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Diffstat (limited to 'buch/chapters/80-wahrscheinlichkeit/images/dreieck.tex')
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diff --git a/buch/chapters/80-wahrscheinlichkeit/images/dreieck.tex b/buch/chapters/80-wahrscheinlichkeit/images/dreieck.tex new file mode 100644 index 0000000..0935992 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/dreieck.tex @@ -0,0 +1,90 @@ +% +% dreieck.tex -- verallgemeinerte Dreiecksungleichung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usepackage{pgf} +\usetikzlibrary{arrows,intersections,math,calc,hobby} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\coordinate (O) at (0,0); + +\input{drei.inc} + +\begin{scope} +\clip (O) rectangle (12.3,8); +\draw[color=red!40] (O) circle[radius=\r]; +\end{scope} + +\draw[->] (-0.1,0) -- (12.3,0) coordinate[label={$\Re z$}]; +\draw[->] (0,-0.1) -- (0,8.3) coordinate[label={right:$\Im z$}]; + +\fill[color=blue] (A1) circle[radius=0.05]; +\fill[color=blue] (A2) circle[radius=0.05]; +\fill[color=blue] (A3) circle[radius=0.05]; +\fill[color=blue] (A4) circle[radius=0.05]; +\fill[color=blue] (A5) circle[radius=0.05]; +\fill[color=blue] (A6) circle[radius=0.05]; +\fill[color=blue] (A7) circle[radius=0.05]; +\fill[color=blue] (A8) circle[radius=0.05]; +\fill[color=blue] (A9) circle[radius=0.05]; +\fill[color=blue] (A10) circle[radius=0.05]; +\draw[color=blue] (O) -- (A1); +\draw[color=blue] (A1) -- (A2); +\draw[color=blue] (A2) -- (A3); +\draw[color=blue] (A3) -- (A4); +\draw[color=blue] (A4) -- (A5); +\draw[color=blue] (A5) -- (A6); +\draw[color=blue] (A6) -- (A7); +\draw[color=blue] (A7) -- (A8); +\draw[color=blue] (A8) -- (A9); +\draw[color=blue] (A9) -- (A10); +\draw[->,color=blue!40] (O) -- (A10); +\node[color=blue] at ($0.5*(A1)$) [left] {$z_1$}; +\node[color=blue] at ($0.5*(A1)+0.5*(A2)$) [left] {$z_2$}; +\node[color=blue] at ($0.5*(A2)+0.5*(A3)$) [above] {$z_3$}; +\node[color=blue] at ($0.5*(A3)+0.5*(A4)$) [above] {$z_4$}; +\node[color=blue] at ($0.5*(A4)+0.5*(A5)$) [below right] {$z_5$}; +\node[color=blue] at ($0.5*(A5)+0.5*(A6)$) [left] {$z_6$}; +\node[color=blue] at ($0.5*(A6)+0.5*(A7)$) [left] {$z_7$}; +\node[color=blue] at ($0.5*(A7)+0.5*(A8)$) [above] {$z_8$}; +\node[color=blue] at ($0.5*(A8)+0.5*(A9)$) [left] {$z_9$}; +\node[color=blue] at ($0.5*(A9)+0.5*(A10)$) [above] {$z_{10}$}; +\node[color=blue] at ($0.8*(A10)$) [rotate=35,below] {$\displaystyle\sum_{i=1}^n z_i$}; + +\draw[->,color=red] (O) -- (B10); +\fill[color=red] (B1) circle[radius=0.05]; +\fill[color=red] (B2) circle[radius=0.05]; +\fill[color=red] (B3) circle[radius=0.05]; +\fill[color=red] (B4) circle[radius=0.05]; +\fill[color=red] (B5) circle[radius=0.05]; +\fill[color=red] (B6) circle[radius=0.05]; +\fill[color=red] (B7) circle[radius=0.05]; +\fill[color=red] (B8) circle[radius=0.05]; +\fill[color=red] (B9) circle[radius=0.05]; +\fill[color=red] (B10) circle[radius=0.05]; + +\node[color=red] at ($0.5*(B1)$) [above] {$|z_1|c$}; +\node[color=red] at ($0.5*(B1)+0.5*(B2)$) [above] {$|z_2|c$}; +\node[color=red] at ($0.5*(B2)+0.5*(B3)$) [above] {$|z_3|c$}; +\node[color=red] at ($0.5*(B3)+0.5*(B4)$) [above] {$|z_4|c$}; +\node[color=red] at ($0.5*(B4)+0.5*(B5)$) [above] {$|z_5|c$}; +\node[color=red] at ($0.5*(B5)+0.5*(B6)$) [above] {$|z_6|c$}; +\node[color=red] at ($0.5*(B6)+0.5*(B7)$) [above] {$|z_7|c$}; +\node[color=red] at ($0.5*(B7)+0.5*(B8)$) [above] {$|z_8|c$}; +\node[color=red] at ($0.5*(B8)+0.5*(B9)$) [above] {$|z_9|c$}; +\node[color=red] at ($0.5*(B9)+0.5*(B10)$) [above] {$|z_{10}|c$}; + +\node[color=red] at ($0.8*(B10)$) [rotate=20,below] {$\displaystyle c\sum_{i=1}^n |z_i|$}; + +\end{tikzpicture} +\end{document} + |