Visualisierung begonnen
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Nis Boerge Wechselberg
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7 changed files with 345 additions and 43 deletions
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main.pdf
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53
main.tex
53
main.tex
|
|
@ -28,6 +28,7 @@
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|||
\newtheorem{beob}{Beobachtung}
|
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\newcommand{\beobautorefname}{Beobachtung}
|
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\newtheorem*{beis}{Beispiel}
|
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\newcommand{\beisautorefname}{Beispiel}
|
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|
||||
|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
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|
|
@ -198,6 +199,7 @@ formalisiert exakt diese Fragestellung.
|
|||
Betrachten wir das Beispiel \(n=2\).
|
||||
|
||||
\begin{beis}[2-Kaffee-Problem]
|
||||
\label{beis:2-kaffee-problem}
|
||||
Sei \(K\) ein 2-Kaffeekränzchen und
|
||||
\(k\) eine K-Kaffeekasse.
|
||||
Nehmen wir an, dass bisher \(p_1\) zweimal
|
||||
|
|
@ -343,21 +345,52 @@ analog zu \autoref{def:kaffeekassentransition}.
|
|||
%% Visualisierung des Kaffeeproblems
|
||||
\section{Visualisierung des Kaffeeproblems}
|
||||
\label{sec:visualisierung}
|
||||
Im folgenden stellen wir Möglichkeiten vor,
|
||||
das Kaffeeproblem für Gruppen aus 2 oder 3 Personen
|
||||
grafisch darzustellen bzw. zu lösen.
|
||||
|
||||
% \begin{figure}
|
||||
% \centering
|
||||
% \includegraphics[scale=1]{2KaffeeProblem}
|
||||
% \caption{%
|
||||
% Visualisierung des \(2\)-Kaffee-Problems.
|
||||
% In diesem Fall schuldet \(p_0\) \(p_1\)
|
||||
% genau \(2\) Kaffees.
|
||||
% }
|
||||
% \label{fig:2_kaffee_problem}
|
||||
% \end{figure}
|
||||
\subsection{Darstellung des 2-Kaffee-Problems}
|
||||
\label{ssec:2-kaffee-problem}
|
||||
Wie bereits in \autoref{beis:2-kaffee-problem} angesprochen,
|
||||
wird nur eine einzelne Komponente der Kaffeekasse benötigt.
|
||||
Somit stellen wir die Kaffeekasse wie in \autoref{fig:2-kaffee-problem} dar.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{2KaffeeProblem}
|
||||
\caption{%
|
||||
Visualisierung des \(2\)-Kaffee-Problems.
|
||||
In diesem Fall schuldet \(p_1\) \(p_2\)
|
||||
noch \(2\) Kaffees.
|
||||
}
|
||||
\label{fig:2-kaffee-problem}
|
||||
\end{figure}
|
||||
|
||||
In der Abbildung lässt sich durch Verschieben
|
||||
des Punktes der Zustand aktualisieren.
|
||||
Hierzu wird der Punkt immer auf diejenige
|
||||
Person zubewegt, die den Kaffee ausgibt.
|
||||
|
||||
|
||||
\subsection{Darstellungen des 3-Kaffee-Problems}
|
||||
Analog zu \autoref{ssec:2-kaffee-problem} kann
|
||||
für die Darstellung des 3-Kaffee-Problems ein
|
||||
kartesisches Koordinatensystem verwendet werden,
|
||||
in dem die Werte von \(\Delta_1\) und \(\Delta_2\)
|
||||
als Koordinaten eingetragen werden.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{3KaffeeKartesisch}
|
||||
\caption{%
|
||||
Visualisierung des \(3\)-Kaffee-Problems mit kartesischen Koordianten.
|
||||
}
|
||||
\label{fig:3-kaffee-kartesisch}
|
||||
\end{figure}
|
||||
|
||||
In \autoref{fig:3-kaffee-kartesisch} ist eine
|
||||
kartesische Darstellung für die Kaffeekasse
|
||||
\(k = (2,-1,-1) \) gegeben.
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
|
|
|||
Loading…
Reference in a new issue