From 0344a846c083c11e9ed93ddc5898dd55c6dd1022 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Wed, 20 Apr 2022 10:30:56 +0200
Subject: lemniscate sine stuff

---
 buch/chapters/110-elliptisch/images/slcl.tex | 88 ++++++++++++++++++++++++++++
 1 file changed, 88 insertions(+)
 create mode 100644 buch/chapters/110-elliptisch/images/slcl.tex

(limited to 'buch/chapters/110-elliptisch/images/slcl.tex')

diff --git a/buch/chapters/110-elliptisch/images/slcl.tex b/buch/chapters/110-elliptisch/images/slcl.tex
new file mode 100644
index 0000000..08241ac
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/slcl.tex
@@ -0,0 +1,88 @@
+%
+% tikztemplate.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}
+\input{slcldata.tex}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+% add image content here
+\def\lemniscateconstant{2.6220575542}
+\pgfmathparse{(3.1415926535/2)/\lemniscateconstant}
+\xdef\scalechange{\pgfmathresult}
+
+\pgfmathparse{\scalechange*(180/3.1415926535)}
+\xdef\ts{\pgfmathresult}
+
+\def\dx{1}
+\def\dy{3}
+
+\draw[line width=0.3pt]
+	({\lemniscateconstant*\dx},0)
+	--
+	({\lemniscateconstant*\dx},{1*\dy});
+\draw[line width=0.3pt]
+	({2*\lemniscateconstant*\dx},0)
+	--
+	({2*\lemniscateconstant*\dx},{-1*\dy});
+\draw[line width=0.3pt]
+	({3*\lemniscateconstant*\dx},0)
+	--
+	({3*\lemniscateconstant*\dx},{-1*\dy});
+\draw[line width=0.3pt]
+	({4*\lemniscateconstant*\dx},0)
+	--
+	({4*\lemniscateconstant*\dx},{1*\dy});
+\draw[line width=0.3pt]
+	({5*\lemniscateconstant*\dx},0)
+	--
+	({5*\lemniscateconstant*\dx},{1*\dy});
+
+\draw[color=red!20,line width=1.4pt]
+	plot[domain=0:13,samples=200] ({\x},{\dy*sin(\ts*\x)});
+\draw[color=blue!20,line width=1.4pt]
+	plot[domain=0:13,samples=200] ({\x},{\dy*cos(\ts*\x)});
+
+\draw[color=red,line width=1.4pt] \slpath;
+\draw[color=blue,line width=1.4pt] \clpath;
+
+\draw[->] (0,{-1*\dy-0.1}) -- (0,{1*\dy+0.4}) coordinate[label={right:$r$}];
+\draw[->] (-0.1,0) -- (13.7,0) coordinate[label={$s$}];
+
+\foreach \i in {1,2,3,4,5}{
+	\draw ({\lemniscateconstant*\i},-0.1) -- ({\lemniscateconstant*\i},0.1);
+}
+\node at ({\lemniscateconstant*\dx},0)   [below left]  {$ \varpi\mathstrut$};
+\node at ({2*\lemniscateconstant*\dx},0) [below left]  {$2\varpi\mathstrut$};
+\node at ({3*\lemniscateconstant*\dx},0) [below right] {$3\varpi\mathstrut$};
+\node at ({4*\lemniscateconstant*\dx},0) [below right] {$4\varpi\mathstrut$};
+\node at ({5*\lemniscateconstant*\dx},0) [below left]  {$5\varpi\mathstrut$};
+
+\node[color=red] at ({1.6*\lemniscateconstant*\dx},{0.6*\dy})
+	[below left] {$\operatorname{sl}(s)$};
+\node[color=red!50] at ({1.5*\lemniscateconstant*\dx},{sin(1.5*90)*\dy*0.90})
+	[above right] {$\sin \bigl(\frac{\pi}{2\varpi}s\bigr)$};
+
+\node[color=blue] at ({1.4*\lemniscateconstant*\dx},{-0.6*\dy})
+	[above right] {$\operatorname{cl}(s)$};
+\node[color=blue!50] at ({1.5*\lemniscateconstant*\dx},{cos(1.5*90)*\dy*0.90})
+	[below left] {$\cos\bigl(\frac{\pi}{2\varpi}s\bigr)$};
+
+\draw (-0.1,{1*\dy}) -- (0.1,{1*\dy});
+\draw (-0.1,{-1*\dy}) -- (0.1,{-1*\dy});
+\node at (0,{1*\dy}) [left] {$1\mathstrut$};
+\node at (0,0) [left] {$0\mathstrut$};
+\node at (0,{-1*\dy}) [left] {$-1\mathstrut$};
+
+\end{tikzpicture}
+\end{document}
+
-- 
cgit v1.2.1


From e1b65ea3e46bf60fec0d6503b701a84f68138a24 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 21 Apr 2022 22:36:54 +0200
Subject: add lecture notes for session 5

---
 buch/chapters/110-elliptisch/images/slcl.tex | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

(limited to 'buch/chapters/110-elliptisch/images/slcl.tex')

diff --git a/buch/chapters/110-elliptisch/images/slcl.tex b/buch/chapters/110-elliptisch/images/slcl.tex
index 08241ac..0af1027 100644
--- a/buch/chapters/110-elliptisch/images/slcl.tex
+++ b/buch/chapters/110-elliptisch/images/slcl.tex
@@ -47,35 +47,35 @@
 	--
 	({5*\lemniscateconstant*\dx},{1*\dy});
 
-\draw[color=red!20,line width=1.4pt]
+\draw[color=red!40,line width=1.4pt]
 	plot[domain=0:13,samples=200] ({\x},{\dy*sin(\ts*\x)});
-\draw[color=blue!20,line width=1.4pt]
+\draw[color=blue!40,line width=1.4pt]
 	plot[domain=0:13,samples=200] ({\x},{\dy*cos(\ts*\x)});
 
 \draw[color=red,line width=1.4pt] \slpath;
 \draw[color=blue,line width=1.4pt] \clpath;
 
 \draw[->] (0,{-1*\dy-0.1}) -- (0,{1*\dy+0.4}) coordinate[label={right:$r$}];
-\draw[->] (-0.1,0) -- (13.7,0) coordinate[label={$s$}];
+\draw[->] (-0.1,0) -- (13.6,0) coordinate[label={$s$}];
 
 \foreach \i in {1,2,3,4,5}{
 	\draw ({\lemniscateconstant*\i},-0.1) -- ({\lemniscateconstant*\i},0.1);
 }
-\node at ({\lemniscateconstant*\dx},0)   [below left]  {$ \varpi\mathstrut$};
-\node at ({2*\lemniscateconstant*\dx},0) [below left]  {$2\varpi\mathstrut$};
-\node at ({3*\lemniscateconstant*\dx},0) [below right] {$3\varpi\mathstrut$};
-\node at ({4*\lemniscateconstant*\dx},0) [below right] {$4\varpi\mathstrut$};
-\node at ({5*\lemniscateconstant*\dx},0) [below left]  {$5\varpi\mathstrut$};
+\node at ({\lemniscateconstant*\dx},0)   [below left]  {$\frac{\varpi}2\mathstrut$};
+\node at ({2*\lemniscateconstant*\dx},0) [below left]  {$\varpi\mathstrut$};
+\node at ({3*\lemniscateconstant*\dx},0) [below right] {$\frac{3\varpi}2\mathstrut$};
+\node at ({4*\lemniscateconstant*\dx},0) [below right] {$2\varpi\mathstrut$};
+\node at ({5*\lemniscateconstant*\dx},0) [below left]  {$\frac{5\varpi}2\mathstrut$};
 
 \node[color=red] at ({1.6*\lemniscateconstant*\dx},{0.6*\dy})
 	[below left] {$\operatorname{sl}(s)$};
 \node[color=red!50] at ({1.5*\lemniscateconstant*\dx},{sin(1.5*90)*\dy*0.90})
-	[above right] {$\sin \bigl(\frac{\pi}{2\varpi}s\bigr)$};
+	[above right] {$\sin \bigl(\frac{\pi}{\varpi}s\bigr)$};
 
 \node[color=blue] at ({1.4*\lemniscateconstant*\dx},{-0.6*\dy})
 	[above right] {$\operatorname{cl}(s)$};
 \node[color=blue!50] at ({1.5*\lemniscateconstant*\dx},{cos(1.5*90)*\dy*0.90})
-	[below left] {$\cos\bigl(\frac{\pi}{2\varpi}s\bigr)$};
+	[below left] {$\cos\bigl(\frac{\pi}{\varpi}s\bigr)$};
 
 \draw (-0.1,{1*\dy}) -- (0.1,{1*\dy});
 \draw (-0.1,{-1*\dy}) -- (0.1,{-1*\dy});
-- 
cgit v1.2.1

