add some info on elliptic functions

5 files changed, 171 insertions, 0 deletions

diff --git a/buch/chapters/030-geometrie/images/Makefile b/buch/chapters/030-geometrie/images/Makefile
new file mode 100644
index 0000000..8796cf6
--- /dev/null
+++ b/buch/chapters/030-geometrie/images/Makefile
@@ -0,0 +1,14 @@
+#
+# Makefile for images
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+
+all:	hyperbelflaeche.pdf polargleichung.pdf
+
+hyperbelflaeche.pdf:	hyperbelflaeche.tex
+	pdflatex hyperbelflaeche.tex
+
+polargleichung.pdf:	polargleichung.tex
+	pdflatex polargleichung.tex
+
diff --git a/buch/chapters/030-geometrie/images/hyperbelflaeche.pdf b/buch/chapters/030-geometrie/images/hyperbelflaeche.pdf
new file mode 100644
index 0000000..a475b07
--- /dev/null
+++ b/buch/chapters/030-geometrie/images/hyperbelflaeche.pdf
diff --git a/buch/chapters/030-geometrie/images/hyperbelflaeche.tex b/buch/chapters/030-geometrie/images/hyperbelflaeche.tex
new file mode 100644
index 0000000..11e865f
--- /dev/null
+++ b/buch/chapters/030-geometrie/images/hyperbelflaeche.tex
@@ -0,0 +1,49 @@
+%
+% hyperbelflaeche.tex -- Argument der Hyperbelfunktionen
+%
+% (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{2}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\fill[color=blue!20]
+	(0,0)
+	--
+	plot[domain=0:1,samples=100] ({cosh(\x)},{sinh(\x)})
+	-- cycle;
+\draw[color=blue] 
+	(0,0)
+	--
+	plot[domain=0:1,samples=100] ({cosh(\x)},{sinh(\x)})
+	-- cycle;
+
+\begin{scope}
+\clip (-1.8,-2) rectangle (2.5,2);
+\draw[color=red,line width=1.4pt] plot[domain=-2:2,samples=100]
+	({cosh(\x)},{sinh(\x)});
+\draw[color=red,line width=1.4pt] plot[domain=-2:2,samples=100]
+	({-cosh(\x)},{sinh(\x)});
+\end{scope}
+
+\fill[color=white] ({cosh(1)},{sinh(1)}) circle[radius=0.03];
+\draw ({cosh(1)},{sinh(1)}) circle[radius=0.03];
+
+\node at ({cosh(1)},{sinh(1)}) [right] {$\gamma(t)=(\cosh t,\sinh t)$};
+
+\draw[->] (-1.8,0) -- (3.1,0) coordinate[label={$x$}];
+\draw[->] (0,-2) -- (0,2.1) coordinate[label={right:$y$}];
+
+\node[color=blue] at (0.8,0.3) {$t$};
+\node at (0,0) [below left] {$O$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/030-geometrie/images/polargleichung.pdf b/buch/chapters/030-geometrie/images/polargleichung.pdf
new file mode 100644
index 0000000..40115ea
--- /dev/null
+++ b/buch/chapters/030-geometrie/images/polargleichung.pdf
diff --git a/buch/chapters/030-geometrie/images/polargleichung.tex b/buch/chapters/030-geometrie/images/polargleichung.tex
new file mode 100644
index 0000000..5210903
--- /dev/null
+++ b/buch/chapters/030-geometrie/images/polargleichung.tex
@@ -0,0 +1,108 @@
+%
+% polargleichung.tex -- Kegelschnitte in Polardarstellung
+%
+% (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{2}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\p{1}
+
+\begin{scope}
+\clip (-4,-3) rectangle (1.1,3);
+\fill[color=blue!20]
+	(0,1)
+	--
+	plot[domain=90:-90,samples=100] ({\x}:{\p/(1+cos(\x))})
+	--
+ 	(0,-1) arc (-90:90:1)
+	--
+	cycle;
+
+\fill[color=blue!20]
+	(0,1) arc (90:270:1)
+	--
+	plot[domain=-90:-145,samples=20] ({\x}:{\p/(1+cos(\x))})
+	--
+	plot[domain=145:90,samples=20] ({\x}:{\p/(1+cos(\x))})
+	--
+	cycle;
+
+\fill[color=darkgreen!20]
+	plot[domain=90:-90,samples=100] ({\x}:{\p/(1+cos(\x))})
+	-- cycle;
+
+\fill[color=darkgreen!20]
+	(0,1)
+	--
+	(0,3)
+	--
+	plot[domain=145:90,samples=20] ({\x}:{\p/(1+cos(\x))})
+	--
+	cycle;
+
+\fill[color=darkgreen!20]
+	(0,-1)
+	--
+	(0,-3)
+	--
+	plot[domain=-145:-90,samples=20] ({\x}:{\p/(1+cos(\x))})
+	--
+	cycle;
+
+\end{scope}
+
+\draw[->] (-4.1,0) -- (1.3,0) coordinate[label={$\varphi=0$}];
+\draw (0,-3.1) -- (0,3.1);
+
+\begin{scope}
+\clip (-4,-3) rectangle (1.1,3);
+\draw[color=red,line width=1.4pt] (0,0) circle[radius=1];
+\foreach \e in {10,20,...,90}{
+	\draw[color=blue!\e!red,line width=1.4pt]
+		plot[domain=0:360,samples=100]
+			(\x:{\p/(1+(\e/100)*cos(\x))});
+}
+
+\draw[color=blue,line width=1.4pt]
+	plot[domain=-145:145,samples=100] ({\x}:{\p/(1+cos(\x))});
+
+\foreach \e in {10,30,50,70,90}{
+	\draw[color=darkgreen!\e!blue,line width=1.4pt]
+		plot[domain={-138+\e/5}:{138-\e/5},samples=100]
+			(\x:{\p/(1+((\e+100)/100)*cos(\x))});
+}
+\end{scope}
+
+\fill[color=white] (0,1) circle[radius=0.04];
+\draw (0,1) circle[radius=0.04];
+\fill[color=white] (0,-1) circle[radius=0.04];
+\draw (0,-1) circle[radius=0.04];
+\node at (0,0.6) [left] {$p$};
+
+\node at (0,0) [below left] {$O$};
+\fill[color=white] (0,0) circle[radius=0.04];
+\draw (0,0) circle[radius=0.04];
+
+\node[color=red] at (45:1) [above right] {$\varepsilon=0$};
+\node[color=red] at ($(45:1)+(0,0.2)$) [above right] {Kreis:};
+\node[color=blue!70!red] at (-3.5,0.7) {$\varepsilon=0.7$};
+\node[color=blue!70!red] at (-3.5,0.9) {Ellipse:};
+\node[color=blue] at (-3.4,2.65) [rotate=-18] {Parabel: $\varepsilon=1$};
+\node[color=darkgreen!90!blue] at (-1,2.8) [right] {Hyperbel: $\varepsilon=1.9$};
+
+%\draw[color=yellow]
+%	plot[domain=90:-90,samples=100] ({\x}:{\p/(1+cos(\x))});
+
+\end{tikzpicture}
+\end{document}
+