Koordinaten im schiefen Koordinatensystem an kartesische koordinaten angepasst, Visualisierung weiter beschrieben
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Nis Börge Wechselberg
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main.pdf
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39
main.tex
39
main.tex
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\usepackage{amssymb}
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\usepackage{gensymb}
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\usepackage{amsthm}
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\usepackage{graphicx}
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\usepackage{todonotes}
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@ -368,9 +370,9 @@ Somit stellen wir die Kaffeekasse wie in \autoref{fig:2-kaffee-problem} dar.
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In der Abbildung lässt sich durch Verschieben
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des Punktes der Zustand aktualisieren.
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Hierzu wird der Punkt immer auf diejenige
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Person zubewegt, die den Kaffee ausgibt.
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Hierzu wird der Punkt immer ``mit dem Kaffee''
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bewegt, also von der ausgebenden Person weg
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und auf die empfangende Person zu.
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\subsection{Darstellungen des 3-Kaffee-Problems}
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Analog zu \autoref{ssec:2-kaffee-problem} kann
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@ -381,7 +383,7 @@ als Koordinaten eingetragen werden.
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\begin{figure}[htbp]
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\centering
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\includegraphics[scale=1]{3KaffeeKartesisch}
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\includegraphics[width=.7\textwidth]{3KaffeeKartesisch}
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\caption{%
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Visualisierung des \(3\)-Kaffee-Problems mit kartesischen Koordianten.
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}
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@ -393,7 +395,7 @@ kartesische Darstellung für die Kaffeekasse
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\(k = (2,-1,-1) \) gegeben.
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Die Aktualisierung der Kaffeekasse,
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und das Ablesen der Lösung des 3-Kaffee-Problems,
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ist hier allerdings relativ kommpliziert.
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ist hier allerdings relativ kompliziert.
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Gibt zum Beispiel \(p_1\) nun \(p_2\) einen Kaffee
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aus, so muss zunächst im Kopf die
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neue Kaffeekasse gebildet werden,
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@ -402,17 +404,34 @@ für \(\Delta_1\) und \(\Delta_2\)
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eingetragen werden.
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Zusätzlich ist der Wert von \(\Delta_3\)
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nur indirekt zu erkennen.
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Dieser ergibt sich aus dem Inversen
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des Achensabschnittes
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Dieser ergibt sich aus dem negativen Achensabschnittes
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der fallenden Diagonalen, auf der der Punkt
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zur Zeit liegt.
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=.7\textwidth]{3KaffeeProblem}
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\caption{%
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Visualisierung des \(3\)-Kaffee-Problems mit schiefen Koordianten
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}
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\label{fig:3-kaffee-schief}
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\end{figure}
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Als alternative Darstellung kann ein
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geradliniges, nichtorthgonales Koordiantensystem
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gewählt werden.
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gewählt werden. In \autoref{fig:3-kaffee-schief}
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In diesem System schneiden sich die
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Achsen mit einem Winkel von 60°
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Achsen mit einem Winkel von 60\degree.
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Bei korrekter Beschriftung der Seiten, können hier
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die selben Koordinaten verwendet werden,
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die bereits im kartesischen Koordinatensystem
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bereechnet wurden.
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Allerdings können hier die Personen an den Seiten
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plaziert werden, um eine einfacher Transition
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zu ermöglichen.
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Auch hier kann nun die Markierung wieder
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``mit dem Kaffee'', von der ausgebenden Person weg
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und auf die empfangende Person zu, verschoben werden.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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