4 files changed, 81 insertions, 1 deletions
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/Makefile b/buch/chapters/80-wahrscheinlichkeit/images/Makefile
index 8042eb1..24c0631 100644
--- a/buch/chapters/80-wahrscheinlichkeit/images/Makefile
+++ b/buch/chapters/80-wahrscheinlichkeit/images/Makefile
@@ -4,7 +4,8 @@
 # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschulen
 #
 all:	dreieck.pdf trenn.pdf vergleich.pdf vergleich.jpg \
-	positiv.pdf positiv.jpg diffusion.png diffusion.pdf
+	positiv.pdf positiv.jpg diffusion.png diffusion.pdf \
+	konvex.pdf
 
 # Visualisierung diffusion in einer primitiven Matrix
 diffusion.pdf:	diffusion.tex diffusion.jpg
@@ -53,3 +54,7 @@ dreieck.pdf:	dreieck.tex drei.inc
 
 drei.inc:	dreieck.m
 	octave dreieck.m
+
+# Konvex
+konvex.pdf:	konvex.tex
+	pdflatex konvex.tex
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/konvex.pdf b/buch/chapters/80-wahrscheinlichkeit/images/konvex.pdf
new file mode 100644
index 0000000..f77cc62
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/konvex.pdf
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/konvex.tex b/buch/chapters/80-wahrscheinlichkeit/images/konvex.tex
new file mode 100644
index 0000000..05bbc60
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/konvex.tex
@@ -0,0 +1,75 @@
+%
+% konvex.tex -- template for standalon tikz images
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math,calc,hobby}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\punkt#1{
+	\fill[color=white] #1 circle[radius=0.05];
+	\draw #1 circle[radius=0.05];
+}
+
+\begin{scope}[xshift=-3cm]
+\coordinate (O) at (0,0);
+\coordinate (A) at (-1,5);
+\coordinate (B) at (3,2);
+\draw[->] (O) -- (A);
+\draw[->] (O) -- (B);
+\begin{scope}
+\clip (-2,0) rectangle (4,6);
+\draw[color=red!40,line width=0.4pt] ($2*(B)-(A)$) -- ($2*(A)-(B)$);
+\end{scope}
+\draw[color=red,line width=1.5pt] (A) -- (B);
+\punkt{(O)}
+\punkt{(A)}
+\punkt{(B)}
+\node at (O) [below left] {$O$};
+\node at (A) [above right] {$A$};
+\node at (B) [above right] {$B$};
+\node at ($0.5*(A)$) [left] {$\vec{a}$};
+\node at ($0.5*(B)$) [below right] {$\vec{b}$};
+\fill[color=white] ($0.6*(A)+0.4*(B)$) circle[radius=0.05];
+\draw[color=red] ($0.6*(A)+0.4*(B)$) circle[radius=0.05];
+\node[color=red] at ($0.6*(A)+0.4*(B)$) [above right] {$t\vec{a}+(1-t)\vec{b}$};
+\end{scope}
+
+\begin{scope}[xshift=4cm]
+\coordinate (O) at (0,0);
+\coordinate (A) at (-1,3);
+\coordinate (B) at (2,5);
+\coordinate (C) at (4,1);
+\draw[->] (O) -- (A);
+\draw[->] (O) -- (B);
+\draw[->] (O) -- (C);
+\fill[color=red!50,opacity=0.5] (A) -- (B) -- (C) -- cycle;
+\draw[color=red,line width=1.5pt,opacity=0.7] (A) -- (B) -- (C) -- cycle;
+\punkt{(O)}
+\punkt{(A)}
+\punkt{(B)}
+\punkt{(C)}
+\node at (O) [below left] {$O$};
+\node at (A) [left] {$P_1$};
+\node at (B) [above] {$P_2$};
+\node at (C) [right] {$P_3$};
+\node at ($0.5*(A)$) [left] {$\vec{p}_1$};
+\node at ($0.3*(B)$) [right] {$\vec{p}_2$};
+\node at ($0.5*(C)$) [below] {$\vec{p}_3$};
+\fill[color=white] ($0.5*(C)+0.3*(A)+0.2*(B)$) circle[radius=0.05];
+\draw[color=red] ($0.5*(C)+0.3*(A)+0.2*(B)$) circle[radius=0.05];
+\node[color=red] at ($0.5*(C)+0.3*(A)+0.2*(B)$) [above] {$\displaystyle\sum_{t=1}^3 t_i\vec{p}_i$};
+\end{scope}
+
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf
index bbcc95a..f065f76 100644
--- a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf
+++ b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf