI/4..PI/2,

               FillColor=[0,0,1,0.8]):

kegleer:=plot::Surface([h*tan(alpha)*cos(t),h*tan(alpha)*sin(t),-h],

            t=0..2*PI,h=0..m+R/tan(betta)

    ,Color=[1,0,0,0.25],FillColorType=Flat, Mesh=[30,30]):

plot(eb,lineM1,lineM2,lineF1,lineF2,F1g,F2g, kro,kru,kutr,

                kotr,Axes=None,kegleer);

MuPAD graphics

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