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Schöneres Bild für Krümmung des Torus
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6 changed files with 20 additions and 8 deletions
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@ -28,5 +28,5 @@ modifiziert.
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\href{https://commons.wikimedia.org/wiki/File:Spherical_triangle_3d_opti.png}{\path{commons.wikimedia.org/wiki/File:Spherical_triangle_3d_opti.png}}
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\item[Abb. \ref{fig:moebius-strip}] Möbiusband: \href{http://tex.stackexchange.com/users/2552/jake}{Jake},
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\href{http://tex.stackexchange.com/a/118573/5645}{\path{tex.stackexchange.com/a/118573/5645}}
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\item[Abb. \ref{fig:torus-gauss-kruemmung}] Krümmung des Torus: Martin Thoma und Jérôme Urhausen, Email vom 17.02.2014.
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\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}}
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\end{itemize}
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@ -668,6 +668,18 @@ Wenn $\pi_1(X,x) = \Set{e}$ für ein $x \in X$ gilt, dann wegen
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\textbf{Liftung} von $f$, wenn $p \circ \tilde{f} = f$ ist.
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\end{definition}
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\begin{figure}[h]
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\centering
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\begin{tikzpicture}
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\node (Y) {$Y$};
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\node (X) [below=0.7cm of Y] {$X$};
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\node (Z) [right=1.3cm of Y] {$Z$};
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\path[anchor=east,->] (Y) edge node {$p$} (X);
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\path[anchor=south,->] (Z) edge node {$\tilde{f}$} (Y);
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\path[anchor=north west,->] (Z) edge node {$f$} (X);
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\end{tikzpicture}
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\end{figure}
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\begin{figure}[htp]
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\centering
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\resizebox{0.95\linewidth}{!}{\input{figures/liftung-torus-r.tex}}
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@ -682,12 +694,12 @@ Wenn $\pi_1(X,x) = \Set{e}$ für ein $x \in X$ gilt, dann wegen
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$\exists z_0 \in Z: f_0(z_0) = f_1(z_0) \Rightarrow f_0 = f_1$
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\end{bemerkung}
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\begin{figure}[htp]
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\centering
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\input{figures/commutative-diagram-2.tex}
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\caption{Situation aus \cref{kor:12.5}}
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\label{fig:situation-kor-12.5}
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\end{figure}
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% \begin{figure}[htp]
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% \centering
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% \input{figures/commutative-diagram-2.tex}
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% \caption{Situation aus \cref{kor:12.5}}
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% \label{fig:situation-kor-12.5}
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% \end{figure}
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\begin{beweis}
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Sei $T = \Set{z \in Z | f_0(z) = f_1(z)}$.
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@ -406,7 +406,7 @@ Im Folgenden werden diese Begriffe jedoch synonym benutzt.
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\item $S = \text{Torus}$. Siehe \cref{fig:torus-gauss-kruemmung}\\
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\begin{figure}[htp]\xindex{Torus}
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\centering
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\input{figures/torus-gauss-kruemmung.tex}
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\includegraphics[width=0.95\linewidth, keepaspectratio]{figures/torus-gauss-kruemmung.pdf}
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\caption{$K(s_1) > 0$, $K(s_2) = 0$, $K(s_3) < 0$}
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\label{fig:torus-gauss-kruemmung}
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\end{figure}
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