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added images of simplexes

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Martin Thoma 2013-11-23 12:45:45 +01:00
parent 01873065be
commit dc7ffd3994
6 changed files with 87 additions and 2 deletions
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documents/GeoTopo/GeoTopo.pdf
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documents/GeoTopo/Kapitel2.tex
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@ -511,7 +511,7 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$.
\begin{beispiel}
\begin{enumerate}[label=\arabic*)]
\item Alle endlichen Gruppen sind 0-Dimensionale Lie-Gruppen.
\item Alle endlichen Gruppen sind 0-dimensionale Lie-Gruppen.
\item $\text{GL}_n(\mdr)$
\item $(\mdr^\times, \cdot)$
\item $(\mdr_{>0}, \cdot)$
@ -577,7 +577,28 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$.
\end{enumerate}
\end{definition}
\todo[inline]{Bilder von 1, 2, 3-simplex}
\begin{figure}[ht]
\centering
\subfloat[0-Simplex $\Delta^0$]{
\parbox{5cm}{\centering\input{figures/topology-simplex-0.tex}}
\label{fig:simplex-0}
}
\subfloat[1-Simplex $\Delta^1$]{
\input{figures/topology-simplex-1.tex}
\label{fig:simplex-1}
}%
\subfloat[2-Simplex $\Delta^2$]{
\input{figures/topology-simplex-2.tex}
\label{fig:simplex-2}
}%
\subfloat[3-Simplex $\Delta^3$]{
\input{figures/topology-simplex-3.tex}
\label{fig:simplex-3}
}%
\label{fig:k-simplexe}
\caption{Beispiele für $k$-Simplexe}
\end{figure}
% Die Übungsaufgaben sollen ganz am Ende des Kapitels sein.
\input{Kapitel2-UB}

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documents/GeoTopo/figures/topology-simplex-0.tex Normal file
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@ -0,0 +1,4 @@
\begin{tikzpicture}[thick]
\draw[thick, fill=black, black] (0cm,0cm) circle(0.1cm);
%\node[below] {$1$};
\end{tikzpicture}

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documents/GeoTopo/figures/topology-simplex-1.tex Normal file
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@ -0,0 +1,25 @@
\begin{tikzpicture}
\tikzstyle{point}=[thick,draw=black,cross out,inner sep=0pt,minimum width=4pt,minimum height=4pt]
\begin{axis}[
legend pos=south west,
axis x line=middle,
axis y line=middle,
grid = major,
width=5cm,
height=5cm,
grid style={dashed, gray!30},
xmin=0, % start the diagram at this x-coordinate
xmax=3, % end the diagram at this x-coordinate
ymin=0, % start the diagram at this y-coordinate
ymax=3, % end the diagram at this y-coordinate
%xlabel=$x$,
%ylabel=$y$,
tick align=outside,
minor tick num=-3,
enlargelimits=true,
tension=0.08]
\addplot[domain=0:2.5, red, thick,samples=20] {-x+2.5};
\node[point,label={[label distance=0cm]45:$e_0$}] at (axis cs:2.5,0) {};
\node[point,label={[label distance=0cm]0:$e_1$}] at (axis cs:0,2.5) {};
\end{axis}
\end{tikzpicture}

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documents/GeoTopo/figures/topology-simplex-2.tex Normal file
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@ -0,0 +1,24 @@
\begin{tikzpicture}
\tikzstyle{point}=[thick,draw=black,cross out,inner sep=0pt,minimum width=4pt,minimum height=4pt]
\begin{axis}[
legend pos=south west,
axis x line=middle,
axis y line=middle,
grid = major,
width=5cm,
height=5cm,
grid style={dashed, gray!30},
xmin=0, % start the diagram at this x-coordinate
xmax=3, % end the diagram at this x-coordinate
ymin=0, % start the diagram at this y-coordinate
ymax=3, % end the diagram at this y-coordinate
tick align=outside,
minor tick num=-3,
enlargelimits=true,
tension=0.08]
\node (a)[point,label={[label distance=0cm]5:$e_0$}] at (axis cs:2.5,0) {};
\node (b)[point,label={[label distance=0cm]5:$e_1$}] at (axis cs:0,2.5) {};
\node (c)[point,label={[label distance=0cm]0:$e_2$}] at (axis cs:2,2) {};
\draw[thick,fill=orange!50] (a.center) -- (b.center) -- (c.center) -- cycle;
\end{axis}
\end{tikzpicture}

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documents/GeoTopo/figures/topology-simplex-3.tex Normal file
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@ -0,0 +1,11 @@
\begin{tikzpicture}
\tikzstyle{point}=[thick,draw=black,cross out,inner sep=0pt,minimum width=4pt,minimum height=4pt]
\node (a)[point,label={[label distance=0cm]180:$e_0$}] at (0,0) {};
\node (b)[point,label={[label distance=0cm]0:$e_1$}] at (2,0) {};
\node (c)[point,label={[label distance=0cm]0:$e_2$}] at (1,2) {};
\node (d)[point,label={[label distance=0cm]0:$e_3$}] at (1,0.7) {};
\draw (a.center) -- (b.center) -- (c.center) -- cycle;
\draw[dashed] (a.center) -- (d.center) -- (b.center);
\draw[dashed] (d.center) -- (c.center);
\end{tikzpicture}