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In \autoref{fig:3-kaffee-kartesisch} ist eine kartesische Darstellung für die Kaffeekasse \(k = (2,-1,-1) \) gegeben. +Die Aktualisierung der Kaffeekasse, +und das Ablesen der Lösung des 3-Kaffee-Problems, +ist hier allerdings relativ kommpliziert. +Gibt zum Beispiel \(p_1\) nun \(p_2\) einen Kaffee +aus, so muss zunächst im Kopf die +neue Kaffeekasse gebildet werden, +und anschliessend die neuen Werte +für \(\Delta_1\) und \(\Delta_2\) +eingetragen werden. +Zusätzlich ist der Wert von \(\Delta_3\) +nur indirekt zu erkennen. +Dieser ergibt sich aus dem Inversen +des Achensabschnittes +der fallenden Diagonalen, auf der der Punkt +zur Zeit liegt. + +Als alternative Darstellung kann ein +geradliniges, nichtorthgonales Koordiantensystem +gewählt werden. +In diesem System schneiden sich die +Achsen mit einem Winkel von 60° + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%