new stuff on tschebyscheff and conic sections

7 files changed, 148 insertions, 0 deletions

diff --git a/buch/chapters/030-geometrie/images/Makefile b/buch/chapters/030-geometrie/images/Makefile
index 457a0a1..af652ab 100644
--- a/buch/chapters/030-geometrie/images/Makefile
+++ b/buch/chapters/030-geometrie/images/Makefile
@@ -7,9 +7,11 @@
 all:									\
 	deftrig.pdf							\
 	einheitskreis.pdf						\
+	ellipse.pdf							\
 	hyperbelflaeche.pdf						\
 	hyperbel.pdf							\
 	kegelschnitte.pdf						\
+	parabel.pdf							\
 	polargleichung.pdf						\
 	zylinder.pdf
 
@@ -19,12 +21,18 @@ deftrig.pdf:	deftrig.tex
 einheitskreis.pdf:	einheitskreis.tex
 	pdflatex einheitskreis.tex
 
+ellipse.pdf:	ellipse.tex
+	pdflatex ellipse.tex
+
 hyperbelflaeche.pdf:	hyperbelflaeche.tex
 	pdflatex hyperbelflaeche.tex
 
 hyperbel.pdf:	hyperbel.tex
 	pdflatex hyperbel.tex
 
+parabel.pdf:	parabel.tex
+	pdflatex parabel.tex
+
 polargleichung.pdf:	polargleichung.tex
 	pdflatex polargleichung.tex
 
diff --git a/buch/chapters/030-geometrie/images/ellipse.pdf b/buch/chapters/030-geometrie/images/ellipse.pdf
new file mode 100644
index 0000000..ee4717c
--- /dev/null
+++ b/buch/chapters/030-geometrie/images/ellipse.pdf
diff --git a/buch/chapters/030-geometrie/images/ellipse.tex b/buch/chapters/030-geometrie/images/ellipse.tex
new file mode 100644
index 0000000..b1d9d9a
--- /dev/null
+++ b/buch/chapters/030-geometrie/images/ellipse.tex
@@ -0,0 +1,81 @@
+%
+% ellipse.tex -- Geometrie einer Ellipse
+%
+% (c) 2022 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{1}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\e{3}
+
+\begin{scope}
+\clip (-6.3,-5.5) rectangle (6.3,5.5);
+\foreach \s in {7,8,9,11,12,13,14,15,16}{
+	%\def\s{9}
+	\pgfmathparse{\s/2}
+	\xdef\a{\pgfmathresult}
+	\pgfmathparse{sqrt(\a*\a-\e*\e)}
+	\xdef\b{\pgfmathresult}
+	\draw[color=red!30,line width=1.4pt] 
+		plot[domain=0:360,samples=100]
+			({\a*cos(\x)},{\b*sin(\x)});
+}
+\end{scope}
+
+\coordinate (O) at (0,0);
+\coordinate (F1) at (3,0);
+\coordinate (F2) at (-3,0);
+\coordinate (A) at (5,0);
+\coordinate (Aminus) at (-5,0);
+\coordinate (B) at (0,4);
+
+\def\winkel{140}
+\pgfmathparse{5*cos(\winkel)}
+\xdef\Px{\pgfmathresult}
+\pgfmathparse{4*sin(\winkel)}
+\xdef\Py{\pgfmathresult}
+\coordinate (P) at (\Px,\Py);
+
+\draw[->] (-6.3,0) -- (6.5,0) coordinate[label={$x$}];
+\draw[->] (0,-5.6) -- (0,5.8) coordinate[label={right:$y$}];
+
+\draw[color=blue,line width=1pt] (0,0) -- (0,4);
+\draw[color=blue,line width=1pt] (0,0) -- (3,0);
+\draw[color=blue,line width=1pt] (0,4) -- (3,0);
+
+\draw[color=red,line width=1.4pt] 
+	plot[domain=0:360,samples=100]
+		({5*cos(\x)},{4*sin(\x)});
+
+\node[color=blue] at ($0.5*(O)+0.5*(F1)$) [above] {$e$};
+\node[color=blue] at ($0.5*(O)+0.5*(B)$) [left] {$b$};
+\node[color=blue] at ($0.5*(F1)+0.5*(B)$) [above right] {$a$};
+
+\fill[color=darkgreen] (P) circle[radius=0.08];
+\node[color=darkgreen] at (P) [above left] {$P$};
+\draw[color=darkgreen,line width=1.4pt] (F1) -- (P) -- (F2);
+\node[color=darkgreen] at ($0.55*(P)+0.45*(F1)$) [below] {$\overline{F_1P}$};
+\node[color=darkgreen] at ($0.50*(P)+0.50*(F2)$) [left] {$\overline{F_2P}$};
+
+\fill[color=red] (A) circle[radius=0.08];
+\node[color=red] at (A) [above right] {$A_+$};
+\fill[color=red] (Aminus) circle[radius=0.08];
+\node[color=red] at (Aminus) [above left] {$A_-$};
+
+\fill[color=blue] (F1) circle[radius=0.08];
+\fill[color=blue] (F2) circle[radius=0.08];
+\node at (F1) [below right] {$F_1$};
+\node at (F2) [below left] {$F_2$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/030-geometrie/images/kegelschnitte.pdf b/buch/chapters/030-geometrie/images/kegelschnitte.pdf
index c2205bf..40a830b 100644
--- a/buch/chapters/030-geometrie/images/kegelschnitte.pdf
+++ b/buch/chapters/030-geometrie/images/kegelschnitte.pdf
diff --git a/buch/chapters/030-geometrie/images/parabel.pdf b/buch/chapters/030-geometrie/images/parabel.pdf
new file mode 100644
index 0000000..76d682e
--- /dev/null
+++ b/buch/chapters/030-geometrie/images/parabel.pdf
diff --git a/buch/chapters/030-geometrie/images/parabel.tex b/buch/chapters/030-geometrie/images/parabel.tex
new file mode 100644
index 0000000..c6eb700
--- /dev/null
+++ b/buch/chapters/030-geometrie/images/parabel.tex
@@ -0,0 +1,59 @@
+%
+% parabel.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,calc}
+\begin{document}
+\def\skala{1}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\f{2.0}
+\def\X{2.7}
+\coordinate (F) at (0,\f);
+
+\begin{scope}
+	\clip (-6.1,-1) rectangle (6.1,4.6);
+	\foreach \x in {-5.5,-5,...,6}{
+		\draw[color=gray!30,line width=1pt]
+			(\x,4.7) -- (\x,{\x*\x/(4*\f)});
+		\draw[color=gray!50,line width=1pt]
+			(\x,{\x*\x/(4*\f)}) -- (F);
+	}
+\end{scope}
+
+\draw[->] (-6.1,0) -- (6.4,0) coordinate[label={$x$}];
+\draw[->] (0,-2.3) -- (0,4.8) coordinate[label={right:$y$}];
+
+\begin{scope}
+	\clip (-6.05,-1) rectangle (6.05,4.6);
+	\draw[color=red,line width=2pt]
+		plot[domain=-6.2:6.2,samples=100] ({\x},{\x*\x/(4*\f)});
+\end{scope}
+
+\fill[color=darkgreen] (\X,{\X*\X/(4*\f)}) circle[radius=0.08];
+\draw[color=darkgreen,line width=1pt] (F) -- (\X,{\X*\X/(4*\f)}) -- (\X,-\f);
+\node[color=darkgreen] at (\X,{\X*\X/(4*\f)})
+	[below right] {$P{\color{black}\mathstrut=(x,y)}$};
+
+\node[color=darkgreen] at (\X,{0.5*(-\f+\X*\X/(4*\f))})
+	[right] {$\overline{Pl}{\color{black}\mathstrut=y+f}$};
+\node[color=darkgreen] at ($0.8*(F)+0.2*(\X,{\X*\X/(4*\f)})+(0,-0.2)$)
+	[above right]
+	{$\overline{PF}{\color{black}\mathstrut=\sqrt{x^2+(y-f)^2}}$};
+
+\node at (F) [above left] {${\color{blue}F}=(0,f)$};
+\draw[color=blue,line width=1pt] (-6,-\f) -- (6,-\f);
+\fill[color=blue] (F) circle[radius=0.08];
+\node[color=blue] at (-4,-\f) [above] {$l$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/030-geometrie/images/zylinder.pdf b/buch/chapters/030-geometrie/images/zylinder.pdf
index 2e73d80..2580050 100644
--- a/buch/chapters/030-geometrie/images/zylinder.pdf
+++ b/buch/chapters/030-geometrie/images/zylinder.pdf