

%% 
%% This is a LaTeX document generated by automatic conversion of a
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%% package file named notebook2e.sty.  Appropriate commands for 
%% loading the package have been included in this document.
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%% The LaTeX package used in this document may require that your 
%% LaTeX implementation support fonts other than the standard 
%% Computer Modern fonts that are used by LaTeX.  For more
%% information see the Additional Information under TeXSave
%% in the Help Browser, or at
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%% http://documents.wolfram.com/functions/TeXSave.html
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%% Implementation-specific instructions for installing TeX-related 
%% files can be found at
%% 
%% http://support.wolfram.com/mathematica/interface/export/virtualfonts.html
%% 
%% 

\documentclass{article}
\usepackage{notebook2e, latexsym}


\begin{document}

Feuerbachkreis

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\Mvariable{SetDirectory}[  \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} "D:/Dokumente\multsp und\multsp Einstellungen/vmesser/Eigene\multsp Dateien/  \\
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\hspace{3.em} \Mvariable{diplom/Mathematica"}];  \\
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\noalign{\vspace{0.625ex}}
\hspace{1.em} \Mvariable{x13},\Mvariable{x14},\Mvariable{x15},\Mvariable{x16},\Mvariable{x17},\Mvariable{x18},y];\\
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(*\Mvariable{Punkte}\multsp \Mvariable{definieren}*)  \\
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\hspace{1.em} A=\Muserfunction{point}[0,0];B=\Muserfunction{point}[\Mvariable{u1},0];\IndentingNewLine   \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} C=\Muserfunction{point}[\Mvariable{u2},\Mvariable{u3}];  \\
\noalign{\vspace{0.625ex}}\Mvariable{Ma}=\Muserfunction{point}[\Mvariable{x1},\Mvariable{x2}];\Mvariable{Mb}=\Muserfunction{point}[\Mvariable{x3},\Mvariable{x4}];\Mvariable{Mc}=\Muserfunction{point}[\Mvariable{x5},0];\IndentingNewLine
  \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} \Mvariable{FA}=\Muserfunction{point}[\Mvariable{x7},\Mvariable{x8}];\Mvariable{FB}=\Muserfunction{point}[\Mvariable{x9},\Mvariable{x10}];\Mvariable{FC}=\Muserfunction{point}[\Mvariable{x11},0];\IndentingNewLine
  \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} \Mvariable{NA}=\Muserfunction{point}[\Mvariable{x13},\Mvariable{x14}];\Mvariable{NB}=\Muserfunction{point}[\Mvariable{x15},\Mvariable{x16}];\Mvariable{NC}=\Muserfunction{point}[\Mvariable{x17},\Mvariable{x18}];\\
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\MathBegin{MathArray}{l}
(*\Mvariable{Hilfskonstruktionen}*)  \\
\noalign{\vspace{0.625ex}}a=\Muserfunction{ppline}[B,C]\\
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\{\Mvariable{u3},\Mvariable{u1}-\Mvariable{u2},-\Mvariable{u1}\multsp \Mvariable{u3}\}
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\{\Mvariable{u3},-\Mvariable{u2},0\}
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c=\Muserfunction{ppline}[A,B]
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\{0,1,0\}
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H=\Muserfunction{intersectionpoint}[\Muserfunction{ppline}[A,\Mvariable{FA}],\Muserfunction{ppline}[C,\Mvariable{FC}]]
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\Big\{\frac{\Mvariable{u3}\multsp \Mvariable{x11}\multsp \Mvariable{x7}}{\Mvariable{u3}\multsp \Mvariable{x7}-\Mvariable{u2}\multsp \Mvariable{x8}+\Mvariable{x11}\multsp
\Mvariable{x8}},\frac{\Mvariable{u3}\multsp \Mvariable{x11}\multsp \Mvariable{x8}}{\Mvariable{u3}\multsp \Mvariable{x7}-\Mvariable{u2}\multsp \Mvariable{x8}+\Mvariable{x11}\multsp
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S=\Muserfunction{intersectionpoint}[\Muserfunction{ppline}[A,\Mvariable{Ma}],\Muserfunction{ppline}[C,\Mvariable{Mc}]]
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\Big\{\frac{\Mvariable{u3}\multsp \Mvariable{x1}\multsp \Mvariable{x5}}{\Mvariable{u3}\multsp \Mvariable{x1}-\Mvariable{u2}\multsp \Mvariable{x2}+\Mvariable{x2}\multsp
\Mvariable{x5}},\frac{\Mvariable{u3}\multsp \Mvariable{x2}\multsp \Mvariable{x5}}{\Mvariable{u3}\multsp \Mvariable{x1}-\Mvariable{u2}\multsp \Mvariable{x2}+\Mvariable{x2}\multsp
\Mvariable{x5}}\Big\}
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\Mvariable{kFeuerbach}=\Muserfunction{p3circle}[\Mvariable{Mc},\Mvariable{FC},\Mvariable{NA}]
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\MathBegin{MathArray}{l}
\Big\{\frac{\Mvariable{x11}\multsp \Mvariable{x14}-\Mvariable{x14}\multsp \Mvariable{x5}}{\Mvariable{x11}-\Mvariable{x5}},\frac{\Mvariable{x14}\multsp
{{\Mvariable{x5}}^2}-{{\Mvariable{x11}}^2}\multsp \Mvariable{x14}}{\Mvariable{x11}-\Mvariable{x5}},  \\
\noalign{\vspace{1.29688ex}}
\hspace{1.em} \frac{\Mvariable{x13}\multsp {{\Mvariable{x11}}^2}-\Mvariable{x5}\multsp {{\Mvariable{x11}}^2}-{{\Mvariable{x13}}^2}\multsp \Mvariable{x11}-{{\Mvariable{x14}}^2}\multsp
\Mvariable{x11}+{{\Mvariable{x5}}^2}\multsp \Mvariable{x11}-\Mvariable{x13}\multsp {{\Mvariable{x5}}^2}+{{\Mvariable{x13}}^2}\multsp \Mvariable{x5}+{{\Mvariable{x14}}^2}\multsp
\Mvariable{x5}}{\Mvariable{x11}-\Mvariable{x5}},  \\
\noalign{\vspace{1.29688ex}}
\hspace{1.em} \frac{{{\Mvariable{x11}}^2}\multsp \Mvariable{x14}\multsp \Mvariable{x5}-\Mvariable{x11}\multsp \Mvariable{x14}\multsp {{\Mvariable{x5}}^2}}{\Mvariable{x11}-\Mvariable{x5}}\Big\}\\
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\Mvariable{MFeuerbach}=\Muserfunction{circlecenter}[\Mvariable{kFeuerbach}]
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\Big\{\frac{\Mvariable{x11}+\Mvariable{x5}}{2},\frac{{{\Mvariable{x13}}^2}-\Mvariable{x11}\multsp \Mvariable{x13}-\Mvariable{x5}\multsp \Mvariable{x13}+{{\Mvariable{x14}}^2}+\Mvariable{x11}\multsp
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\Mvariable{gEuler}=\Muserfunction{ppline}[H,S]
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\MathBegin{MathArray}{l}
\Big\{\frac{\Mvariable{x2}\multsp \Mvariable{x5}\multsp \Mvariable{x7}\multsp {{\Mvariable{u3}}^2}-\Mvariable{x1}\multsp \Mvariable{x11}\multsp \Mvariable{x8}\multsp
{{\Mvariable{u3}}^2}+\Mvariable{u2}\multsp \Mvariable{x11}\multsp \Mvariable{x2}\multsp \Mvariable{x8}\multsp \Mvariable{u3}-\Mvariable{u2}\multsp
\Mvariable{x2}\multsp \Mvariable{x5}\multsp \Mvariable{x8}\multsp \Mvariable{u3}}{\Mvariable{u3}},  \\
\noalign{\vspace{1.21875ex}}
\hspace{1.em} \frac{1}{\Mvariable{u3}}(\Mvariable{x1}\multsp \Mvariable{x11}\multsp \Mvariable{x7}\multsp {{\Mvariable{u3}}^2}-\Mvariable{x1}\multsp
\Mvariable{x5}\multsp \Mvariable{x7}\multsp {{\Mvariable{u3}}^2}-\Mvariable{u2}\multsp \Mvariable{x11}\multsp \Mvariable{x2}\multsp \Mvariable{x7}\multsp
\Mvariable{u3}+\Mvariable{x11}\multsp \Mvariable{x2}\multsp \Mvariable{x5}\multsp \Mvariable{x7}\multsp \Mvariable{u3}+  \\
\noalign{\vspace{1.29688ex}}
\hspace{4.em} \Mvariable{u2}\multsp \Mvariable{x1}\multsp \Mvariable{x5}\multsp \Mvariable{x8}\multsp \Mvariable{u3}-\Mvariable{x1}\multsp \Mvariable{x11}\multsp
\Mvariable{x5}\multsp \Mvariable{x8}\multsp \Mvariable{u3}),\frac{{{\Mvariable{u3}}^2}\multsp \Mvariable{x1}\multsp \Mvariable{x11}\multsp \Mvariable{x5}\multsp
\Mvariable{x8}-{{\Mvariable{u3}}^2}\multsp \Mvariable{x11}\multsp \Mvariable{x2}\multsp \Mvariable{x5}\multsp \Mvariable{x7}}{\Mvariable{u3}}\Big\}\\
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\Mvariable{kUmkreis}=\Muserfunction{p3circle}[A,B,C]
}

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\Big\{\Mvariable{u3},-\Mvariable{u1}\multsp \Mvariable{u3},\frac{\Mvariable{u2}\multsp {{\Mvariable{u1}}^2}-{{\Mvariable{u2}}^2}\multsp \Mvariable{u1}-{{\Mvariable{u3}}^2}\multsp
\Mvariable{u1}}{\Mvariable{u1}},0\Big\}
}

\dispSFinmath{
\Mvariable{MUmkreis}=\Muserfunction{circlecenter}[\Mvariable{kUmkreis}]
}

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\Big\{\frac{\Mvariable{u1}}{2},\frac{{{\Mvariable{u2}}^2}-\Mvariable{u1}\multsp \Mvariable{u2}+{{\Mvariable{u3}}^2}}{2\multsp \Mvariable{u3}}\Big\}
}

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\MathBegin{MathArray}{l}
(*\Mvariable{Konstruktion}\multsp \Mvariable{Seitenmittelpunkte}*)  \\
\noalign{\vspace{0.625ex}}\Muserfunction{AddGleichung}[\Muserfunction{midpoint}[B,C]-\Mvariable{Ma}];\IndentingNewLine   \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} \Muserfunction{AddGleichung}[\Muserfunction{midpoint}[A,C]-\Mvariable{Mb}];\IndentingNewLine   \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} \Muserfunction{AddGleichung}[\Muserfunction{midpoint}[B,A]-\Mvariable{Mc}];\\
\MathEnd{MathArray}
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\dispSFinmath{
\MathBegin{MathArray}{l}
(*\Mvariable{H\ODoubleDot henfu\ss punkte}*)  \\
\noalign{\vspace{0.625ex}}\Muserfunction{AddGleichung}[\Muserfunction{pedalpoint}[A,a]-\Mvariable{FA}];\IndentingNewLine   \\
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\hspace{1.em} \Muserfunction{AddGleichung}[\Muserfunction{pedalpoint}[B,b]-\Mvariable{FB}];\IndentingNewLine   \\
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\hspace{1.em} \Muserfunction{AddGleichung}[\Muserfunction{pedalpoint}[C,c]-\Mvariable{FC}];\\
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\MathBegin{MathArray}{l}
(*\Mvariable{Seitendrittel}*)  \\
\noalign{\vspace{0.625ex}}\Muserfunction{AddGleichung}[\Muserfunction{midpoint}[H,A]-\Mvariable{NA}];\IndentingNewLine   \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} \Muserfunction{AddGleichung}[\Muserfunction{midpoint}[H,B]-\Mvariable{NB}];\IndentingNewLine   \\
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\MathBegin{MathArray}{l}
(*\multsp \Mvariable{polynomials}\multsp *)  \\
\noalign{\vspace{0.625ex}}\Mvariable{polys}=\Mfunction{Map}[\Mfunction{Numerator}[\Mfunction{Together}[\#]]\multsp \&,\multsp \Mvariable{Gleichungen}]\\
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\MathBegin{MathArray}{l}
\{\Mvariable{u1}+\Mvariable{u2}-2\multsp \Mvariable{x1},\Mvariable{u3}-2\multsp \Mvariable{x2},\Mvariable{u2}-2\multsp \Mvariable{x3},\Mvariable{u3}-2\multsp
\Mvariable{x4},  \\
\noalign{\vspace{0.601563ex}}
\hspace{1.em} \Mvariable{u1}-2\multsp \Mvariable{x5},0,-\Mvariable{x7}\multsp {{\Mvariable{u1}}^2}+{{\Mvariable{u3}}^2}\multsp \Mvariable{u1}+2\multsp
\Mvariable{u2}\multsp \Mvariable{x7}\multsp \Mvariable{u1}-{{\Mvariable{u2}}^2}\multsp \Mvariable{x7}-{{\Mvariable{u3}}^2}\multsp \Mvariable{x7},
 \\
\noalign{\vspace{0.601563ex}}
\hspace{1.em} \Mvariable{u3}\multsp {{\Mvariable{u1}}^2}-\Mvariable{x8}\multsp {{\Mvariable{u1}}^2}-\Mvariable{u2}\multsp \Mvariable{u3}\multsp \Mvariable{u1}+2\multsp
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 \\
\noalign{\vspace{0.601563ex}}
\hspace{1.em} \Mvariable{u1}\multsp {{\Mvariable{u2}}^2}-\Mvariable{x9}\multsp {{\Mvariable{u2}}^2}-{{\Mvariable{u3}}^2}\multsp \Mvariable{x9},-\Mvariable{x10}\multsp
{{\Mvariable{u2}}^2}+\Mvariable{u1}\multsp \Mvariable{u3}\multsp \Mvariable{u2}-{{\Mvariable{u3}}^2}\multsp \Mvariable{x10},  \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} \Mvariable{u2}-\Mvariable{x11},0,\Mvariable{u3}\multsp \Mvariable{x11}\multsp \Mvariable{x7}-2\multsp \Mvariable{u3}\multsp \Mvariable{x13}\multsp
\Mvariable{x7}+2\multsp \Mvariable{u2}\multsp \Mvariable{x13}\multsp \Mvariable{x8}-2\multsp \Mvariable{x11}\multsp \Mvariable{x13}\multsp \Mvariable{x8},
 \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} -2\multsp \Mvariable{u3}\multsp \Mvariable{x14}\multsp \Mvariable{x7}+\Mvariable{u3}\multsp \Mvariable{x11}\multsp \Mvariable{x8}+2\multsp
\Mvariable{u2}\multsp \Mvariable{x14}\multsp \Mvariable{x8}-2\multsp \Mvariable{x11}\multsp \Mvariable{x14}\multsp \Mvariable{x8},  \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} \Mvariable{u1}\multsp \Mvariable{u3}\multsp \Mvariable{x7}+\Mvariable{u3}\multsp \Mvariable{x11}\multsp \Mvariable{x7}-2\multsp \Mvariable{u3}\multsp
\Mvariable{x15}\multsp \Mvariable{x7}-\Mvariable{u1}\multsp \Mvariable{u2}\multsp \Mvariable{x8}+\Mvariable{u1}\multsp \Mvariable{x11}\multsp \Mvariable{x8}+2\multsp
\Mvariable{u2}\multsp \Mvariable{x15}\multsp \Mvariable{x8}-2\multsp \Mvariable{x11}\multsp \Mvariable{x15}\multsp \Mvariable{x8},  \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} -2\multsp \Mvariable{u3}\multsp \Mvariable{x16}\multsp \Mvariable{x7}+\Mvariable{u3}\multsp \Mvariable{x11}\multsp \Mvariable{x8}+2\multsp
\Mvariable{u2}\multsp \Mvariable{x16}\multsp \Mvariable{x8}-2\multsp \Mvariable{x11}\multsp \Mvariable{x16}\multsp \Mvariable{x8},  \\
\noalign{\vspace{0.601563ex}}
\hspace{1.em} -\Mvariable{x8}\multsp {{\Mvariable{u2}}^2}+\Mvariable{u3}\multsp \Mvariable{x7}\multsp \Mvariable{u2}+\Mvariable{x11}\multsp \Mvariable{x8}\multsp
\Mvariable{u2}+2\multsp \Mvariable{x17}\multsp \Mvariable{x8}\multsp \Mvariable{u2}+\Mvariable{u3}\multsp \Mvariable{x11}\multsp \Mvariable{x7}-2\multsp
\Mvariable{u3}\multsp \Mvariable{x17}\multsp \Mvariable{x7}-2\multsp \Mvariable{x11}\multsp \Mvariable{x17}\multsp \Mvariable{x8},  \\
\noalign{\vspace{0.601563ex}}
\hspace{1.em} \Mvariable{x7}\multsp {{\Mvariable{u3}}^2}-2\multsp \Mvariable{x18}\multsp \Mvariable{x7}\multsp \Mvariable{u3}-\Mvariable{u2}\multsp
\Mvariable{x8}\multsp \Mvariable{u3}+2\multsp \Mvariable{x11}\multsp \Mvariable{x8}\multsp \Mvariable{u3}+2\multsp \Mvariable{u2}\multsp \Mvariable{x18}\multsp
\Mvariable{x8}-2\multsp \Mvariable{x11}\multsp \Mvariable{x18}\multsp \Mvariable{x8}\}\\
\MathEnd{MathArray}
}

\dispSFinmath{
\MathBegin{MathArray}{l}
(*\Mvariable{conclusion}\multsp \Mvariable{Feuerbachkreis}*)  \\
\noalign{\vspace{0.625ex}}\Mvariable{zz}=\{\Mvariable{FA},\Mvariable{FB},\Mvariable{FC},\Mvariable{NA},\Mvariable{NB},\Mvariable{NC},\Mvariable{Ma},\Mvariable{Mb},\Mvariable{Mc}\};\\
\MathEnd{MathArray}
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\dispSFinmath{
\Mvariable{cons}=\Mfunction{Map}[\multsp (\Muserfunction{oncircle}[\#1,\Mvariable{kFeuerbach}])\&,\Mvariable{zz}];
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\dispSFinmath{
\Mfunction{Map}[\Muserfunction{IdealMember}[\#1,\Mvariable{polys},\Mvariable{vars}]\&,\Mvariable{cons}]//\Mfunction{Timing}
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\{0.22\multsp \Mvariable{Second},\{\Mvariable{True},\Mvariable{True},\Mvariable{True},\Mvariable{True},\Mvariable{True},\Mvariable{True},\Mvariable{True},\Mvariable{True},\Mvariable{True}\}\}
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\dispSFinmath{
\MathBegin{MathArray}{l}
(*\Mvariable{conclusion}\multsp \Mvariable{Euler}\multsp \Mvariable{Gerade}*)  \\
\noalign{\vspace{0.625ex}}\Mvariable{conEuler1}=\Muserfunction{online}[\Mvariable{MFeuerbach},\Mvariable{gEuler}];\IndentingNewLine   \\
\noalign{\vspace{0.625ex}}
\hspace{1.em} \Mvariable{conEuler2}=\Muserfunction{online}[\Mvariable{MUmkreis},\Mvariable{gEuler}];\\
\MathEnd{MathArray}
}

\dispSFinmath{
\MathBegin{MathArray}{l}
\{\Muserfunction{IdealMember}[\Mvariable{conEuler1},\Mvariable{polys},\Mvariable{vars}],  \\
\noalign{\vspace{0.625ex}}
\hspace{2.em} \Muserfunction{IdealMember}[\Mvariable{conEuler2},\Mvariable{polys},\Mvariable{vars}]\}//\Mfunction{Timing}\\
\MathEnd{MathArray}
}

\dispSFoutmath{
\{0.321\multsp \Mvariable{Second},\{\Mvariable{True},\Mvariable{True}\}\}
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\end{document}
