new stuff on tschebyscheff and conic sections

6 files changed, 176 insertions, 1 deletions

diff --git a/buch/chapters/010-potenzen/images/Makefile b/buch/chapters/010-potenzen/images/Makefile
index a4b4f0d..bd6b6c1 100644
--- a/buch/chapters/010-potenzen/images/Makefile
+++ b/buch/chapters/010-potenzen/images/Makefile
@@ -3,7 +3,14 @@
 #
 # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 #
-all:	wurzel.pdf
+all:	wurzel.pdf lissajous.pdf lissajous-chebyshef.pdf
 
 wurzel.pdf:	wurzel.tex
 	pdflatex wurzel.tex
+
+lissajous.pdf:  lissajous.tex lissajous.jpg
+	pdflatex lissajous.tex
+
+lissajous-chebyshef.pdf:        lissajous-chebyshef.tex lissajous.jpg
+	pdflatex lissajous-chebyshef.tex
+
diff --git a/buch/chapters/010-potenzen/images/lissajous-chebyshef.pdf b/buch/chapters/010-potenzen/images/lissajous-chebyshef.pdf
new file mode 100644
index 0000000..ea82479
--- /dev/null
+++ b/buch/chapters/010-potenzen/images/lissajous-chebyshef.pdf
diff --git a/buch/chapters/010-potenzen/images/lissajous-chebyshef.tex b/buch/chapters/010-potenzen/images/lissajous-chebyshef.tex
new file mode 100644
index 0000000..cb8e461
--- /dev/null
+++ b/buch/chapters/010-potenzen/images/lissajous-chebyshef.tex
@@ -0,0 +1,84 @@
+%
+% lissajous.tex -- annotated lissajous figure
+%
+% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil
+%
+\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]
+
+\fill[color=black] (-7.1,-2.4) rectangle (7.5,2.4);
+\begin{scope}
+	\clip (-7,-2) rectangle (7,2);
+	\node at (0,-0.065) [rotate=-0.5]
+		{\includegraphics[width=14cm]{lissajous.jpg}};
+\end{scope}
+
+\draw[->,color=white] (-7,0) -- (7.5,0);
+
+\def\xupper{1.7}
+\xdef\xlower{-\xupper}
+\draw[line width=0.7pt,color=white] (-7.1,\xupper) -- (7.5,\xupper);
+\draw[line width=0.7pt,color=white] (-7.1,\xlower) -- (7.5,\xlower);
+
+
+%\fill[color=red] (-6.315,0) circle[radius=0.08];
+%\fill[color=red] (-5.92,0) circle[radius=0.08];
+%\fill[color=red] (-5.2,0) circle[radius=0.08];
+%\fill[color=red] (-4.13,0) circle[radius=0.08];
+%\fill[color=red] (-2.85,0) circle[radius=0.08];
+%\fill[color=red] (-1.37,0) circle[radius=0.08];
+%\fill[color=red] (0.2,0) circle[radius=0.08];
+%\fill[color=red] (1.73,0) circle[radius=0.08];
+%\fill[color=red] (3.21,0) circle[radius=0.08];
+%\fill[color=red] (4.52,0) circle[radius=0.08];
+%\fill[color=red] (5.57,0) circle[radius=0.08];
+%\fill[color=red] (6.32,0) circle[radius=0.08];
+%\fill[color=red] (6.71,0) circle[radius=0.08];
+%
+\node[color=red] at (-6.315,0) [above left] {$x_0\mathstrut$};
+\node[color=red] at (-5.92,0) [above right] {$x_1\mathstrut$};
+\node[color=red] at (-5.2,0) [below right] {$x_2\mathstrut$};
+\node[color=red] at (-4.13,0) [above right] {$x_3\mathstrut$};
+\node[color=red] at (-2.85,0) [below right] {$x_4\mathstrut$};
+\node[color=red] at (-1.37,0) [above right] {$x_5\mathstrut$};
+\node[color=red] at (0.2,0) [above left] {$x_6\mathstrut$};
+\node[color=red] at (1.73,0) [below left] {$x_7\mathstrut$};
+\node[color=red] at (3.21,0) [above left] {$x_8\mathstrut$};
+\node[color=red] at (4.52,0) [below left] {$x_9\mathstrut$};
+\node[color=red] at (5.57,0) [above left] {$x_{10}\mathstrut$};
+\node[color=red] at ({6.32+0.1},0) [below left] {$x_{11}\mathstrut$};
+\node[color=red] at ({6.71},0) [below right] {$x_{12}\mathstrut$};
+
+\def\xamplitude{6.57}
+\def\yamplitude{1.66}
+
+\begin{scope}[xshift=0.20cm]
+\draw[color=red,line width=1pt] plot[domain=0:180,samples=1000]
+	({\xamplitude*cos(\x)},{\yamplitude*cos(13*\x)});
+
+\foreach \k in {0,...,13}{
+	\pgfmathparse{(90+180*\k)/13}
+	\xdef\winkel{\pgfmathresult}
+	\fill[color=red] 
+	({\xamplitude*cos(\winkel)},{\yamplitude*cos(13*\winkel)})
+		circle[radius=0.08];
+}
+
+\node[color=white] at (0,{\yamplitude+0.4})
+	{$\displaystyle \max \{\, l(x)\;|\; {-1}\le x \le 1 \} $};
+\node[color=white] at (0,{-\yamplitude-0.4}) 
+	{$\displaystyle \min \{\, l(x)\;|\; {-1}\le x \le 1 \} $};
+
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/010-potenzen/images/lissajous.jpg b/buch/chapters/010-potenzen/images/lissajous.jpg
new file mode 100644
index 0000000..0e0eb17
--- /dev/null
+++ b/buch/chapters/010-potenzen/images/lissajous.jpg
diff --git a/buch/chapters/010-potenzen/images/lissajous.pdf b/buch/chapters/010-potenzen/images/lissajous.pdf
new file mode 100644
index 0000000..74d62c7
--- /dev/null
+++ b/buch/chapters/010-potenzen/images/lissajous.pdf
diff --git a/buch/chapters/010-potenzen/images/lissajous.tex b/buch/chapters/010-potenzen/images/lissajous.tex
new file mode 100644
index 0000000..eb36347
--- /dev/null
+++ b/buch/chapters/010-potenzen/images/lissajous.tex
@@ -0,0 +1,84 @@
+%
+% lissajous.tex -- annotated lissajous figure
+%
+% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{0.99}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\fill[color=black] (-7.1,-2.4) rectangle (7.5,2.4);
+\begin{scope}
+	\clip (-7,-2) rectangle (7,2);
+	\node at (0,-0.065) [rotate=-0.5]
+		{\includegraphics[width=14cm]{lissajous.jpg}};
+\end{scope}
+
+%\draw[->,color=white] (-7,0) -- (7.1,0);
+
+\def\xupper{1.7}
+\xdef\xlower{-\xupper}
+%\draw[line width=0.7pt,color=white] (-7.1,\xupper) -- (7.1,\xupper);
+%\draw[line width=0.7pt,color=white] (-7.1,\xlower) -- (7.1,\xlower);
+
+
+%\fill[color=red] (-6.315,0) circle[radius=0.08];
+%\fill[color=red] (-5.92,0) circle[radius=0.08];
+%\fill[color=red] (-5.2,0) circle[radius=0.08];
+%\fill[color=red] (-4.13,0) circle[radius=0.08];
+%\fill[color=red] (-2.85,0) circle[radius=0.08];
+%\fill[color=red] (-1.37,0) circle[radius=0.08];
+%\fill[color=red] (0.2,0) circle[radius=0.08];
+%\fill[color=red] (1.73,0) circle[radius=0.08];
+%\fill[color=red] (3.21,0) circle[radius=0.08];
+%\fill[color=red] (4.52,0) circle[radius=0.08];
+%\fill[color=red] (5.57,0) circle[radius=0.08];
+%\fill[color=red] (6.32,0) circle[radius=0.08];
+%\fill[color=red] (6.71,0) circle[radius=0.08];
+%
+%\node[color=red] at (-6.315,0) [above left] {$x_0\mathstrut$};
+%\node[color=red] at (-5.92,0) [above right] {$x_1\mathstrut$};
+%\node[color=red] at (-5.2,0) [below right] {$x_2\mathstrut$};
+%\node[color=red] at (-4.13,0) [above right] {$x_3\mathstrut$};
+%\node[color=red] at (-2.85,0) [below right] {$x_4\mathstrut$};
+%\node[color=red] at (-1.37,0) [above right] {$x_5\mathstrut$};
+%\node[color=red] at (0.2,0) [above left] {$x_6\mathstrut$};
+%\node[color=red] at (1.73,0) [below left] {$x_7\mathstrut$};
+%\node[color=red] at (3.21,0) [above left] {$x_8\mathstrut$};
+%\node[color=red] at (4.52,0) [below left] {$x_9\mathstrut$};
+%\node[color=red] at (5.57,0) [above left] {$x_{10}\mathstrut$};
+%\node[color=red] at ({6.32+0.1},0) [below left] {$x_{11}\mathstrut$};
+%\node[color=red] at ({6.71-0.2},0) [below right] {$x_{12}\mathstrut$};
+
+\def\xamplitude{6.57}
+\def\yamplitude{1.66}
+
+\begin{scope}[xshift=0.20cm]
+%\draw[color=red,line width=1pt] plot[domain=0:180,samples=1000]
+%	({\xamplitude*cos(\x)},{\yamplitude*cos(13*\x)});
+
+\foreach \k in {0,...,13}{
+	\pgfmathparse{(90+180*\k)/13}
+	\xdef\winkel{\pgfmathresult}
+%	\fill[color=red] 
+%	({\xamplitude*cos(\winkel)},{\yamplitude*cos(13*\winkel)})
+%		circle[radius=0.08];
+}
+
+%\node[color=white] at (0,{\yamplitude+0.4})
+%	{$\displaystyle \max \{\, l(x)\;|\; {-1}\le x \le 1 \} $};
+%\node[color=white] at (0,{-\yamplitude-0.4}) 
+%	{$\displaystyle \min \{\, l(x)\;|\; {-1}\le x \le 1 \} $};
+
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+