diff --git a/material/ab1.pdf b/material/ab1.pdf index 8d02cbd..d0cb77a 100644 Binary files a/material/ab1.pdf and b/material/ab1.pdf differ diff --git a/material/ab1.tex b/material/ab1.tex index df12b98..6d921ea 100644 --- a/material/ab1.tex +++ b/material/ab1.tex @@ -104,11 +104,11 @@ after skip=10pt } -\newtcolorbox{taskbox}[1][]{ +\newtcolorbox{extrataskbox}[1][]{ before title={\refstepcounter{commoncounter}}, % KRITISCH: vor dem Titel! - title={Aufgabe \thecommoncounter: #1}, + title={Zusatzaufgabe: #1}, colback=white, - colframe=white!75!orange, + colframe=white!75!red, fonttitle=\bfseries, boxrule=0.6mm, coltitle=black, @@ -242,12 +242,102 @@ \begin{center} \textit{Die Summe des Steins ist die Summe der darüberliegenden Steine. } \end{center} - \begin{figure}[H] + \begin{figure}[!ht] \centering - \includegraphics[width=0.7\linewidth]{pyramide_01} + \begin{circuitikz}[x=0.8cm,y=0.8cm] + + % oberste Reihe + \draw[dashed,gray!60] (8.875,16.25) rectangle (10.25,14.875); + \node[text=gray!60] at (9.55,15.5625) {0}; + + \draw (10.25,16.25) rectangle (13,14.875); + \node[anchor=center] at (11.6,15.5625) {1}; + + \draw[dashed,gray!60] (13,16.25) rectangle (14.375,14.875); + \node[text=gray!60] at (13.75,15.5625) {0}; + + % zweite Reihe + \draw[dashed,gray!60] (7.5,14.875) rectangle (8.875,13.5); + \node[text=gray!60] at (8.175,14.1875) {0}; + + \draw (8.875,14.875) rectangle (11.625,13.5); + + \draw (11.625,14.875) rectangle (14.375,13.5); + + \draw[dashed,gray!60] (14.375,14.875) rectangle (15.75,13.5); + \node[text=gray!60] at (15,14.1875) {0}; + + % dritte Reihe + \draw[dashed,gray!60] (6.125,13.5) rectangle (7.5,12.125); + \node[text=gray!60] at (6.8,12.8125) {0}; + + \draw (7.5,13.5) rectangle (10.25,12.125); + + \draw (10.25,13.5) rectangle (13,12.125); + + \draw (13,13.5) rectangle (15.75,12.125); + + \draw[dashed,gray!60] (15.75,13.5) rectangle (17.125,12.125); + \node[text=gray!60] at (16.375,12.8125) {0}; + + % unterste Reihe + \draw[dashed,gray!60] (4.75,12.125) rectangle (6.125,10.75); + \node[text=gray!60] at (5.425,11.4375) {0}; + + \draw (6.125,12.125) rectangle (8.875,10.75); + + \draw (8.875,12.125) rectangle (11.625,10.75); + + \draw (11.625,12.125) rectangle (14.375,10.75); + + \draw (14.375,12.125) rectangle (17.125,10.75); + + \draw[dashed,gray!60] (17.125,12.125) rectangle (18.5,10.75); + \node[text=gray!60] at (17.875,11.4375) {0}; + + \end{circuitikz} \end{figure} + \item Berechne die Steine der Pyramide: + \begin{figure}[!ht] + \centering + \begin{circuitikz}[x=0.8cm,y=0.8cm] + + \draw (10.25,16.25) rectangle (13,14.875); + \node at (10.875,15.5625) {$\binom{0}{0}=$}; + + \draw (8.875,14.875) rectangle (11.625,13.5); + \node at (9.5,14.1875) {$\binom{1}{0}=$}; + + \draw (11.625,14.875) rectangle (14.375,13.5); + \node at (12.25,14.1875) {$\binom{1}{1}=$}; + + \draw (10.25,13.5) rectangle (13,12.125); + \node at (10.875,12.8125) {$\binom{2}{0}=$}; + + \draw (7.5,13.5) rectangle (10.25,12.125); + \node at (8.125,12.8125) {$\binom{2}{1}=$}; + + \draw (13,13.5) rectangle (15.75,12.125); + \node at (13.625,12.8125) {$\binom{2}{2}=$}; + + \draw (11.625,12.125) rectangle (14.375,10.75); + \node at (12.25,11.4375) {$\binom{3}{0}=$}; + + \draw (8.875,12.125) rectangle (11.625,10.75); + \node at (9.5,11.4375) {$\binom{3}{1}=$}; + + \draw (6.125,12.125) rectangle (8.875,10.75); + \node at (6.75,11.4375) {$\binom{3}{2}=$}; + + \draw (14.375,12.125) rectangle (17.125,10.75); + \node at (15,11.4375) {$\binom{3}{3}=$}; + \end{circuitikz} + \end{figure} \end{enumerate} + \begin{extrataskbox} + Entwirf einen Computeralgorithmus, der den Binomialkoeffizienten berechnet, ohne dass dieser die Fakultät benutzt! + \end{extrataskbox} \label{LastPage} \end{document}