From 2db90bfe4b174570424c408f04000902411d8755 Mon Sep 17 00:00:00 2001
From: Joshua Baer <the.baer.joshua@gmail.ch>
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

