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

---
 vorlesungen/slides/4/galois/konstruktion.tex | 294 +++++++++++++--------------
 1 file changed, 147 insertions(+), 147 deletions(-)

(limited to 'vorlesungen/slides/4/galois/konstruktion.tex')

diff --git a/vorlesungen/slides/4/galois/konstruktion.tex b/vorlesungen/slides/4/galois/konstruktion.tex
index 094b570..b461d44 100644
--- a/vorlesungen/slides/4/galois/konstruktion.tex
+++ b/vorlesungen/slides/4/galois/konstruktion.tex
@@ -1,147 +1,147 @@
-%
-% konstruktion.tex
-%
-% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-%
-\begin{frame}[t]
-\frametitle{Konstruktion mit Zirkel und Lineal}
-\vspace{-20pt}
-\begin{columns}[t,onlytextwidth]
-\begin{column}{0.48\textwidth}
-\begin{block}{Strahlensatz}
-\uncover<6->{%
-Jedes beliebige rationale Streckenverhältnis $\frac{p}{q}$
-kann mit Zirkel und Lineal konstruiert werden.}
-\end{block}
-\end{column}
-\begin{column}{0.48\textwidth}
-\uncover<7->{%
-\begin{block}{Kreis--Gerade}
-Aus $c$ und $a$ konstruiere $b=\sqrt{c^2-a^2}$
-\uncover<13->{%
-$\Rightarrow$ jede beliebige Quadratwurzel kann konstruiert werden}
-\end{block}}
-\end{column}
-\end{columns}
-\begin{columns}[t,onlytextwidth]
-\begin{column}{0.48\textwidth}
-\begin{center}
-\begin{tikzpicture}[>=latex,thick]
-\def\s{0.5}
-\def\t{0.45}
-
-\coordinate (A) at (0,0);
-\coordinate (B) at ({10*\t},0);
-
-\uncover<2->{
-	\draw (0,0) -- (30:{10.5*\s});
-}
-
-\uncover<3->{
-	\foreach \x in {0,...,10}{
-		\fill (30:{\x*\s}) circle[radius=0.03];
-	}
-	\foreach \x in {0,1,2,3,4,7,8,9}{
-		\node at (30:{\x*\s}) [above] {\tiny $\x$};
-	}
-	\node at (30:{10*\s}) [above right] {$q=10$};
-}
-
-\uncover<4->{
-	\foreach \x in {1,...,10}{
-		\fill (0:{\x*\t}) circle[radius=0.03];
-		\draw[->,line width=0.2pt] (30:{\x*\s}) -- (0:{\x*\t});
-	}
-}
-
-\draw (A) -- (0:{10.5*\t});
-\node at (A) [below left] {$A$};
-\node at (B) [below right] {$B$};
-\fill (A) circle[radius=0.05];
-\fill (B) circle[radius=0.05];
-
-\uncover<5->{
-	\node at (30:{6*\s}) [above left] {$p=6$};
-	\draw[line width=0.2pt] (0,0) -- (0,-0.4);
-	\draw[line width=0.2pt] ({6*\t},0) -- ({6*\t},-0.4);
-	\draw[<->] (0,-0.3) -- ({6*\t},-0.3);
-	\node at ({3*\t},-0.4) [below]
-		{$\displaystyle\frac{p}{q}\cdot\overline{AB}$};
-}
-
-\end{tikzpicture}
-\end{center}
-\end{column}
-\begin{column}{0.48\textwidth}
-\uncover<8->{%
-\begin{center}
-\begin{tikzpicture}[>=latex,thick]
-
-%\foreach \x in {8,...,14}{
-%	\only<\x>{\node at (4,4) {$\x$};}
-%}
-
-\def\r{4}
-\def\a{50}
-
-\coordinate (A) at ({\r*cos(\a)},0);
-
-\uncover<10->{
-	\fill[color=gray] (\r,0) -- (\r,0.3) arc (90:180:0.3) -- cycle;
-	\fill[color=gray]
-		(95:\r) -- ($(95:\r)+(185:0.3)$) arc (185:275:0.3) -- cycle;
-}
-
-\draw[->] (0,0) -- (95:\r);
-\node at (95:{0.5*\r}) [left] {$c$};
-
-\begin{scope}
-	\clip (-1,-0.3) rectangle (4.5,4.1);
-	\uncover<10->{
-		\draw (-1,0) -- (5,0);
-		\draw[->] (0,0) -- (\r,0);
-		\draw (0,0) circle[radius=\r];
-		\draw ({\r*cos(\a)},-1) -- ({\r*cos(\a)},5);
-	}
-\end{scope}
-
-\uncover<11->{
-	\fill[color=blue!20] (0,0) -- (A) -- (\a:\r) -- cycle;
-}
-
-\uncover<9->{
-	\fill[color=gray!80] (A) -- ($(A)+(0,0.5)$) arc (90:180:0.5) -- cycle;
-	\fill[color=gray!120] ($(A)+(-0.2,0.2)$) circle[radius=0.07];
-	\draw ({\r*cos(\a)},-0.3) -- ({\r*cos(\a)},4.1);
-}
-
-\uncover<11->{
-	\draw[color=blue,line width=1.4pt] (0,0) -- (\a:\r);
-	\node[color=blue] at (\a:{0.5*\r}) [above left] {$c$};
-}
-
-\draw[color=blue,line width=1.4pt] (0,0) -- ({\r*cos(\a)},0);
-\fill[color=blue] (0,0) circle[radius=0.04];
-\fill[color=blue] (A) circle[radius=0.04];
-\node[color=blue] at ({0.5*\r*cos(\a)},0) [below] {$a$};
-
-\uncover<12->{
-	\fill[color=white,opacity=0.8]
-		({\r*cos(\a)+0.1},{0.5*\r*sin(\a)-0.25})
-		rectangle
-		({\r*cos(\a)+2},{0.5*\r*sin(\a)+0.25});
-
-	\node[color=red] at ({\r*cos(\a)},{0.5*\r*sin(\a)}) [right]
-		{$b=\sqrt{c^2-a^2}$};
-	\draw[color=red,line width=1.4pt] ({\r*cos(\a)},0) -- (\a:\r);
-	\fill[color=red] (\a:\r) circle[radius=0.05];
-	\fill[color=red] (A) circle[radius=0.05];
-}
-
-\end{tikzpicture}
-\end{center}}
-\end{column}
-\end{columns}
-\uncover<14->{{\usebeamercolor[fg]{title}Folgerung:}
-Konstruierbar sind Körpererweiterungen $[F:E] = 2^l$}
-\end{frame}
+%
+% konstruktion.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\begin{frame}[t]
+\frametitle{Konstruktion mit Zirkel und Lineal}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Strahlensatz}
+\uncover<6->{%
+Jedes beliebige rationale Streckenverhältnis $\frac{p}{q}$
+kann mit Zirkel und Lineal konstruiert werden.}
+\end{block}
+\end{column}
+\begin{column}{0.48\textwidth}
+\uncover<7->{%
+\begin{block}{Kreis--Gerade}
+Aus $c$ und $a$ konstruiere $b=\sqrt{c^2-a^2}$
+\uncover<13->{%
+$\Rightarrow$ jede beliebige Quadratwurzel kann konstruiert werden}
+\end{block}}
+\end{column}
+\end{columns}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\def\s{0.5}
+\def\t{0.45}
+
+\coordinate (A) at (0,0);
+\coordinate (B) at ({10*\t},0);
+
+\uncover<2->{
+	\draw (0,0) -- (30:{10.5*\s});
+}
+
+\uncover<3->{
+	\foreach \x in {0,...,10}{
+		\fill (30:{\x*\s}) circle[radius=0.03];
+	}
+	\foreach \x in {0,1,2,3,4,7,8,9}{
+		\node at (30:{\x*\s}) [above] {\tiny $\x$};
+	}
+	\node at (30:{10*\s}) [above right] {$q=10$};
+}
+
+\uncover<4->{
+	\foreach \x in {1,...,10}{
+		\fill (0:{\x*\t}) circle[radius=0.03];
+		\draw[->,line width=0.2pt] (30:{\x*\s}) -- (0:{\x*\t});
+	}
+}
+
+\draw (A) -- (0:{10.5*\t});
+\node at (A) [below left] {$A$};
+\node at (B) [below right] {$B$};
+\fill (A) circle[radius=0.05];
+\fill (B) circle[radius=0.05];
+
+\uncover<5->{
+	\node at (30:{6*\s}) [above left] {$p=6$};
+	\draw[line width=0.2pt] (0,0) -- (0,-0.4);
+	\draw[line width=0.2pt] ({6*\t},0) -- ({6*\t},-0.4);
+	\draw[<->] (0,-0.3) -- ({6*\t},-0.3);
+	\node at ({3*\t},-0.4) [below]
+		{$\displaystyle\frac{p}{q}\cdot\overline{AB}$};
+}
+
+\end{tikzpicture}
+\end{center}
+\end{column}
+\begin{column}{0.48\textwidth}
+\uncover<8->{%
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+%\foreach \x in {8,...,14}{
+%	\only<\x>{\node at (4,4) {$\x$};}
+%}
+
+\def\r{4}
+\def\a{50}
+
+\coordinate (A) at ({\r*cos(\a)},0);
+
+\uncover<10->{
+	\fill[color=gray] (\r,0) -- (\r,0.3) arc (90:180:0.3) -- cycle;
+	\fill[color=gray]
+		(95:\r) -- ($(95:\r)+(185:0.3)$) arc (185:275:0.3) -- cycle;
+}
+
+\draw[->] (0,0) -- (95:\r);
+\node at (95:{0.5*\r}) [left] {$c$};
+
+\begin{scope}
+	\clip (-1,-0.3) rectangle (4.5,4.1);
+	\uncover<10->{
+		\draw (-1,0) -- (5,0);
+		\draw[->] (0,0) -- (\r,0);
+		\draw (0,0) circle[radius=\r];
+		\draw ({\r*cos(\a)},-1) -- ({\r*cos(\a)},5);
+	}
+\end{scope}
+
+\uncover<11->{
+	\fill[color=blue!20] (0,0) -- (A) -- (\a:\r) -- cycle;
+}
+
+\uncover<9->{
+	\fill[color=gray!80] (A) -- ($(A)+(0,0.5)$) arc (90:180:0.5) -- cycle;
+	\fill[color=gray!120] ($(A)+(-0.2,0.2)$) circle[radius=0.07];
+	\draw ({\r*cos(\a)},-0.3) -- ({\r*cos(\a)},4.1);
+}
+
+\uncover<11->{
+	\draw[color=blue,line width=1.4pt] (0,0) -- (\a:\r);
+	\node[color=blue] at (\a:{0.5*\r}) [above left] {$c$};
+}
+
+\draw[color=blue,line width=1.4pt] (0,0) -- ({\r*cos(\a)},0);
+\fill[color=blue] (0,0) circle[radius=0.04];
+\fill[color=blue] (A) circle[radius=0.04];
+\node[color=blue] at ({0.5*\r*cos(\a)},0) [below] {$a$};
+
+\uncover<12->{
+	\fill[color=white,opacity=0.8]
+		({\r*cos(\a)+0.1},{0.5*\r*sin(\a)-0.25})
+		rectangle
+		({\r*cos(\a)+2},{0.5*\r*sin(\a)+0.25});
+
+	\node[color=red] at ({\r*cos(\a)},{0.5*\r*sin(\a)}) [right]
+		{$b=\sqrt{c^2-a^2}$};
+	\draw[color=red,line width=1.4pt] ({\r*cos(\a)},0) -- (\a:\r);
+	\fill[color=red] (\a:\r) circle[radius=0.05];
+	\fill[color=red] (A) circle[radius=0.05];
+}
+
+\end{tikzpicture}
+\end{center}}
+\end{column}
+\end{columns}
+\uncover<14->{{\usebeamercolor[fg]{title}Folgerung:}
+Konstruierbar sind Körpererweiterungen $[F:E] = 2^l$}
+\end{frame}
-- 
cgit v1.2.1

