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Diffstat (limited to '')
| -rw-r--r-- | buch/chapters/030-geometrie/images/Makefile | 14 | ||||
| -rw-r--r-- | buch/chapters/030-geometrie/images/hyperbelflaeche.pdf | bin | 0 -> 20736 bytes | |||
| -rw-r--r-- | buch/chapters/030-geometrie/images/hyperbelflaeche.tex | 49 | ||||
| -rw-r--r-- | buch/chapters/030-geometrie/images/polargleichung.pdf | bin | 0 -> 35148 bytes | |||
| -rw-r--r-- | buch/chapters/030-geometrie/images/polargleichung.tex | 108 |
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 Binary files differnew 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 Binary files differnew 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} + |