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Schöneres Bild für Krümmung des Torus
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MartinThoma committed Feb 20, 2014
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2 changes: 1 addition & 1 deletion documents/GeoTopo/Bildquellen.tex
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Expand Up @@ -28,5 +28,5 @@ \chapter*{Bildquellen\markboth{Bildquellen}{Bildquellen}}
\href{https://commons.wikimedia.org/wiki/File:Spherical_triangle_3d_opti.png}{\path{commons.wikimedia.org/wiki/File:Spherical_triangle_3d_opti.png}}
\item[Abb. \ref{fig:moebius-strip}] Möbiusband: \href{http://tex.stackexchange.com/users/2552/jake}{Jake},
\href{http://tex.stackexchange.com/a/118573/5645}{\path{tex.stackexchange.com/a/118573/5645}}
\item[Abb. \ref{fig:torus-gauss-kruemmung}] Krümmung des Torus: Martin Thoma und Jérôme Urhausen, Email vom 17.02.2014.
\item[Abb. \ref{fig:torus-gauss-kruemmung}] Krümmung des Torus: \href{http://tex.stackexchange.com/users/484/charles-staats}{Charles Staats}, \href{http://tex.stackexchange.com/a/149991/5645}{\path{tex.stackexchange.com/a/149991/5645}}
\end{itemize}
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24 changes: 18 additions & 6 deletions documents/GeoTopo/Kapitel3.tex
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Expand Up @@ -668,6 +668,18 @@ \section{Überlagerungen}\index{Ueberlagerung@""Uberlagerung|(}
\textbf{Liftung} von $f$, wenn $p \circ \tilde{f} = f$ ist.
\end{definition}

\begin{figure}[h]
\centering
\begin{tikzpicture}
\node (Y) {$Y$};
\node (X) [below=0.7cm of Y] {$X$};
\node (Z) [right=1.3cm of Y] {$Z$};
\path[anchor=east,->] (Y) edge node {$p$} (X);
\path[anchor=south,->] (Z) edge node {$\tilde{f}$} (Y);
\path[anchor=north west,->] (Z) edge node {$f$} (X);
\end{tikzpicture}
\end{figure}

\begin{figure}[htp]
\centering
\resizebox{0.95\linewidth}{!}{\input{figures/liftung-torus-r.tex}}
Expand All @@ -682,12 +694,12 @@ \section{Überlagerungen}\index{Ueberlagerung@""Uberlagerung|(}
$\exists z_0 \in Z: f_0(z_0) = f_1(z_0) \Rightarrow f_0 = f_1$
\end{bemerkung}

\begin{figure}[htp]
\centering
\input{figures/commutative-diagram-2.tex}
\caption{Situation aus \cref{kor:12.5}}
\label{fig:situation-kor-12.5}
\end{figure}
% \begin{figure}[htp]
% \centering
% \input{figures/commutative-diagram-2.tex}
% \caption{Situation aus \cref{kor:12.5}}
% \label{fig:situation-kor-12.5}
% \end{figure}

\begin{beweis}
Sei $T = \Set{z \in Z | f_0(z) = f_1(z)}$.
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2 changes: 1 addition & 1 deletion documents/GeoTopo/Kapitel5.tex
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Expand Up @@ -406,7 +406,7 @@ \section{Gauß-Krümmung}\index{Gauß-Krümmung|(}
\item $S = \text{Torus}$. Siehe \cref{fig:torus-gauss-kruemmung}\\
\begin{figure}[htp]\xindex{Torus}
\centering
\input{figures/torus-gauss-kruemmung.tex}
\includegraphics[width=0.95\linewidth, keepaspectratio]{figures/torus-gauss-kruemmung.pdf}
\caption{$K(s_1) > 0$, $K(s_2) = 0$, $K(s_3) < 0$}
\label{fig:torus-gauss-kruemmung}
\end{figure}
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