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45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 213 "   Di
e Relationskurve kann - optisch ansprechend - als Schnittkurve eines G
raphen einer Funktion mit zwei Variablen \n   mit der xy-Ebene dargest
ellt werden. Hierzu betrachte die Funktion  f(x,y) = y^2 - x^4 + x^6.
" }{MPLTEXT 1 0 2 "\n\n" }{TEXT -1 0 "" }{MPLTEXT 1 0 124 " plot3d(y^2
-x^4+x^6,x=-1.3..1.3, y=-1.4..1.4,grid=[100,100],style=patchcontour, c
ontours=10, axes=boxed,view=-0.2..1.3);\n\n  " }{TEXT -1 295 "Um Eif
\366rmiges zu erzeugen, gehe von einer Wurzelfunktion aus und schneide
 den zugeh\366rigen Rotationsk\366rper mit einer Ebene,\n     die para
llel zur xy-Ebene ist und von dieser den Abstand h hat. Die Schnittkur
ve (in die xy-Ebene projiziert) wird durch   (f(x))^2 = y^2 + h beschr
ieben (G. Roolfs)\n " }{MPLTEXT 1 0 74 "f:=x->1/5*x*sqrt(12-2*x);\n pl
ot(f(x),x=0..6,scaling=constrained);\n\nh:=0.8:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 88 "implicitplot(y^2+h-(f(x))^2=0,x=1..6.5,y=-1.5..1.5,gr
id=[100,100],scaling=constrained);\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 121 "plot3d(y^2+h-(f(x))^2 ,x=-3..6.5, y=-2..2, grid=[100,100],style
=patchcontour, axes=boxed,view=0..2,scaling=constrained);\n" }}{PARA 
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