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Sven Riwoldt
2020-10-24 13:47:37 +02:00
commit 2149d34295
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17
tikzgrafiken/.project Normal file
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<?xml version="1.0" encoding="UTF-8"?>
<projectDescription>
<name>PIKZ</name>
<comment></comment>
<projects>
</projects>
<buildSpec>
<buildCommand>
<name>net.sourceforge.texlipse.builder.TexlipseBuilder</name>
<arguments>
</arguments>
</buildCommand>
</buildSpec>
<natures>
<nature>net.sourceforge.texlipse.builder.TexlipseNature</nature>
</natures>
</projectDescription>

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tikzgrafiken/08_1_1.pdf Normal file
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tikzgrafiken/08_1_1.tex Normal file
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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usetikzlibrary{positioning}
\usepackage{verbatim}
\begin{document}
\begin{tikzpicture}[scale=1.5, on grid]
\draw [help lines](-2,-2) grid (2,2);
\draw[-triangle 45, color=blue] (-0.75,0.5) -- (0.75,-0.5) node[sloped,below] { $-$};
\draw[-triangle 45, color=red] (0.75,0.5) -- (-0.75,-0.5) node[sloped,below] { $+$};
\node[] at (0,0) {$\left( {\begin{array}{*{20}c}
{a_{11} } & {a_{12} } \\
{a_{21} } & {a_{22} } \\
\end{array}} \right)
$};
\end{tikzpicture}
\end{document}

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tikzgrafiken/3dGittter.tex Normal file
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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usetikzlibrary{positioning}
\usetikzlibrary{calc}
\usepackage{verbatim}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{document}
\begin{tikzpicture}[scale=1.5]
%\foreach \x in {0,...,5}
% \fill[ball color=red] (\x,0,0) circle (0.05);
%\foreach \x in {0,...,5}
% \fill[ball color=red] (\x,1,0) circle (0.05);
%\foreach \x in {0,...,5}
% \fill[ball color=red] (\x,2,0) circle (0.05);
%\foreach \x in {0,...,5}
% \fill[ball color=red] (\x,3,0) circle (0.05);
%\foreach \x in {0,...,5}
% \fill[ball color=red] (\x,4,0) circle (0.05);
%\foreach \x in {0,...,5}
% \fill[ball color=red] (\x,5,0) circle (0.05);
%\foreach \y in {0,...,5}
% \fill[ball color=red] (0,\y,0) circle (0.05);
%\foreach \y in {0,...,5}
% \fill[ball color=red] (1,\y,0) circle (0.05);
\foreach \x in {0,...,3}
\foreach \y in {0,...,3}
\foreach \z in {0,...,3}
\fill[ball color=gray] (\x,\y,-\z) circle (0.05);
%\fill[ball color=red] (3,3,2) circle (0.05);
%\fill[ball color=red] (0,0,0) circle (0.05);
% \draw[color=gray, style=thin] (0,0,0) -- (1,0,0);
% \draw[color=gray, style=thin] (0,0,0) -- (0,1,0);
% \draw[color=gray, style=thin] (0,0,0) -- (0,0,-1);
% \draw[color=gray, style=thin] (0,1,0) -- (1,1,0);
% \draw[color=gray, style=thin] (1,0,0) -- (1,1,0);
% \draw[color=gray, style=thin] (1,0,0) -- (1,0,-1);
% \draw[color=gray, style=thin] (1,1,0) -- (1,1,-1);
% \draw[color=gray, style=thin] (1,0,-1) -- (1,1,-1);
% \draw[color=gray, style=thin] (0,0,-1) -- (1,0,-1);
% \draw[color=gray, style=thin] (0,1,0) -- (0,1,-1);
% \draw[color=gray, style=thin] (0,0,-1) -- (0,1,-1);
% \draw[color=gray, style=thin] (0,1,-1) -- (1,1,-1);
% \draw[color=blue, style=thin] (1,0,0) -- (2,0,0);
% \draw[color=blue, style=thin] (1,0,0) -- (1,0,-1);
% \draw[color=blue, style=thin] (2,0,0) -- (2,0,-1);
\end{tikzpicture}
\end{document}

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tikzgrafiken/Loesung001.pdf Normal file
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tikzgrafiken/Loesung001.tex Normal file
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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usetikzlibrary{positioning}
\usepackage{verbatim}
\begin{document}
\begin{tikzpicture}[scale=1, on grid]
%\draw [help lines](-4,-2) grid (12,7);
\draw[-triangle 45] (-3.5,0) -- (11,0) node[right] {$x$};
\foreach \x in {-3,-2,-1, 1,2,3,4,5,6,7,8,9,10}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
\draw[-triangle 45] (0,-1) -- (0,6) node[above] {$y$};
\foreach \y in {-1,1,2,3,4,5}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};
\draw[-triangle 45, color=violet] (0,0) -- (3,4) node[midway,sloped,above] {$\vec a$};
\draw [color=violet, dashed, thin] (3,-0.4) node[below, sloped] {$a_1$} -- (3,4);
\draw [color=violet, dashed, thin] (-0.4,4) node[above, left] {$a_2$} -- (3,4);
\draw[-triangle 45, color=red] (0,0) -- (10,5) node[midway,sloped,above] {$\vec b$};
\draw [color=red, dashed, thin] (10,-0.4) node[below, sloped] {$b_1$} -- (10,5);
\draw [color=red, dashed, thin] (-0.4,5) node[above, left] {$b_2$} -- (10,5);
\draw[-triangle 45, color=blue] (0,0) -- (10/2,5/2) node[midway,sloped,above] {$\frac{1}{2}\vec b$};
\draw [color=blue, dashed, thin] (10/2,-0.4) node[below, sloped] {$\frac{1}{2} b_1$} -- (10/2,5/2);
\draw [color=blue, dashed, thin] (-0.4,5/2) node[above, left] {$\frac{1}{2} b_2$} -- (10/2,5/2);
\draw [-triangle 45,color=magenta, dashed, thin] (10/2,5/2) -- (3,4);
\end{tikzpicture}
\end{document}

2
tikzgrafiken/function.cos.gnuplot Normal file
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set terminal table; set output "function.cos.table"; set format "%.5f"
set samples 25; plot [x=0:4] cos(x)

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tikzgrafiken/function.cos.table Normal file
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#Curve 0 of 1, 25 points
#x y type
0.00000 1.00000 i
0.16667 0.98614 i
0.33333 0.94496 i
0.50000 0.87758 i
0.66667 0.78589 i
0.83333 0.67241 i
1.00000 0.54030 i
1.16667 0.39322 i
1.33333 0.23524 i
1.50000 0.07074 i
1.66667 -0.09572 i
1.83333 -0.25953 i
2.00000 -0.41615 i
2.16667 -0.56123 i
2.33333 -0.69076 i
2.50000 -0.80114 i
2.66667 -0.88933 i
2.83333 -0.95286 i
3.00000 -0.98999 i
3.16667 -0.99969 i
3.33333 -0.98167 i
3.50000 -0.93646 i
3.66667 -0.86529 i
3.83333 -0.77014 i
4.00000 -0.65364 i
#Curve 0 of 1, 25 points
#x y type
-2.00000 1.00000 i
-1.74167 0.74167 i
-1.48333 0.48333 i
-1.22500 0.22500 i
-0.96667 0.03333 i
-0.70833 0.29167 i
-0.45000 0.55000 i
-0.19167 0.80833 i
0.06667 1.06667 i
0.32500 1.32500 i
0.58333 1.58333 i
0.84167 1.84167 i
1.10000 2.10000 i
1.35833 2.35833 i
1.61667 2.61667 i
1.87500 2.87500 i
2.13333 3.13333 i
2.39167 3.39167 i
2.65000 3.65000 i
2.90833 3.90833 i
3.16667 4.16667 i
3.42500 4.42500 i
3.68333 4.68333 i
3.94167 4.94167 i
4.20000 5.20000 i
#Curve 0 of 1, 25 points
#x y type
-2.00000 1.00000 i
-1.74167 0.74167 i
-1.48333 0.48333 i
-1.22500 0.22500 i
-0.96667 0.03333 i
-0.70833 0.29167 i
-0.45000 0.55000 i
-0.19167 0.80833 i
0.06667 1.06667 i
0.32500 1.32500 i
0.58333 1.58333 i
0.84167 1.84167 i
1.10000 2.10000 i
1.35833 2.35833 i
1.61667 2.61667 i
1.87500 2.87500 i
2.13333 3.13333 i
2.39167 3.39167 i
2.65000 3.65000 i
2.90833 3.90833 i
3.16667 4.16667 i
3.42500 4.42500 i
3.68333 4.68333 i
3.94167 4.94167 i
4.20000 5.20000 i

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tikzgrafiken/function.exp.gnuplot Normal file
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set terminal table; set output "function.exp.table"; set format "%.5f"
set samples 25; plot [x=0:4] 0.05*exp(x)

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tikzgrafiken/function.exp.table Normal file
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#Curve 0 of 1, 25 points
#x y type
0.00000 0.05000 i
0.16667 0.05907 i
0.33333 0.06978 i
0.50000 0.08244 i
0.66667 0.09739 i
0.83333 0.11505 i
1.00000 0.13591 i
1.16667 0.16056 i
1.33333 0.18968 i
1.50000 0.22408 i
1.66667 0.26472 i
1.83333 0.31274 i
2.00000 0.36945 i
2.16667 0.43646 i
2.33333 0.51561 i
2.50000 0.60912 i
2.66667 0.71960 i
2.83333 0.85010 i
3.00000 1.00428 i
3.16667 1.18641 i
3.33333 1.40158 i
3.50000 1.65577 i
3.66667 1.95606 i
3.83333 2.31082 i
4.00000 2.72991 i
#Curve 0 of 1, 25 points
#x y type
0.00000 0.05000 i
0.16667 0.05907 i
0.33333 0.06978 i
0.50000 0.08244 i
0.66667 0.09739 i
0.83333 0.11505 i
1.00000 0.13591 i
1.16667 0.16056 i
1.33333 0.18968 i
1.50000 0.22408 i
1.66667 0.26472 i
1.83333 0.31274 i
2.00000 0.36945 i
2.16667 0.43646 i
2.33333 0.51561 i
2.50000 0.60912 i
2.66667 0.71960 i
2.83333 0.85010 i
3.00000 1.00428 i
3.16667 1.18641 i
3.33333 1.40158 i
3.50000 1.65577 i
3.66667 1.95606 i
3.83333 2.31082 i
4.00000 2.72991 i

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tikzgrafiken/function.pdf Normal file
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tikzgrafiken/function.sin.gnuplot Normal file
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set terminal table; set output "function.sin.table"; set format "%.5f"
set samples 25; plot [x=0:4] sin(x)

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tikzgrafiken/function.sin.table Normal file
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#Curve 0 of 1, 25 points
#x y type
0.00000 0.00000 i
0.16667 0.16590 i
0.33333 0.32719 i
0.50000 0.47943 i
0.66667 0.61837 i
0.83333 0.74018 i
1.00000 0.84147 i
1.16667 0.91944 i
1.33333 0.97194 i
1.50000 0.99749 i
1.66667 0.99541 i
1.83333 0.96573 i
2.00000 0.90930 i
2.16667 0.82766 i
2.33333 0.72309 i
2.50000 0.59847 i
2.66667 0.45727 i
2.83333 0.30340 i
3.00000 0.14112 i
3.16667 -0.02507 i
3.33333 -0.19057 i
3.50000 -0.35078 i
3.66667 -0.50128 i
3.83333 -0.63788 i
4.00000 -0.75680 i

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tikzgrafiken/function.tex Normal file
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\documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage{tikz}
% GNUPLOT required
\begin{document}
\pagestyle{empty}
\begin{tikzpicture}[domain=0:4]
\draw[very thin,color=gray] (-0.1,-1.1) grid (3.9,3.9);
\draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$};
\draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$};
\draw[color=red] plot[id=x] function{x}
node[right] {$f(x) =x$};
\draw[color=blue] plot[id=cos] function{cos(x)}
node[right] {$f(x) = \cos x$};
\draw[color=orange] plot[id=exp] function{0.05*exp(x)}
node[right] {$f(x) = \frac{1}{20} \mathrm e^x$};
\end{tikzpicture}
\end{document}
%%latex -shell-escape myfile.tex
%%%& -shell-escape -enable-write18

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tikzgrafiken/function.x.gnuplot Normal file
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set terminal table; set output "function.x.table"; set format "%.5f"
set samples 25; plot [x=0:4] x

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tikzgrafiken/function.x.table Normal file
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#Curve 0 of 1, 25 points
#x y type
0.00000 0.00000 i
0.16667 0.16667 i
0.33333 0.33333 i
0.50000 0.50000 i
0.66667 0.66667 i
0.83333 0.83333 i
1.00000 1.00000 i
1.16667 1.16667 i
1.33333 1.33333 i
1.50000 1.50000 i
1.66667 1.66667 i
1.83333 1.83333 i
2.00000 2.00000 i
2.16667 2.16667 i
2.33333 2.33333 i
2.50000 2.50000 i
2.66667 2.66667 i
2.83333 2.83333 i
3.00000 3.00000 i
3.16667 3.16667 i
3.33333 3.33333 i
3.50000 3.50000 i
3.66667 3.66667 i
3.83333 3.83333 i
4.00000 4.00000 i

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tikzgrafiken/function2.exp.gnuplot Normal file
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set terminal table; set output "function2.exp.table"; set format "%.5f"
set samples 25; plot [x=0:4] 0.05*exp(x)

2
tikzgrafiken/function2.f3.gnuplot Normal file
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set terminal table; set output "function2.f3.table"; set format "%.5f"
set samples 50; plot [x=0.658:3] exp(-x*x*0.5/0.16)

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tikzgrafiken/function2.f3.table Normal file
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#Curve 0 of 1, 50 points
#x y type
0.65800 0.25846 i
0.70580 0.21083 i
0.75359 0.16954 i
0.80139 0.13440 i
0.84918 0.10503 i
0.89698 0.08092 i
0.94478 0.06146 i
0.99257 0.04602 i
1.04037 0.03397 i
1.08816 0.02472 i
1.13596 0.01773 i
1.18376 0.01254 i
1.23155 0.00874 i
1.27935 0.00601 i
1.32714 0.00407 i
1.37494 0.00272 i
1.42273 0.00179 i
1.47053 0.00116 i
1.51833 0.00074 i
1.56612 0.00047 i
1.61392 0.00029 i
1.66171 0.00018 i
1.70951 0.00011 i
1.75731 0.00006 i
1.80510 0.00004 i
1.85290 0.00002 i
1.90069 0.00001 i
1.94849 0.00001 i
1.99629 0.00000 i
2.04408 0.00000 i
2.09188 0.00000 i
2.13967 0.00000 i
2.18747 0.00000 i
2.23527 0.00000 i
2.28306 0.00000 i
2.33086 0.00000 i
2.37865 0.00000 i
2.42645 0.00000 i
2.47424 0.00000 i
2.52204 0.00000 i
2.56984 0.00000 i
2.61763 0.00000 i
2.66543 0.00000 i
2.71322 0.00000 i
2.76102 0.00000 i
2.80882 0.00000 i
2.85661 0.00000 i
2.90441 0.00000 i
2.95220 0.00000 i
3.00000 0.00000 i

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tikzgrafiken/function2.pdf Normal file
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tikzgrafiken/function2.sin.gnuplot Normal file
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set terminal table; set output "function2.sin.table"; set format "%.5f"
set samples 25; plot [x=0:4] sin(x)

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tikzgrafiken/function2.tex Normal file
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\documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage{tikz}
% GNUPLOT required
\begin{document}
\pagestyle{empty}
\begin{tikzpicture}
\draw[very thin,color=gray] (-0.1,-0.1) grid (3.9,3.9);
\draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$};
\draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$};
\foreach \x/\xtext in {1/a,2/b}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\xtext$};
% \draw [color=red, thin] (1,0) -- (1,1);
% \draw [color=red, thin] (2,0) -- (2,1.2599210498948731647672106072782);
% \draw [color=red, thin] (1,0) -- (2,0);
% \draw [color=red, thin] plot[id=w3_ausschnitt, smooth, domain=1:2, samples=200] function{x**(1./3.)};
\draw[color=orange] plot[id=w3, smooth, domain=0:3.5, samples=200] function{x**(1./3.)} node[right] {$f(x) = \sqrt[3]{x}$};
%\fill[red!30] (1,0) -- plot[id=f3,domain=0.658:3,samples=50] function {exp(-x*x*0.5/0.16)} -- (3,0) -- cycle;
\fill[red!50] (1,0) -- plot[id=w3_ausschnitt,domain=1:2,samples=200] function {x**(1./3.)} -- (2,0) -- cycle;
\end{tikzpicture}
\end{document}

2
tikzgrafiken/function2.w3.gnuplot Normal file
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set terminal table; set output "function2.w3.table"; set format "%.5f"
set samples 200; plot [x=0:3.5] x**(1./3.)

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tikzgrafiken/function2.w3.table Normal file
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#Curve 0 of 1, 200 points
#x y type
0.00000 0.00000 i
0.01759 0.26006 i
0.03518 0.32765 i
0.05276 0.37507 i
0.07035 0.41282 i
0.08794 0.44469 i
0.10553 0.47256 i
0.12312 0.49747 i
0.14070 0.52012 i
0.15829 0.54094 i
0.17588 0.56028 i
0.19347 0.57837 i
0.21106 0.59539 i
0.22864 0.61149 i
0.24623 0.62678 i
0.26382 0.64136 i
0.28141 0.65531 i
0.29899 0.66868 i
0.31658 0.68155 i
0.33417 0.69394 i
0.35176 0.70591 i
0.36935 0.71748 i
0.38693 0.72870 i
0.40452 0.73957 i
0.42211 0.75014 i
0.43970 0.76042 i
0.45729 0.77042 i
0.47487 0.78018 i
0.49246 0.78969 i
0.51005 0.79898 i
0.52764 0.80806 i
0.54523 0.81694 i
0.56281 0.82564 i
0.58040 0.83415 i
0.59799 0.84249 i
0.61558 0.85067 i
0.63317 0.85870 i
0.65075 0.86657 i
0.66834 0.87431 i
0.68593 0.88191 i
0.70352 0.88939 i
0.72111 0.89674 i
0.73869 0.90397 i
0.75628 0.91109 i
0.77387 0.91810 i
0.79146 0.92500 i
0.80905 0.93180 i
0.82663 0.93851 i
0.84422 0.94512 i
0.86181 0.95163 i
0.87940 0.95807 i
0.89698 0.96441 i
0.91457 0.97067 i
0.93216 0.97686 i
0.94975 0.98296 i
0.96734 0.98899 i
0.98492 0.99495 i
1.00251 1.00084 i
1.02010 1.00666 i
1.03769 1.01241 i
1.05528 1.01810 i
1.07286 1.02372 i
1.09045 1.02928 i
1.10804 1.03479 i
1.12563 1.04024 i
1.14322 1.04563 i
1.16080 1.05096 i
1.17839 1.05624 i
1.19598 1.06147 i
1.21357 1.06665 i
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1.24874 1.07686 i
1.26633 1.08189 i
1.28392 1.08687 i
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1.60050 1.16973 i
1.61809 1.17400 i
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1.65327 1.18244 i
1.67085 1.18662 i
1.68844 1.19077 i
1.70603 1.19489 i
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1.86432 1.23076 i
1.88191 1.23462 i
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1.95226 1.24982 i
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2.00503 1.26098 i
2.02261 1.26465 i
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2.14573 1.28981 i
2.16332 1.29332 i
2.18090 1.29682 i
2.19849 1.30029 i
2.21608 1.30375 i
2.23367 1.30719 i
2.25126 1.31061 i
2.26884 1.31402 i
2.28643 1.31741 i
2.30402 1.32077 i
2.32161 1.32413 i
2.33920 1.32746 i
2.35678 1.33078 i
2.37437 1.33408 i
2.39196 1.33737 i
2.40955 1.34064 i
2.42714 1.34389 i
2.44472 1.34713 i
2.46231 1.35035 i
2.47990 1.35356 i
2.49749 1.35675 i
2.51508 1.35993 i
2.53266 1.36309 i
2.55025 1.36624 i
2.56784 1.36938 i
2.58543 1.37249 i
2.60302 1.37560 i
2.62060 1.37869 i
2.63819 1.38177 i
2.65578 1.38483 i
2.67337 1.38788 i
2.69095 1.39092 i
2.70854 1.39394 i
2.72613 1.39695 i
2.74372 1.39995 i
2.76131 1.40294 i
2.77889 1.40591 i
2.79648 1.40887 i
2.81407 1.41182 i
2.83166 1.41475 i
2.84925 1.41767 i
2.86683 1.42059 i
2.88442 1.42349 i
2.90201 1.42637 i
2.91960 1.42925 i
2.93719 1.43211 i
2.95477 1.43497 i
2.97236 1.43781 i
2.98995 1.44064 i
3.00754 1.44346 i
3.02513 1.44626 i
3.04271 1.44906 i
3.06030 1.45185 i
3.07789 1.45462 i
3.09548 1.45739 i
3.11307 1.46015 i
3.13065 1.46289 i
3.14824 1.46562 i
3.16583 1.46835 i
3.18342 1.47106 i
3.20101 1.47377 i
3.21859 1.47646 i
3.23618 1.47915 i
3.25377 1.48182 i
3.27136 1.48449 i
3.28894 1.48714 i
3.30653 1.48979 i
3.32412 1.49242 i
3.34171 1.49505 i
3.35930 1.49767 i
3.37688 1.50028 i
3.39447 1.50288 i
3.41206 1.50547 i
3.42965 1.50805 i
3.44724 1.51063 i
3.46482 1.51319 i
3.48241 1.51575 i
3.50000 1.51829 i

2
tikzgrafiken/function2.w3_ausschnitt.gnuplot Normal file
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set terminal table; set output "function2.w3_ausschnitt.table"; set format "%.5f"
set samples 200; plot [x=1:2] x**(1./3.)

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tikzgrafiken/function2.w3_ausschnitt.table Normal file
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#Curve 0 of 1, 200 points
#x y type
1.00000 1.00000 i
1.00503 1.00167 i
1.01005 1.00334 i
1.01508 1.00500 i
1.02010 1.00666 i
1.02513 1.00831 i
1.03015 1.00995 i
1.03518 1.01159 i
1.04020 1.01322 i
1.04523 1.01485 i
1.05025 1.01648 i
1.05528 1.01810 i
1.06030 1.01971 i
1.06533 1.02132 i
1.07035 1.02292 i
1.07538 1.02452 i
1.08040 1.02611 i
1.08543 1.02770 i
1.09045 1.02928 i
1.09548 1.03086 i
1.10050 1.03244 i
1.10553 1.03401 i
1.11055 1.03557 i
1.11558 1.03713 i
1.12060 1.03869 i
1.12563 1.04024 i
1.13065 1.04178 i
1.13568 1.04332 i
1.14070 1.04486 i
1.14573 1.04639 i
1.15075 1.04792 i
1.15578 1.04944 i
1.16080 1.05096 i
1.16583 1.05247 i
1.17085 1.05398 i
1.17588 1.05549 i
1.18090 1.05699 i
1.18593 1.05849 i
1.19095 1.05998 i
1.19598 1.06147 i
1.20101 1.06296 i
1.20603 1.06444 i
1.21106 1.06591 i
1.21608 1.06738 i
1.22111 1.06885 i
1.22613 1.07032 i
1.23116 1.07178 i
1.23618 1.07323 i
1.24121 1.07469 i
1.24623 1.07613 i
1.25126 1.07758 i
1.25628 1.07902 i
1.26131 1.08046 i
1.26633 1.08189 i
1.27136 1.08332 i
1.27638 1.08474 i
1.28141 1.08616 i
1.28643 1.08758 i
1.29146 1.08900 i
1.29648 1.09041 i
1.30151 1.09181 i
1.30653 1.09322 i
1.31156 1.09462 i
1.31658 1.09601 i
1.32161 1.09741 i
1.32663 1.09880 i
1.33166 1.10018 i
1.33668 1.10156 i
1.34171 1.10294 i
1.34673 1.10432 i
1.35176 1.10569 i
1.35678 1.10706 i
1.36181 1.10842 i
1.36683 1.10978 i
1.37186 1.11114 i
1.37688 1.11250 i
1.38191 1.11385 i
1.38693 1.11520 i
1.39196 1.11654 i
1.39698 1.11789 i
1.40201 1.11922 i
1.40704 1.12056 i
1.41206 1.12189 i
1.41709 1.12322 i
1.42211 1.12455 i
1.42714 1.12587 i
1.43216 1.12719 i
1.43719 1.12851 i
1.44221 1.12982 i
1.44724 1.13113 i
1.45226 1.13244 i
1.45729 1.13374 i
1.46231 1.13505 i
1.46734 1.13634 i
1.47236 1.13764 i
1.47739 1.13893 i
1.48241 1.14022 i
1.48744 1.14151 i
1.49246 1.14279 i
1.49749 1.14407 i
1.50251 1.14535 i
1.50754 1.14663 i
1.51256 1.14790 i
1.51759 1.14917 i
1.52261 1.15044 i
1.52764 1.15170 i
1.53266 1.15296 i
1.53769 1.15422 i
1.54271 1.15548 i
1.54774 1.15673 i
1.55276 1.15798 i
1.55779 1.15923 i
1.56281 1.16047 i
1.56784 1.16172 i
1.57286 1.16296 i
1.57789 1.16419 i
1.58291 1.16543 i
1.58794 1.16666 i
1.59296 1.16789 i
1.59799 1.16912 i
1.60302 1.17034 i
1.60804 1.17156 i
1.61307 1.17278 i
1.61809 1.17400 i
1.62312 1.17521 i
1.62814 1.17642 i
1.63317 1.17763 i
1.63819 1.17884 i
1.64322 1.18004 i
1.64824 1.18125 i
1.65327 1.18244 i
1.65829 1.18364 i
1.66332 1.18484 i
1.66834 1.18603 i
1.67337 1.18722 i
1.67839 1.18840 i
1.68342 1.18959 i
1.68844 1.19077 i
1.69347 1.19195 i
1.69849 1.19313 i
1.70352 1.19431 i
1.70854 1.19548 i
1.71357 1.19665 i
1.71859 1.19782 i
1.72362 1.19898 i
1.72864 1.20015 i
1.73367 1.20131 i
1.73869 1.20247 i
1.74372 1.20363 i
1.74874 1.20478 i
1.75377 1.20594 i
1.75879 1.20709 i
1.76382 1.20823 i
1.76884 1.20938 i
1.77387 1.21053 i
1.77889 1.21167 i
1.78392 1.21281 i
1.78894 1.21394 i
1.79397 1.21508 i
1.79899 1.21621 i
1.80402 1.21735 i
1.80905 1.21847 i
1.81407 1.21960 i
1.81910 1.22073 i
1.82412 1.22185 i
1.82915 1.22297 i
1.83417 1.22409 i
1.83920 1.22521 i
1.84422 1.22632 i
1.84925 1.22743 i
1.85427 1.22855 i
1.85930 1.22965 i
1.86432 1.23076 i
1.86935 1.23187 i
1.87437 1.23297 i
1.87940 1.23407 i
1.88442 1.23517 i
1.88945 1.23627 i
1.89447 1.23736 i
1.89950 1.23845 i
1.90452 1.23954 i
1.90955 1.24063 i
1.91457 1.24172 i
1.91960 1.24281 i
1.92462 1.24389 i
1.92965 1.24497 i
1.93467 1.24605 i
1.93970 1.24713 i
1.94472 1.24821 i
1.94975 1.24928 i
1.95477 1.25035 i
1.95980 1.25142 i
1.96482 1.25249 i
1.96985 1.25356 i
1.97487 1.25462 i
1.97990 1.25569 i
1.98492 1.25675 i
1.98995 1.25781 i
1.99497 1.25886 i
2.00000 1.25992 i

2
tikzgrafiken/function2.x.gnuplot Normal file
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set terminal table; set output "function2.x.table"; set format "%.5f"
set samples 25; plot [x=0:4] x

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tikzgrafiken/function2_1.pdf Normal file
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tikzgrafiken/function2_1.tex Normal file
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\documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage{tikz}
\usetikzlibrary{calc}
% GNUPLOT required
\begin{document}
\pagestyle{empty}
\begin{tikzpicture}
\draw[very thin,color=gray] (-0.1,-0.1) grid (3.9,3.9);
\draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$};
\draw[->] (0,-1.2) -- (0,4.2) node[above] {$f(x)$};
\foreach \x/\xtext in {1/a,2/b}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\xtext$};
% \draw [color=red, thin] (1,0) -- (1,1);
% \draw [color=red, thin] (2,0) -- (2,1.2599210498948731647672106072782);
% \draw [color=red, thin] (1,0) -- (2,0);
% \draw [color=red, thin] plot[id=w3_ausschnitt, smooth, domain=1:2, samples=200] function{x**(1./3.)};
%\fill[red] (1,0) -- plot[id=w3_ausschnitt,domain=1:2,samples=200] function {x**(1./3.)} -- (2,0) -- cycle;
\draw [fill=red] (1,0) -- plot[id=w3_ausschnitt,domain=1:2,samples=200] function {x**(1./3.)} -- (2,0) -- cycle;
\draw[color=orange] plot[id=w3, smooth, domain=0:3.5, samples=200] function{x**(1./3.)} node[right] {$f(x) = \sqrt[3]{x}$};
%\fill[red!30] (1,0) -- plot[id=f3,domain=0.658:3,samples=50] function {exp(-x*x*0.5/0.16)} -- (3,0) -- cycle;
%\pgfmathsetmacro\wert2{\pgfmathpow{1.5}{\pgfmathdivide{1.}{3.}}}
%\pgfmathsetmacro\wert2{1.5**0.33333333333}
%\pgfmathpow{1.5}{\pgfmathdivide{1.}{3.}}
\draw [fill=black!50] (1,0) rectangle +(0.5,1);
% \draw [fill=black!50] (1.5,0) rectangle +(0.5,(\pgfmathparse{pow(2,7)} \pgfmathresult));
\pgfmathparse{pow(1.5, (1/3))};
\pgfmathsetmacro\wert{\pgfmathresult} %%Die Variable darf keine Zahl in Namen enthalten
\draw [fill=black!50] (1.5,0) rectangle +(0.5,\wert);
% \draw [fill=black!50] (1.5,0) rectangle +(0.5,\pgfmathparse{\pgfmathpow{1.5}{\pgfmathdivide{1.}{3.}}} \pgfmathresult);
% \fill [color=black!50] (1.5,0) rectangle +(0.5, 1.1447142425533318678);
\end{tikzpicture}
\end{document}

2
tikzgrafiken/function2_1.w3.gnuplot Normal file
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set terminal table; set output "function2_1.w3.table"; set format "%.5f"
set samples 200; plot [x=0:3.5] x**(1./3.)

204
tikzgrafiken/function2_1.w3.table Normal file
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#Curve 0 of 1, 200 points
#x y type
0.00000 0.00000 i
0.01759 0.26006 i
0.03518 0.32765 i
0.05276 0.37507 i
0.07035 0.41282 i
0.08794 0.44469 i
0.10553 0.47256 i
0.12312 0.49747 i
0.14070 0.52012 i
0.15829 0.54094 i
0.17588 0.56028 i
0.19347 0.57837 i
0.21106 0.59539 i
0.22864 0.61149 i
0.24623 0.62678 i
0.26382 0.64136 i
0.28141 0.65531 i
0.29899 0.66868 i
0.31658 0.68155 i
0.33417 0.69394 i
0.35176 0.70591 i
0.36935 0.71748 i
0.38693 0.72870 i
0.40452 0.73957 i
0.42211 0.75014 i
0.43970 0.76042 i
0.45729 0.77042 i
0.47487 0.78018 i
0.49246 0.78969 i
0.51005 0.79898 i
0.52764 0.80806 i
0.54523 0.81694 i
0.56281 0.82564 i
0.58040 0.83415 i
0.59799 0.84249 i
0.61558 0.85067 i
0.63317 0.85870 i
0.65075 0.86657 i
0.66834 0.87431 i
0.68593 0.88191 i
0.70352 0.88939 i
0.72111 0.89674 i
0.73869 0.90397 i
0.75628 0.91109 i
0.77387 0.91810 i
0.79146 0.92500 i
0.80905 0.93180 i
0.82663 0.93851 i
0.84422 0.94512 i
0.86181 0.95163 i
0.87940 0.95807 i
0.89698 0.96441 i
0.91457 0.97067 i
0.93216 0.97686 i
0.94975 0.98296 i
0.96734 0.98899 i
0.98492 0.99495 i
1.00251 1.00084 i
1.02010 1.00666 i
1.03769 1.01241 i
1.05528 1.01810 i
1.07286 1.02372 i
1.09045 1.02928 i
1.10804 1.03479 i
1.12563 1.04024 i
1.14322 1.04563 i
1.16080 1.05096 i
1.17839 1.05624 i
1.19598 1.06147 i
1.21357 1.06665 i
1.23116 1.07178 i
1.24874 1.07686 i
1.26633 1.08189 i
1.28392 1.08687 i
1.30151 1.09181 i
1.31910 1.09671 i
1.33668 1.10156 i
1.35427 1.10637 i
1.37186 1.11114 i
1.38945 1.11587 i
1.40704 1.12056 i
1.42462 1.12521 i
1.44221 1.12982 i
1.45980 1.13440 i
1.47739 1.13893 i
1.49497 1.14343 i
1.51256 1.14790 i
1.53015 1.15233 i
1.54774 1.15673 i
1.56533 1.16110 i
1.58291 1.16543 i
1.60050 1.16973 i
1.61809 1.17400 i
1.63568 1.17824 i
1.65327 1.18244 i
1.67085 1.18662 i
1.68844 1.19077 i
1.70603 1.19489 i
1.72362 1.19898 i
1.74121 1.20305 i
1.75879 1.20709 i
1.77638 1.21110 i
1.79397 1.21508 i
1.81156 1.21904 i
1.82915 1.22297 i
1.84673 1.22688 i
1.86432 1.23076 i
1.88191 1.23462 i
1.89950 1.23845 i
1.91709 1.24226 i
1.93467 1.24605 i
1.95226 1.24982 i
1.96985 1.25356 i
1.98744 1.25728 i
2.00503 1.26098 i
2.02261 1.26465 i
2.04020 1.26831 i
2.05779 1.27194 i
2.07538 1.27555 i
2.09296 1.27915 i
2.11055 1.28272 i
2.12814 1.28627 i
2.14573 1.28981 i
2.16332 1.29332 i
2.18090 1.29682 i
2.19849 1.30029 i
2.21608 1.30375 i
2.23367 1.30719 i
2.25126 1.31061 i
2.26884 1.31402 i
2.28643 1.31741 i
2.30402 1.32077 i
2.32161 1.32413 i
2.33920 1.32746 i
2.35678 1.33078 i
2.37437 1.33408 i
2.39196 1.33737 i
2.40955 1.34064 i
2.42714 1.34389 i
2.44472 1.34713 i
2.46231 1.35035 i
2.47990 1.35356 i
2.49749 1.35675 i
2.51508 1.35993 i
2.53266 1.36309 i
2.55025 1.36624 i
2.56784 1.36938 i
2.58543 1.37249 i
2.60302 1.37560 i
2.62060 1.37869 i
2.63819 1.38177 i
2.65578 1.38483 i
2.67337 1.38788 i
2.69095 1.39092 i
2.70854 1.39394 i
2.72613 1.39695 i
2.74372 1.39995 i
2.76131 1.40294 i
2.77889 1.40591 i
2.79648 1.40887 i
2.81407 1.41182 i
2.83166 1.41475 i
2.84925 1.41767 i
2.86683 1.42059 i
2.88442 1.42349 i
2.90201 1.42637 i
2.91960 1.42925 i
2.93719 1.43211 i
2.95477 1.43497 i
2.97236 1.43781 i
2.98995 1.44064 i
3.00754 1.44346 i
3.02513 1.44626 i
3.04271 1.44906 i
3.06030 1.45185 i
3.07789 1.45462 i
3.09548 1.45739 i
3.11307 1.46015 i
3.13065 1.46289 i
3.14824 1.46562 i
3.16583 1.46835 i
3.18342 1.47106 i
3.20101 1.47377 i
3.21859 1.47646 i
3.23618 1.47915 i
3.25377 1.48182 i
3.27136 1.48449 i
3.28894 1.48714 i
3.30653 1.48979 i
3.32412 1.49242 i
3.34171 1.49505 i
3.35930 1.49767 i
3.37688 1.50028 i
3.39447 1.50288 i
3.41206 1.50547 i
3.42965 1.50805 i
3.44724 1.51063 i
3.46482 1.51319 i
3.48241 1.51575 i
3.50000 1.51829 i

2
tikzgrafiken/function2_1.w3_ausschnitt.gnuplot Normal file
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set terminal table; set output "function2_1.w3_ausschnitt.table"; set format "%.5f"
set samples 200; plot [x=1:2] x**(1./3.)

204
tikzgrafiken/function2_1.w3_ausschnitt.table Normal file
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#Curve 0 of 1, 200 points
#x y type
1.00000 1.00000 i
1.00503 1.00167 i
1.01005 1.00334 i
1.01508 1.00500 i
1.02010 1.00666 i
1.02513 1.00831 i
1.03015 1.00995 i
1.03518 1.01159 i
1.04020 1.01322 i
1.04523 1.01485 i
1.05025 1.01648 i
1.05528 1.01810 i
1.06030 1.01971 i
1.06533 1.02132 i
1.07035 1.02292 i
1.07538 1.02452 i
1.08040 1.02611 i
1.08543 1.02770 i
1.09045 1.02928 i
1.09548 1.03086 i
1.10050 1.03244 i
1.10553 1.03401 i
1.11055 1.03557 i
1.11558 1.03713 i
1.12060 1.03869 i
1.12563 1.04024 i
1.13065 1.04178 i
1.13568 1.04332 i
1.14070 1.04486 i
1.14573 1.04639 i
1.15075 1.04792 i
1.15578 1.04944 i
1.16080 1.05096 i
1.16583 1.05247 i
1.17085 1.05398 i
1.17588 1.05549 i
1.18090 1.05699 i
1.18593 1.05849 i
1.19095 1.05998 i
1.19598 1.06147 i
1.20101 1.06296 i
1.20603 1.06444 i
1.21106 1.06591 i
1.21608 1.06738 i
1.22111 1.06885 i
1.22613 1.07032 i
1.23116 1.07178 i
1.23618 1.07323 i
1.24121 1.07469 i
1.24623 1.07613 i
1.25126 1.07758 i
1.25628 1.07902 i
1.26131 1.08046 i
1.26633 1.08189 i
1.27136 1.08332 i
1.27638 1.08474 i
1.28141 1.08616 i
1.28643 1.08758 i
1.29146 1.08900 i
1.29648 1.09041 i
1.30151 1.09181 i
1.30653 1.09322 i
1.31156 1.09462 i
1.31658 1.09601 i
1.32161 1.09741 i
1.32663 1.09880 i
1.33166 1.10018 i
1.33668 1.10156 i
1.34171 1.10294 i
1.34673 1.10432 i
1.35176 1.10569 i
1.35678 1.10706 i
1.36181 1.10842 i
1.36683 1.10978 i
1.37186 1.11114 i
1.37688 1.11250 i
1.38191 1.11385 i
1.38693 1.11520 i
1.39196 1.11654 i
1.39698 1.11789 i
1.40201 1.11922 i
1.40704 1.12056 i
1.41206 1.12189 i
1.41709 1.12322 i
1.42211 1.12455 i
1.42714 1.12587 i
1.43216 1.12719 i
1.43719 1.12851 i
1.44221 1.12982 i
1.44724 1.13113 i
1.45226 1.13244 i
1.45729 1.13374 i
1.46231 1.13505 i
1.46734 1.13634 i
1.47236 1.13764 i
1.47739 1.13893 i
1.48241 1.14022 i
1.48744 1.14151 i
1.49246 1.14279 i
1.49749 1.14407 i
1.50251 1.14535 i
1.50754 1.14663 i
1.51256 1.14790 i
1.51759 1.14917 i
1.52261 1.15044 i
1.52764 1.15170 i
1.53266 1.15296 i
1.53769 1.15422 i
1.54271 1.15548 i
1.54774 1.15673 i
1.55276 1.15798 i
1.55779 1.15923 i
1.56281 1.16047 i
1.56784 1.16172 i
1.57286 1.16296 i
1.57789 1.16419 i
1.58291 1.16543 i
1.58794 1.16666 i
1.59296 1.16789 i
1.59799 1.16912 i
1.60302 1.17034 i
1.60804 1.17156 i
1.61307 1.17278 i
1.61809 1.17400 i
1.62312 1.17521 i
1.62814 1.17642 i
1.63317 1.17763 i
1.63819 1.17884 i
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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usepackage{verbatim}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{document}
\begin{tikzpicture}[scale=1.2]
%\begin{tikzpicture}[scale=3]
%\draw[step=0.1, color=lightgray] (-1,-1) grid(4.5,4.5);
%\draw[help lines] (-3,-1) grid (4,1);
\draw [thick](-2.5,0) -- (3.5,0);
\draw [thick, style=dotted](3.5,0) -- (4,0);
\draw [thick, style=dotted](-3,0) -- (-2.5,0);
\foreach \x/\xtext in {-2/x_2,0,1, 3/x_1}
\draw[xshift=\x cm, thick] (0pt,1pt) -- (0pt,-1pt) node[below,fill=white]
{$\xtext$};
\draw[snake=brace, mirror snake, color=blue] (-2,-0.4) -- (0,-0.4) node[midway,sloped,below] {$|x_1|$};
\draw[snake=brace, mirror snake, color=red] (0,-0.4) -- (3,-0.4) node[midway,sloped,below] {$|x_2|$};
% \foreach \x in {1,2,3}
% \draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usepackage{verbatim}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{document}
\begin{tikzpicture}[scale=1.2]
%\begin{tikzpicture}[scale=3]
%\draw[step=0.1, color=lightgray] (-1,-1) grid(4.5,4.5);
%\draw[help lines] (-3,-1) grid (4,1);
\draw [thick](-2.5,0) -- (3.5,0);
\draw [thick, style=dotted](3.5,0) -- (4,0);
\draw [thick, style=dotted](-3,0) -- (-2.5,0);
\foreach \x/\xtext in {-2/x_2,0,1, 3/x_1}
\draw[xshift=\x cm, thick] (0pt,1pt) -- (0pt,-1pt) node[below,fill=white]
{$\xtext$};
\draw[snake=brace, mirror snake, color=blue] (-2,-0.4) -- (0,-0.4) node[midway,sloped,below] {$|x_1|$};
\draw[snake=brace, mirror snake, color=red] (0,-0.4) -- (3,-0.4) node[midway,sloped,below] {$|x_2|$};
% \foreach \x in {1,2,3}
% \draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usepackage{verbatim}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{document}
\begin{tikzpicture}[scale=1.5]
%\begin{tikzpicture}[scale=3]
%\draw[step=0.1, color=lightgray] (-1,-1) grid(4.5,4.5);
\draw[help lines] (-5,-5) grid (5,5);
%\draw[-triangle 45] (0,0) -- (4,0) node[right] {$x$};
\draw [-triangle 45] (0,0) -- (xyz cs:x=4) node[right] {$x$};
\foreach \x/\xtext in {0,1,2,3/a_1}
\draw[xshift=\x cm, thick] (0pt,1pt) -- (0pt,-1pt) node[below]
{$\xtext$};
\draw [-triangle 45] (0,0) -- (xyz cs:y=4); % node[anchor=north] {$y$};
\foreach \y/\ytext in {1,2,3/a_2}
\draw[yshift=\y cm, thick] (1pt,0pt) -- (-1pt, 0pt) node[left]
{$\ytext$};
\draw [-triangle 45] (0,0) -- (xyz cs:z=4);%node[anchor = north] {$z$}
\foreach \z/\zt in {1,2/a_3,3}
% \draw [shift=\z cm, thick] {0.1, 0, \z} -- {-0.1, 0, \z};
% \draw[shift=\z cm, thick] (0pt,1pt) -- (0pt,-1pt) node[left] {$z$};
\draw [thick] (0.025pt, 0, \z) -- (-0.025pt, 0, \z) node[left] {$\zt$};
%http://www.statistiker-wg.de/pgf/tutorials.htm
\path %(.42,-.767) node[below] {$x$}
(0,4.05) node[above] {$y$}
% (-1.5,-1.653) node[left] {$z$ (3. Koordinate)};
(0, 0,4.2) node {$z$ (3. Koordinate)};
\draw [color=red, dashed, thin] (0,0,2) -- (3,0,2);
\draw [color=red, dashed, thin] (0,0,2) -- (0,3,2);
\draw [color=red, dashed, thin] (0,3,2) -- (3,3,2);
\draw [color=blue, dashed, thin] (3,0,0) -- (3,0,2);
\draw [color=blue, dashed, thin] (3,0,2) -- (3,3,2);
\draw [color=blue, dashed, thin] (3,0,0) -- (3,3,0);
\draw [color=blue, dashed, thin] (3,3,0) -- (3,3,2);
\draw [color=green, dashed, thin] (0,3,0) -- (0,3,2);
\draw [color=green, dashed, thin] (0,3,2) -- (3,3,2);
\draw [color=green, dashed, thin] (0,3,0) -- (3,3,0);
\draw (3.1,3,2.1) node[right, text width=15mm]{Punkt $\left ( a_1, a_2, a_3 \right )$};
\fill[ball color=gray] (3,3,2) circle (0.05); % 3D lighting effect
%\fill[white] (0,0) circle (\R); % just a white circle
%\draw (0,0) circle (0.05);
% \draw[-triangle 45] (0,0) -- (0,4) node[right] {$z$};
% \foreach \z in {1,2,3}
% \draw (\z cm,1pt) -- (\z cm,-1pt) node[anchor=north] {$\z$};
\end{tikzpicture}
\end{document}

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\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{tikzpicture}[scale=1.5]
%\begin{tikzpicture}[scale=3]
%\draw[step=0.1, color=lightgray] (-1,-1) grid(4.5,4.5);
\draw[help lines] (-5,-5) grid (5,5);
%\draw[-triangle 45] (0,0) -- (4,0) node[right] {$x$};
\draw [-triangle 45] (0,0) -- (xyz cs:x=4) node[right] {$x$};
\foreach \x/\xtext in {0,1,2,3/a_1}
\draw[xshift=\x cm, thick] (0pt,1pt) -- (0pt,-1pt) node[below]
{$\xtext$};
\draw [-triangle 45] (0,0) -- (xyz cs:y=4); % node[anchor=north] {$y$};
\foreach \y/\ytext in {1,2,3/a_2}
\draw[yshift=\y cm, thick] (1pt,0pt) -- (-1pt, 0pt) node[left]
{$\ytext$};
\draw [-triangle 45] (0,0) -- (xyz cs:z=4);%node[anchor = north] {$z$}
\foreach \z/\zt in {1,2/a_3,3}
% \draw [shift=\z cm, thick] {0.1, 0, \z} -- {-0.1, 0, \z};
% \draw[shift=\z cm, thick] (0pt,1pt) -- (0pt,-1pt) node[left] {$z$};
\draw [thick] (0.025pt, 0, \z) -- (-0.025pt, 0, \z) node[left] {$\zt$};
%http://www.statistiker-wg.de/pgf/tutorials.htm
\path %(.42,-.767) node[below] {$x$}
(0,4.05) node[above] {$y$}
% (-1.5,-1.653) node[left] {$z$ (3. Koordinate)};
(0, 0,4.2) node {$z$ (3. Koordinate)};
\draw [color=red, dashed, ultra thick] (0,0,2) -- (3,0,2);
\draw [color=red, dashed, ultra thick] (0,0,2) -- (0,3,2);
\draw [color=red, dashed, ultra thick] (0,3,2) -- (3,3,2);
\draw [color=blue, dashed, ultra thick] (3,0,0) -- (3,0,2);
\draw [color=blue, dashed, ultra thick] (3,0,2) -- (3,3,2);
\draw [color=blue, dashed, ultra thick] (3,0,0) -- (3,3,0);
\draw [color=blue, dashed, ultra thick] (3,3,0) -- (3,3,2);
\draw [color=green, dashed, ultra thick] (0,3,0) -- (0,3,2);
\draw [color=green, dashed, ultra thick] (0,3,2) -- (3,3,2);
\draw [color=green, dashed, ultra thick] (0,3,0) -- (3,3,0);
\draw (3.1,3,2.1) node[right, text width=15mm]{Punkt $\left ( a_1, a_2, a_3 \right )$};
\fill[ball color=gray] (3,3,2) circle (0.05); % 3D lighting effect
%\fill[white] (0,0) circle (\R); % just a white circle
%\draw (0,0) circle (0.05);
% \draw[-triangle 45] (0,0) -- (0,4) node[right] {$z$};
% \foreach \z in {1,2,3}
% \draw (\z cm,1pt) -- (\z cm,-1pt) node[anchor=north] {$\z$};
\end{tikzpicture}

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usepackage{verbatim}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{document}
\begin{tikzpicture}[scale=1.5]
%\begin{tikzpicture}[scale=3]
%\draw[step=0.1, color=lightgray] (-1,-1) grid(4.5,4.5);
\draw[help lines] (-5,-5) grid (5,5);
%\draw[-triangle 45] (0,0) -- (4,0) node[right] {$x$};
\draw [-triangle 45] (0,0) -- (xyz cs:x=4) node[right] {$x$};
\foreach \x/\xtext in {0,1,2,3/a_1}
\draw[xshift=\x cm, thick] (0pt,1pt) -- (0pt,-1pt) node[below]
{$\xtext$};
\draw [-triangle 45] (0,0) -- (xyz cs:y=4); % node[anchor=north] {$y$};
\foreach \y/\ytext in {1,2,3/a_2}
\draw[yshift=\y cm, thick] (1pt,0pt) -- (-1pt, 0pt) node[left]
{$\ytext$};
\draw [-triangle 45] (0,0) -- (xyz cs:z=4);%node[anchor = north] {$z$}
\foreach \z/\zt in {1,2/a_3,3}
% \draw [shift=\z cm, thick] {0.1, 0, \z} -- {-0.1, 0, \z};
% \draw[shift=\z cm, thick] (0pt,1pt) -- (0pt,-1pt) node[left] {$z$};
\draw [thick] (0.025pt, 0, \z) -- (-0.025pt, 0, \z) node[left] {$\zt$};
\draw [color=orange, thick, -triangle 45](0,0,0) -- (3,3,2) node[sloped,above] {Vektor ("Pfeil") $\vec a$} ;
%http://www.statistiker-wg.de/pgf/tutorials.htm
\path %(.42,-.767) node[below] {$x$}
(0,4.05) node[above] {$y$}
% (-1.5,-1.653) node[left] {$z$ (3. Koordinate)};
(0, 0,4.2) node {$z$ (3. Koordinate)};
\draw [color=red, dashed, thin] (0,0,2) -- (3,0,2);
\draw [color=red, dashed, thin] (0,0,2) -- (0,3,2);
\draw [color=red, dashed, thin] (0,3,2) -- (3,3,2);
\draw [color=blue, dashed, thin] (3,0,0) -- (3,0,2);
\draw [color=blue, dashed, thin] (3,0,2) -- (3,3,2);
\draw [color=blue, dashed, thin] (3,0,0) -- (3,3,0);
\draw [color=blue, dashed, thin] (3,3,0) -- (3,3,2);
\draw [color=green, dashed, thin] (0,3,0) -- (0,3,2);
\draw [color=green, dashed, thin] (0,3,2) -- (3,3,2);
\draw [color=green, dashed, thin] (0,3,0) -- (3,3,0);
%\draw (3.1,3,2.1) node[right, text width=15mm]{Punkt $\left ( a_1, a_2, a_3 \right )$};
%\fill[ball color=gray] (3,3,2) circle (0.05); % 3D lighting effect
%\fill[white] (0,0) circle (\R); % just a white circle
%\draw (0,0) circle (0.05);
% \draw[-triangle 45] (0,0) -- (0,4) node[right] {$z$};
% \foreach \z in {1,2,3}
% \draw (\z cm,1pt) -- (\z cm,-1pt) node[anchor=north] {$\z$};
\end{tikzpicture}
\end{document}

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\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{tikzpicture}[scale=1.5]
%\begin{tikzpicture}[scale=3]
%\draw[step=0.1, color=lightgray] (-1,-1) grid(4.5,4.5);
\draw[help lines] (-5,-5) grid (5,5);
%\draw[-triangle 45] (0,0) -- (4,0) node[right] {$x$};
\draw [-triangle 45] (0,0) -- (xyz cs:x=4) node[right] {$x$};
\foreach \x/\xtext in {0,1,2,3/a_1}
\draw[xshift=\x cm, thick] (0pt,1pt) -- (0pt,-1pt) node[below]
{$\xtext$};
\draw [-triangle 45] (0,0) -- (xyz cs:y=4); % node[anchor=north] {$y$};
\foreach \y/\ytext in {1,2,3/a_2}
\draw[yshift=\y cm, thick] (1pt,0pt) -- (-1pt, 0pt) node[left]
{$\ytext$};
\draw [-triangle 45] (0,0) -- (xyz cs:z=4);%node[anchor = north] {$z$}
\foreach \z/\zt in {1,2/a_3,3}
% \draw [shift=\z cm, thick] {0.1, 0, \z} -- {-0.1, 0, \z};
% \draw[shift=\z cm, thick] (0pt,1pt) -- (0pt,-1pt) node[left] {$z$};
\draw [thick] (0.025pt, 0, \z) -- (-0.025pt, 0, \z) node[left] {$\zt$};
\draw [color=orange, thick, -triangle 45](0,0,0) -- (3,3,2) node[sloped,above] {Vektor ("Pfeil") $\vec a$} ;
%http://www.statistiker-wg.de/pgf/tutorials.htm
\path %(.42,-.767) node[below] {$x$}
(0,4.05) node[above] {$y$}
% (-1.5,-1.653) node[left] {$z$ (3. Koordinate)};
(0, 0,4.2) node {$z$ (3. Koordinate)};
\draw [color=red, dashed, thin] (0,0,2) -- (3,0,2);
\draw [color=red, dashed, thin] (0,0,2) -- (0,3,2);
\draw [color=red, dashed, thin] (0,3,2) -- (3,3,2);
\draw [color=blue, dashed, thin] (3,0,0) -- (3,0,2);
\draw [color=blue, dashed, thin] (3,0,2) -- (3,3,2);
\draw [color=blue, dashed, thin] (3,0,0) -- (3,3,0);
\draw [color=blue, dashed, thin] (3,3,0) -- (3,3,2);
\draw [color=green, dashed, thin] (0,3,0) -- (0,3,2);
\draw [color=green, dashed, thin] (0,3,2) -- (3,3,2);
\draw [color=green, dashed, thin] (0,3,0) -- (3,3,0);
%\draw (3.1,3,2.1) node[right, text width=15mm]{Punkt $\left ( a_1, a_2, a_3 \right )$};
%\fill[ball color=gray] (3,3,2) circle (0.05); % 3D lighting effect
%\fill[white] (0,0) circle (\R); % just a white circle
%\draw (0,0) circle (0.05);
% \draw[-triangle 45] (0,0) -- (0,4) node[right] {$z$};
% \foreach \z in {1,2,3}
% \draw (\z cm,1pt) -- (\z cm,-1pt) node[anchor=north] {$\z$};
\end{tikzpicture}

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usepackage{verbatim}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{document}
\begin{tikzpicture}[scale=1.5]
%\begin{tikzpicture}[scale=3]
%\draw[step=0.1, color=lightgray] (-1,-1) grid(4.5,4.5);
\draw[help lines] (0,0) grid (7,3);
\draw[-triangle 45] (0,0) -- (4,0) node[midway,sloped,above] {$\vec a$};
\draw[-triangle 45] (0,0) -- (2,2) node[midway,sloped,above] {$\vec b$};
\draw[style=dashed] (2,2) -- (6,2);
\draw[style=dashed] (4,0) -- (6,2);
\draw (0,0) +(0:1cm) arc (0:45:1cm);
\path (0,0) ++(22.5:.75cm) node{$\alpha$};
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usetikzlibrary{shapes,decorations,shadows}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.shapes}
\usetikzlibrary{fadings}
\usetikzlibrary{patterns}
\usetikzlibrary{calc}
\usepackage{verbatim}
\usepackage{graphicx}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{document}
%\includegraphics[scale=0.2]{reHa.png}
%\vspace{-10.5cm}
%\definecolor{black}{RGB}{185,6,10}
\begin{tikzpicture}[y=0.25pt, x=0.25pt,yscale=-1]%[y=0.10pt, x=0.1pt,yscale=-1]
%\draw[step=50, color=lightgray] (-100,-100) grid(450,400);
\begin{scope}[draw]
\path[draw] (163.8820,231.8290) .. controls (164.1900,232.2690) and
(163.5180,232.6730) .. (164.2590,232.7770) .. controls (167.9240,223.7170) and
(169.3140,213.7190) .. (170.7730,203.8170) .. controls (171.4170,199.4490) and
(171.9040,194.3700) .. (171.3940,189.8290) .. controls (170.9860,186.1960) and
(169.3040,182.7270) .. (169.7720,179.0090) .. controls (170.1610,175.9140) and
(171.6440,173.6740) .. (171.6470,170.1420) .. controls (171.6480,168.3860) and
(171.4770,166.6150) .. (171.1830,164.8800) .. controls (170.7040,162.0600) and
(170.9640,159.2760) .. (171.1420,156.4460) .. controls (171.3210,153.5970) and
(172.2490,150.7960) .. (172.4070,147.9260) .. controls (172.5640,145.0590) and
(172.1900,142.4980) .. (173.1240,139.7690) .. controls (174.0950,136.9320) and
(174.0360,133.4170) .. (174.1670,130.4210) .. controls (174.2600,128.3030) and
(174.2660,126.3650) .. (174.8170,124.3000) .. controls (176.0280,119.7650) and
(176.7350,114.8870) .. (176.2660,110.1950) .. controls (176.1150,108.6810) and
(176.3730,107.4700) .. (176.5480,105.9890) .. controls (176.7340,104.4200) and
(176.5830,102.8530) .. (176.6980,101.2800) .. controls (176.9200,98.2660) and
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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usetikzlibrary{positioning}
\usepackage{verbatim}
\begin{document}
\begin{tikzpicture}[scale=1.5, on grid]
%\foreach \x in {0,...,4}
% \foreach \y in {0,...,3}
% \foreach \z in {0,...,5}
% \fill[ball color=gray] (\x,\y,-\z) circle (0.05);
%\begin{scope}[every node/.append style={yslant=0},yslant=0]
% \draw [help lines](0,0) grid (5,5);
%\end{scope}
%\begin{scope}[every node/.append style={yslant=-1},yslant=-1]
% \draw [help lines](0,0) grid (5,5);
%\end{scope}
%\begin{tikzpicture}[scale=3]
%\draw[step=0.1, color=lightgray] (-1,-1) grid(4.5,4.5);
%\draw[help lines] (0,0) grid (3,3);
%\draw[help lines] (0,0,-1) grid (3,3,-1);
%\draw[help lines] (0,0,-2) grid (3,3,-2);
%initial
\draw[-triangle 45, color=blue] (0,0,0) -- (4,0,0) node[midway,sloped,above] {$\vec a$}; %x
\draw[-triangle 45,style=dashed, color=red] (0,0,0) -- (1,1,-1) node[midway,sloped,above] {$\vec b$}; %z
\draw[-triangle 45, color=orange] (0,0,0) -- (1,3,0) node[midway,sloped,above] {$\vec c$}; %y
%vorn
\draw[-, color=blue] (1,3,0) -- (5,3,0);
\draw[-, color=red] (4,0,0) -- (5,1,-1) ;
\draw[-, color=orange] (4,0,0) -- (5,3,0);
%untere Vebindung im z (hinten)
\draw[-, color=blue, style=dashed] (1,1,-1) -- (5,1,-1);
%vec b oben
\draw[-, color=red] (1,3,0) -- (2,4,-1) ;
\draw[-, color=red] (5,3,0) -- (6,4,-1) ;
%vec a oben / hinten
\draw[-, color=blue] (2,4,-1) -- (6,4,-1) ;
%vec c beide hinteren
\draw[-, color=orange, style=dashed] (1,1,-1) -- (2,4,-1) ;
\draw[-, color=orange] (5,1,-1) -- (6,4,-1);
%\draw[-, color=blue] (1,3) -- (4,3) node[midway,sloped,above] {};
%\draw[-, color=red] (3,0,0) -- (4,1,-2) node[midway,sloped,above] {};
%\draw[-, style=dashed, color=blue] (1,1,-2) -- (4,1,-2) node[midway,sloped,above] {};
%\draw[-, color=red] (1,3,-2) -- (2,4,-2) node[midway,sloped,above] {};
% \draw[style=dashed] (2,2) -- (6,2);
% \draw[style=dashed] (4,0) -- (6,2);
% \draw (0,0) +(0:1cm) arc (0:45:1cm);
% \path (0,0) ++(22.5:.75cm) node{$\alpha$};
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz,ifthen}
\usetikzlibrary{calc}
\pagestyle{empty}
\begin{document}
%% some definitions
\def\tikzplane#1#2#3#4#5{%
\pgfmathsetmacro\Xx{#2}% x coordiante of X axis unit vector
\pgfmathsetmacro\Xy{#3}% y coordiante of X axis unit vector
\pgfmathsetmacro\Yx{#4}% x coordiante of Y axis unit vector
\pgfmathsetmacro\Yy{#5}% y coordiante of Y axis unit vector
\tikzstyle{#1}=[cm={\Xx,\Xy,\Yx,\Yy,(0,0)}]% transformation matrix
}
\def\pgfmathsincos#1#2#3{%
\pgfmathsetmacro#1{sin(#3)}%
\pgfmathsetmacro#2{cos(#3)}%
}
% sphere radius
\def\R{4}
% elevation angle
\def\angEl{32}
% azimuth angle
\def\angAz{110}
% longitude of point P
\def\angPhi{-50}
% latitude of point P
\def\angBeta{-30}
\begin{tikzpicture}[>=latex] % option '>=latex' for nice arrows
\draw (0,0) circle (\R);
\foreach \t in {-80,-70,...,80} {
\pgfmathsincos\sint\cost{\t}
\pgfmathsincos\sinEl\cosEl{\angEl}
\pgfmathsetmacro\y{\R*\cosEl*\sint*1cm}
\tikzstyle{latitude circle}=[yshift=\y,yscale=\sinEl,scale=\cost]
\pgfmathsetmacro\sinLon{\sint/\cost*\sinEl/\cosEl}
\pgfmathtruncatemacro\testval{\sinLon}
\ifnum\testval=0
\pgfmathsetmacro\ang{asin(\sinLon)} % angle of "visibility"
\draw[latitude circle] (\ang:\R) arc (\ang:-\ang-180:\R);
\draw[latitude circle,dashed] (180-\ang:\R) arc (180-\ang:\ang:
\R);
\fi
\ifnum\testval>0
\draw[latitude circle] (0,0) circle(\R);
\fi
\ifnum\testval<0
\draw[latitude circle,dashed] (0,0) circle(\R);
\fi
}
\foreach \t in {-5,-35,...,-175} {
\pgfmathsincos\sint\cost{\t}
\pgfmathsincos\sinEl\cosEl{\angEl}
\tikzplane{xyplane}{\cost}{\sint*\sinEl}{0}{\cosEl}
\pgfmathsetmacro\ang{atan(\sint*\cosEl/\sinEl)} % angle of
"visibility"
\draw[xyplane,->] (180:1.7*\R) -- (0:1.7*\R);
\draw[xyplane] (\ang:\R) arc (\ang:\ang+180:\R);
\draw[xyplane,dashed] (\ang-180:\R) arc (\ang-180:\ang:\R);
}
\draw[->] (-90:1.3*\R) -- (90:1.3*\R);
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz}
\usepackage{verbatim}
\begin{comment}
:Title: Intersecting lines
:Tags: Axes, Basics, Coordinate systems
An example of using the intersection coordinate systems. Both the ``intersection`` and
``perpendicular`` coordinate system are used. The latter is a special case of the former,
but has the shorter and more convenient ``-|`` and ``|-`` syntax.
\end{comment}
\begin{document}
\begin{tikzpicture}[scale=1.5, >=stealth]
% Zeichne Grid
%\draw[step=0.1, color=lightgray] (-1,-1) grid(4,3.5);
% Draw axes
\draw [<->] (0,3) node (yaxis) [above] {$y$}|- (3,0) node (xaxis) [right] {$x$};
\draw [color=red](0,0) -- +(2.5,2.5);
\draw plot[only marks, mark=x, mark options={blue}] coordinates{(2.5,2.5)}
node[above, color=blue] {Punkt $(a_1,a_2)$};
\foreach \y in {0,1,2}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};
\foreach \x in {0,1,2}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
%\draw [color=green] (2.4,2.4) -- +(2.6,2.6) node[right] {Punkt $(a_1,a_2)$};
% \draw [color=blue](0,3) coordinate (a_1) -- (2,2) coordinate (a_2);
% Draw two intersecting lines
\draw [color=green, dashed] (-0.1,2.5) -- (2.5,2.5);
\draw [color=green, dashed] (2.5,-0.1) -- (2.5,2.5);
\node[green] at (-0.25,2.5) {$a_2$};
\node[green] at (2.5,-0.25) {$a_1$};
\node[right] at (0.05,2.2) {\tiny{2. Koordinate}};
\node[right] at (1,-0.4) {\tiny{1. Koordinate}};
% Calculate the intersection of the lines a_1 -- a_2 and b_1 -- b_2
% and store the coordinate in c.
% \coordinate (c) at (intersection of a_1--a_2 and b_1--b_2);
% Draw lines indicating intersection with y and x axis. Here we use
% the perpendicular coordinate system
% \draw[dashed] (yaxis |- c) node[left] {$y'$}
% -| (xaxis -| c) node[below] {$x'$};
% Draw a dot to indicate intersection point
% \fill[red] (c) circle (2pt);
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz}
\usepackage{verbatim}
\begin{comment}
\end{comment}
\begin{document}
\begin{tikzpicture}[scale=1.5, >=stealth]
% Zeichne Grid
\draw[step=0.1, color=lightgray] (-1,-1) grid(4,3.5);
% Draw axes
\draw [<->] (0,3) node (yaxis) [above] {$y$}|- (3,0) node (xaxis) [right] {$x$};
\draw [color=red, thick, ->](0,0) -- +(2.5,2.5);
\draw [thick, ->](2.8,2.2) node[anchor=west] {''Pfeil''} -- (2.5,2.5) ;
\foreach \y in {0,2,4}
\draw (1pt,\y*0.5 cm) -- (-1pt,\y*0.5 cm) node[anchor=east] {$\y$};
\foreach \x in {0,2,4}
\draw (\x*0.5 cm,1pt) -- (\x*0.5 cm,-1pt) node[anchor=north] {$\x$};
\draw [color=blue, dashed] (-0.1,2.5) -- (2.5,2.5);
\draw [color=blue, dashed] (2.5,-0.1) -- (2.5,2.5);
\node[blue] at (-0.25,2.5) {$a_2$};
\node[blue] at (2.5,-0.25) {$a_1$};
\node[right] at (1.4,2.1) {Vektor $\vec a$};
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usepackage{verbatim}
\begin{comment}
\end{comment}
\begin{document}
\begin{tikzpicture}[scale=1.5]
% Zeichne Grid
%\draw[step=0.1, color=lightgray] (-1.5,-1.5) grid(8,6);
% Draw axes
\draw [triangle 45-triangle 45] (0,5.5) node (yaxis) [above] {$y$}|- (7.5,0) node (xaxis) [right] {$x$};
\draw [color=red, thick, -triangle 45](0,0) -- (5,1) node[midway,sloped,above] {$\vec b$};
\draw [color=red, dashed, thin] (5,-0.1) -- (5,1);% node[pos=-0.05]{$b_1$} ;
\draw [color=red, dashed, thin] (-0.1,1) -- (5,1);% node[pos=-0.05]{$b_2$};
\node[red] at (5,-0.25) {$b_1$};
\node[red, left] at (-0.05,1) {$b_2$};
\draw [color=red, thin, -triangle 45, dashed](2,4) -- (7,5);
\draw [color=orange, thick, -triangle 45](0,0) -- (2,4) node[midway,sloped,above] {$\vec a$};
\draw [color=orange, dashed, thin] (2,-0.1) -- (2,4);
\draw [color=orange, dashed, thin] (-0.1,4) -- (2,4);
\node[orange] at (2,-0.25) {$a_1$};
\node[orange, left] at (-0.05,4) {$a_2$};
\draw [color=orange, thin, -triangle 45, dashed](5,1) -- (7,5);
\draw [color=blue, thick, -triangle 45](0,0) -- (7,5) node[midway,sloped,above] {$\vec a + \vec b$};
\draw [color=blue, dashed, thin] (7,-0.1) -- (7,5); %node[pos=-0.025]{$a_1+b_1$} ;
\draw [color=blue, dashed, thin] (-0.1,5) -- (7,5); %node[anchor=west, pos=-0.1]{\fbox{$a_2+b_2$}};
\node[blue] at (7,-0.25) {$a_1+b_1$};
\node[blue, left] at (-0.05,5) {$a_2+b_2$};
\foreach \y in {0,3}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};
\foreach \x in {0,3,6}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
\node[right] at (3.0,5.5) (x) {Parallelogramm};
\node[right,color=white] at (3.0,3.3) (y) {xx};
\draw[-open triangle 45,gray] (x) .. controls +(down:1cm) and +(left:1cm) .. (y);
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usepackage{verbatim}
\begin{comment}
\end{comment}
\begin{document}
\begin{tikzpicture}[scale=1.5]
% \draw[step=0.1, color=lightgray] (-5,-1.5) grid(6,5);
% \draw [triangle 45-triangle 45] (-4.5,5.5) node (yaxis) [above] {$y$}|- (3.5,0) node (xaxis) [right] {$x$};
\draw[-triangle 45] (-4.5,0) -- (5.5,0) node[right] {$x$};
\foreach \x in {-4,-2,-1,1,3,4}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
\draw[-triangle 45] (0,-1) -- (0,4) node[above] {$y$};
\foreach \y in {2}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};
%Vector a
\draw [color=red, thick, -triangle 45](0,0) -- (2,3) node[midway,sloped,above] {$\vec a$};
\draw [color=red, dashed, thin] (2,-0.1) -- (2,3);
\draw [color=red, dashed, thin] (-0.1,3) -- (2,3);
\node[red] at (2,-0.25) {$a_1$};
\node[red] at (-0.25, 3) {$a_2$};
%Vector b
\draw [color=green!65!black, thick, -triangle 45](0,0) -- (5,1) node[midway,sloped,above] {$\vec b$};
\draw [color=green!65!black, dashed, thin] (5,-0.1) -- (5,1);
\draw [color=green!65!black, dashed, thin] (-0.1,1) -- (5,1);
\draw [color=green!65!black, thick, -triangle 45, dashed](2,3) -- (-3,2) ;
\node[green!65!black] at (5,-0.25) {$b_1$};
\node[green!65!black, left] at (-0.05,1) {$b_2$};
%Vector a b
\draw [color=blue, thick, -triangle 45](0,0) -- (-3,2) node[midway,sloped,above] {$\vec a - \vec b$};
\draw [color=blue, dashed, thin] (-3,-0.1) -- (-3,2);
\draw [color=blue, dashed, thin] (-0.1,2) -- (-3,2);
\draw [color=blue, thick, -triangle 45, dashed](5,1) -- (2,3) ;
\node[blue, right] at (0,2) {$a_2-b_2$};
\node[blue] at (-3,-0.25) {$a_1-b_1$};
% \draw [color=red, dashed, thin] (5,-0.1) -- (5,1);% node[pos=-0.05]{$b_1$} ;
% \draw [color=red, dashed, thin] (-0.1,1) -- (5,1);% node[pos=-0.05]{$b_2$};
% \draw [color=red, thin, -triangle 45, dashed](2,4) -- (7,5);
% \draw [color=orange, thick, -triangle 45](0,0) -- (2,4) node[midway,sloped,above] {$\vec a$};
% \draw [color=orange, dashed, thin] (2,-0.1) -- (2,4);
% \draw [color=orange, dashed, thin] (-0.1,4) -- (2,4);
%
% \node[orange, left] at (-0.05,4) {$a_2$};
% \draw [color=orange, thin, -triangle 45, dashed](5,1) -- (7,5);
% \draw [color=blue, thick, -triangle 45](0,0) -- (7,5) node[midway,sloped,above] {$\vec a + \vec b$};
% \draw [color=blue, dashed, thin] (7,-0.1) -- (7,5); %node[pos=-0.025]{$a_1+b_1$} ;
% \draw [color=blue, dashed, thin] (-0.1,5) -- (7,5); %node[anchor=west, pos=-0.1]{\fbox{$a_2+b_2$}};
% \node[blue] at (7,-0.25) {$a_1+b_1$};
% \node[blue, left] at (-0.05,5) {$a_2+b_2$};
% \foreach \y in {0,3}
% \draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};
% \foreach \x in {0,3,6}
% \draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
% \node[right] at (3.0,5.5) (x) {Parallelogramm};
% \node[right,color=white] at (3.0,3.3) (y) {xx};
% \draw[-open triangle 45,gray] (x) .. controls +(down:1cm) and +(left:1cm) .. (y);
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usepackage{verbatim}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{document}
\begin{tikzpicture}[scale=1.2]
% \draw[step=0.1, color=lightgray] (-5,-2.5) grid(7,5);
\draw[-triangle 45] (-4.5,0) -- (6.5,0) node[right] {$x$};
\foreach \x in {-4,-2,2,4,6}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
\draw[-triangle 45] (0,-2.5) -- (0,4) node[above] {$y$};
\foreach \y in {-2,2}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};
\draw [color=red, thick, -triangle 45](0,0) -- (2,1) node[midway,sloped,above] {$\vec a$};
\draw [color=red, dashed, thin] (2,-0.1) -- (2,1);
\draw [color=red, dashed, thin] (-0.1,1) -- (2,1);
\node[red] at (2,-0.5) {$a_1$};
\node[red, left] at (-0.1, 1) {$a_2$};
\draw [color=green!65!black, thick, -triangle 45](0,0) -- (-4,-2) node[midway,sloped,above] {$-2 \cdot \vec a$};
\draw [color=green!65!black, dashed, thin] (-4,0.1) -- (-4,-2);
\draw [color=green!65!black, dashed, thin] (0.1,-2) -- (-4,-2);
\node[green!65!black, right] at (0.25,-2) {$-2\cdot a_2$};
\draw [color=blue, thin, -triangle 45, dashed](0,0) -- (6,3) node[midway,sloped,above] {$3 \cdot \vec a$};
\draw [color=blue, dashed, thin] (6,-0.1) -- (6,3);
\draw [color=blue, dashed, thin] (-0.1,3) -- (6,3);
\node[blue] at (6,-0.5) {$3 \cdot \vec a_1$};
\node[blue,left] at (-0.1,3) {$3 \cdot \vec a_2$};
\draw (-0.5,2.5) node[left, text width=4cm, color=green!65!black]{$k<0$: Richtung \"andern und Strecken/Stauchen um Faktor $-k$ \underline{hier: $-k=2$}};
\draw (1.5,3) node[right, text width=4cm, color=blue]{$k>0$: Strecken/Stauchen um Faktor k \underline{hier: $k=3$}};
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usepackage{verbatim}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{document}
\begin{tikzpicture}[scale=1.2]
%\begin{tikzpicture}[scale=3]
%\draw[step=0.1, color=lightgray] (-1,-1) grid(4.5,4.5);
% \draw[help lines] (0,0) grid (4,4);
\draw[-triangle 45] (0,0) -- (4,0) node[right] {$x$};
\foreach \x in {1,2,3}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
\draw[-triangle 45] (0,0) -- (0,4) node[above] {$y$};
\foreach \y in {1,2,3}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};
\draw [color=blue, thick, -triangle 45](0,0) -- (3,3) node[midway,sloped,above] {$\vec a$} ;
\draw [color=blue, dashed, thin] (0,3) -- (3,3);
\draw [color=blue, dashed, thin] (3,0) -- (3,3);
\draw[snake=brace, mirror snake, color=red] (0,-0.1) -- (3,-0.1) node[midway,sloped,below] {$a_1$};
\draw[snake=brace, mirror snake, color=green!65!black] (3.1,0) -- (3.1,3) node[midway, right] {$a_2$};
\draw [fill=black](2.8,0.2) circle (0.25mm);
\draw (0.1,3.5) node[right, text width=55mm, color=orange](y){L\"ange $\sqrt{a_1^2+a_2^2}$ nach Pythagoras};
\draw[->,orange] (y) .. controls +(down:1cm) and +(up:1cm) .. (2,2);
% \draw[draw=green!50!black] (3,0) -- (3mm,0mm) arc (3:90:3mm); %-- cycle;
\draw (3,0) +(90:5mm) arc (90:180:5mm);
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usepackage{verbatim}
\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
\begin{document}
\begin{tikzpicture}[scale=1.2]
%\begin{tikzpicture}[scale=3]
%\draw[step=0.1, color=lightgray] (-1,-1) grid(4.5,4.5);
% \draw[help lines] (0,0) grid (4,4);
\draw[-triangle 45] (0,0) -- (4,0) node[right] {$x$};
\foreach \x in {1,2,3}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
\draw[-triangle 45] (0,0) -- (0,4) node[above] {$y$};
\foreach \y in {1,2,3}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};
\draw [color=blue, thick, -triangle 45](0,0) -- (1,3) node[sloped,above] {$\vec b$} ;
\draw [color=red, thick, -triangle 45](0,0) -- (3,1) node[right] {$\vec a$} ;
\draw (0,0) +(19:25mm) arc (19:71:25mm);
\draw (0.5,1) node[right, text width=15mm]{$\alpha \left ( \vec a, \vec b \right )$};
\end{tikzpicture}
\end{document}

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\documentclass{article}
\usepackage{tikz}
\usepackage{verbatim}
\begin{comment}
:Title: Intersecting lines
:Tags: Axes, Basics, Coordinate systems
An example of using the intersection coordinate systems. Both the ``intersection`` and
``perpendicular`` coordinate system are used. The latter is a special case of the former,
but has the shorter and more convenient ``-|`` and ``|-`` syntax.
\end{comment}
\begin{document}
\begin{tikzpicture}[scale=1]
% Zeichne Grid
\draw[step=0.1, color=lightgray] (-3,-3) grid(4,3.5);
% Draw axes
%\draw [<->] (-3,3) node (yaxis) [above] {$y$}|- (3,-3) node (xaxis) [right] {$x$};
\draw[style=-latex] (-4,0) -- (4,0) node[right] {$x$};
\foreach \x in {-3,-2,-1,1,2,3}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};
\draw[style=-latex] (0,-4) -- (0,4) node[above] {$y$};
\foreach \y/\ytext in {-3,-2,-1,1,2,3}
\draw (1pt,\y cm) -- (-3pt,\y cm) node[anchor=east] {$\ytext$};
\definecolor{myblue}{HTML}{92dcec}
\definecolor{myred}{HTML}{FF6B6B}
\definecolor{html001}{HTML}{EBFF6B}
\begin{tikzpicture}
%\draw[fill=myblue, thick] (0,0) -- (0:3cm) arc (0:35:2cm);
% \draw[fill=myred, thick] (1,0) -- (0:2cm) arc (0:60:2cm);
%\draw[fill=html001, thick] (0,1) -- (0:2cm) arc (0:45:2cm);
%%\draw (3mm,0mm) arc (0:30:3mm); \draw (x,y) arc (Winkelbeginn:Winkelende:Radius)
%\draw (0,0) -- (0:2cm) arc (0:350:2cm);
%\shadedraw[left color=gray,right color=green, draw=green!50!black] (0,0) -- (28mm,0mm) arc (0:30:28mm) -- cycle;
%\shadedraw[left color=yellow,right color=red, draw=red!50!yellow] (0,0) -- (38mm,10mm) arc (0:45:38mm) -- cycle;
%\draw[fill=myblue, thick] (0,1cm) -- (0:2cm) arc (0:35:2cm);
%\draw (0,0) -- (90:1cm) arc (90:360:1cm) arc (0:30:1cm) -- cycle;
%\filldraw[fill=green!20!white, draw=green!50!black](0,0) -- (-3mm,0mm) arc (0:30:-3mm) -- cycle;
%\draw (60:5pt) -- +(30:1cm) arc (30:90:1cm) -- cycle;
% \draw [->] (0,0) arc (160:30:10mm);
\begin{scope}[rotate=60, color=blue]\draw (0,0) -- (0:1cm) arc (-60:120:0.5cm) -- cycle;
\end{scope}
\end{tikzpicture}
\end{tikzpicture}
\end{document}