From 2db90bfe4b174570424c408f04000902411d8755 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Mon, 12 Apr 2021 21:51:55 +0200 Subject: update to current state of book --- buch/chapters/60-gruppen/images/karten.tex | 224 ++++++++++++++--------------- 1 file changed, 112 insertions(+), 112 deletions(-) (limited to 'buch/chapters/60-gruppen/images/karten.tex') diff --git a/buch/chapters/60-gruppen/images/karten.tex b/buch/chapters/60-gruppen/images/karten.tex index c8eb4a3..67c8d70 100644 --- a/buch/chapters/60-gruppen/images/karten.tex +++ b/buch/chapters/60-gruppen/images/karten.tex @@ -1,112 +1,112 @@ -% -% karten.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} -\begin{document} -\def\skala{1} -\begin{tikzpicture}[>=latex,thick,scale=\skala] - -\definecolor{darkgreen}{rgb}{0,0.6,0} - -\node at (0,0) {\includegraphics[width=10cm]{torus.png}}; - -\def\s{3} - -\node at (-3.5,-0.4) {$U_\alpha$}; -\node at (2.0,-0.4) {$U_\beta$}; - -\draw[->] (-2,-2.2) -- (-3,-4.3); -\node at (-2.5,-3.25) [left] {$\varphi_\alpha$}; - -\draw[->] (1.4,-1.7) -- (3,-4.3); -\node at (2.5,-3.25) [right] {$\varphi_\beta$}; - -\begin{scope}[xshift=-4.5cm,yshift=-8cm] - \begin{scope} - \clip (0,{-0.2*\s}) rectangle ({1*\s},{1.2*\s}); - \begin{scope}[xshift=1.8cm,yshift=0.6cm,rotate=30] - \fill[color=gray!20] - (0,{-0.2*\s}) rectangle ({1*\s},{1.2*\s}); - \foreach \x in {0,0.2,...,1}{ - \draw[color=darkgreen] - ({\x*\s},{-0.2*\s}) - -- - ({\x*\s},{1.2*\s}); - } - \foreach \y in {-0.2,0,...,1.2}{ - \draw[color=orange] - (0,{\y*\s}) - -- - ({1*\s},{\y*\s}); - } - \end{scope} - \end{scope} - - \foreach \x in {0,0.2,...,1}{ - \draw[color=blue,line width=1.4pt] - ({\x*\s},{-0.2*\s}) -- ({\x*\s},{1.2*\s}); - } - \foreach \y in {-0.2,0,...,1.2}{ - \draw[color=red,line width=1.4pt] - (0,{\y*\s}) -- ({1*\s},{\y*\s}); - } - - \draw[->] ({\s*(-0.1)},0) -- ({1.1*\s},0) coordinate[label={$x_1$}]; - \draw[->] (0,{-0.3*\s}) -- (0,{1.3*\s}) coordinate[label={left:$x_2$}]; - - \node at ({1*\s},{1.2*\s}) [above right] {$\mathbb{R}^2$}; - -\end{scope} - -\begin{scope}[xshift=1.5cm,yshift=-8cm] - \begin{scope} - \clip (0,{-0.2*\s}) rectangle ({1*\s},{1.2*\s}); - % x = - [ (sqrt(3)/2)*0.6+(1/2)*0.2 ] = -0.6196 - % y = - [ (-1/2)*0.6 + (sqrt(3)/2)*0.2 ] = - \begin{scope}[xshift=-1.8588cm,yshift=0.3804cm,rotate=-30] - \fill[color=gray!20] - (0,{-0.2*\s}) rectangle ({1*\s},{1.2*\s}); - \foreach \x in {0,0.2,...,1}{ - \draw[color=blue] - ({\x*\s},{-0.2*\s}) - -- - ({\x*\s},{1.2*\s}); - } - \foreach \y in {-0.2,0,...,1.2}{ - \draw[color=red] - (0,{\y*\s}) - -- - ({1*\s},{\y*\s}); - } - \end{scope} - \end{scope} - - \foreach \x in {0,0.2,...,1}{ - \draw[color=darkgreen,line width=1.4pt] - ({\x*\s},{-0.2*\s}) -- ({\x*\s},{1.2*\s}); - } - \foreach \y in {-0.2,0,...,1.2}{ - \draw[color=orange,line width=1.4pt] (0,{\y*\s}) -- ({1*\s},{\y*\s}); - } - \draw[->] ({\s*(-0.1)},0) -- ({1.1*\s},0) coordinate[label={$x_1$}]; - \draw[->] (0,{-0.3*\s}) -- (0,{1.3*\s}) coordinate[label={left:$x_2$}]; - \node at ({1*\s},{1.2*\s}) [above right] {$\mathbb{R}^2$}; -\end{scope} - -\draw[<-,color=white,opacity=0.8,line width=5pt] (2.5,-6.5) arc (55:100:6.5); -\draw[<-,shorten >= 0.1cm,shorten <= 0.3cm] (2.5,-6.5) arc (55:100:6.5); - -\node at (0,-5.9) - {$\varphi_{\beta\alpha}=\varphi_\beta\circ\varphi_\alpha^{-1}$}; - -\end{tikzpicture} -\end{document} - +% +% karten.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} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\node at (0,0) {\includegraphics[width=10cm]{torus.png}}; + +\def\s{3} + +\node at (-3.5,-0.4) {$U_\alpha$}; +\node at (2.0,-0.4) {$U_\beta$}; + +\draw[->] (-2,-2.2) -- (-3,-4.3); +\node at (-2.5,-3.25) [left] {$\varphi_\alpha$}; + +\draw[->] (1.4,-1.7) -- (3,-4.3); +\node at (2.5,-3.25) [right] {$\varphi_\beta$}; + +\begin{scope}[xshift=-4.5cm,yshift=-8cm] + \begin{scope} + \clip (0,{-0.2*\s}) rectangle ({1*\s},{1.2*\s}); + \begin{scope}[xshift=1.8cm,yshift=0.6cm,rotate=30] + \fill[color=gray!20] + (0,{-0.2*\s}) rectangle ({1*\s},{1.2*\s}); + \foreach \x in {0,0.2,...,1}{ + \draw[color=darkgreen] + ({\x*\s},{-0.2*\s}) + -- + ({\x*\s},{1.2*\s}); + } + \foreach \y in {-0.2,0,...,1.2}{ + \draw[color=orange] + (0,{\y*\s}) + -- + ({1*\s},{\y*\s}); + } + \end{scope} + \end{scope} + + \foreach \x in {0,0.2,...,1}{ + \draw[color=blue,line width=1.4pt] + ({\x*\s},{-0.2*\s}) -- ({\x*\s},{1.2*\s}); + } + \foreach \y in {-0.2,0,...,1.2}{ + \draw[color=red,line width=1.4pt] + (0,{\y*\s}) -- ({1*\s},{\y*\s}); + } + + \draw[->] ({\s*(-0.1)},0) -- ({1.1*\s},0) coordinate[label={$x_1$}]; + \draw[->] (0,{-0.3*\s}) -- (0,{1.3*\s}) coordinate[label={left:$x_2$}]; + + \node at ({1*\s},{1.2*\s}) [above right] {$\mathbb{R}^2$}; + +\end{scope} + +\begin{scope}[xshift=1.5cm,yshift=-8cm] + \begin{scope} + \clip (0,{-0.2*\s}) rectangle ({1*\s},{1.2*\s}); + % x = - [ (sqrt(3)/2)*0.6+(1/2)*0.2 ] = -0.6196 + % y = - [ (-1/2)*0.6 + (sqrt(3)/2)*0.2 ] = + \begin{scope}[xshift=-1.8588cm,yshift=0.3804cm,rotate=-30] + \fill[color=gray!20] + (0,{-0.2*\s}) rectangle ({1*\s},{1.2*\s}); + \foreach \x in {0,0.2,...,1}{ + \draw[color=blue] + ({\x*\s},{-0.2*\s}) + -- + ({\x*\s},{1.2*\s}); + } + \foreach \y in {-0.2,0,...,1.2}{ + \draw[color=red] + (0,{\y*\s}) + -- + ({1*\s},{\y*\s}); + } + \end{scope} + \end{scope} + + \foreach \x in {0,0.2,...,1}{ + \draw[color=darkgreen,line width=1.4pt] + ({\x*\s},{-0.2*\s}) -- ({\x*\s},{1.2*\s}); + } + \foreach \y in {-0.2,0,...,1.2}{ + \draw[color=orange,line width=1.4pt] (0,{\y*\s}) -- ({1*\s},{\y*\s}); + } + \draw[->] ({\s*(-0.1)},0) -- ({1.1*\s},0) coordinate[label={$x_1$}]; + \draw[->] (0,{-0.3*\s}) -- (0,{1.3*\s}) coordinate[label={left:$x_2$}]; + \node at ({1*\s},{1.2*\s}) [above right] {$\mathbb{R}^2$}; +\end{scope} + +\draw[<-,color=white,opacity=0.8,line width=5pt] (2.5,-6.5) arc (55:100:6.5); +\draw[<-,shorten >= 0.1cm,shorten <= 0.3cm] (2.5,-6.5) arc (55:100:6.5); + +\node at (0,-5.9) + {$\varphi_{\beta\alpha}=\varphi_\beta\circ\varphi_\alpha^{-1}$}; + +\end{tikzpicture} +\end{document} + -- cgit v1.2.1