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%
% kruemmung.tex -- Krümmung einer ebenen Kurve
%
% (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}
\begin{document}
\def\skala{1}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\begin{scope}
\clip (-1,-1) rectangle (4,4);
\def\r{3}
\def\winkel{30}
\fill[color=blue!20] (0,0) -- (0:{0.6*\r}) arc (0:\winkel:{0.6*\r}) -- cycle;
\fill[color=blue!20] (\winkel:\r)
-- ($(\winkel:\r)+(0,{0.6*\r})$) arc (90:{90+\winkel}:{0.6*\r}) -- cycle;
\node[color=blue] at ({0.5*\winkel}:{0.45*\r}) {$\Delta\varphi$};
\node[color=blue] at ($(\winkel:\r)+({90+0.5*\winkel}:{0.45*\r})$)
{$\Delta\varphi$};
\draw[line width=0.3pt] (0,0) circle[radius=\r];
\draw[->] (0,0) -- (0:\r);
\draw[->] (0,0) -- (\winkel:\r);
\draw[->] (0:\r) -- ($(0:\r)+(90:0.7*\r)$);
\draw[->] (\winkel:\r) -- ($(\winkel:\r)+({90+\winkel}:0.7*\r)$);
\draw[->,color=gray] (\winkel:\r) -- ($(\winkel:\r)+(0,0.7*\r)$);
\draw[color=red,line width=1.4pt] (0:\r) arc (0:\winkel:\r);
\node[color=red] at ({0.5*\winkel}:\r) [left] {$\Delta s$};
\fill[color=red] (0:\r) circle[radius=0.05];
\fill[color=red] (\winkel:\r) circle[radius=0.05];
\node at (\winkel:{0.5*\r}) [above] {$r$};
\node at (0:{0.5*\r}) [below] {$r$};
\end{scope}
\end{tikzpicture}
\end{document}
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