Vorlesung vom 23.01.2014 geTeXt

documents/GeoTopo/Arbeitszeit.md

@@ -44,3 +44,4 @@ in dem Erstellen dieses Skripts steckt:
 |23.01.2014 | 10:30 - 12:15 | TikZ'en von Bildern
 |24.01.2014 | 15:00 - 15:15 | Flag um Dokument in A4 (für den Bildschirm) bzw. A5 (zum drucken und binden)
 |24.01.2014 | 23:00 - 00:15 | Digitalisieren der Vorlesung von 23.01.2014
+|25.01.2014 | 09:30 - 12:45 | Digitalisieren der Vorlesung von 23.01.2014

documents/GeoTopo/figures/hyberbolische-geometrie-1.tex

@@ -0,0 +1,17 @@
+\begin{tikzpicture}
+    \tkzSetUpPoint[shape=circle,size=3,color=black,fill=black]
+    \tkzSetUpLine[line width=1]
+    \tkzInit[xmax=7,ymax=3,xmin=-1,ymin=0]
+    \tkzDefPoints{2/0/m1,4/0/m2,1/1.1/a1,1/0/a1x, 2.5/2.0/a2,2.5/0/a2x}
+    \tkzDrawSegments(a1x,a1 a2x,a2)
+    \tkzAxeXY[ticks=false]
+
+    \tkzDrawArc[R,line width=1pt,color=red](m1,1.5 cm)(0,180)
+    \tkzDrawArc[R,line width=1pt](m2,2.5 cm)(0,180)
+    \tkzDrawPoints(m1,m2,a1,a2)
+    \tkzLabelPoint[above](m1) {$m$}
+    \tkzLabelPoint[above](m2) {$\lambda^2 m$}
+    \tkzLabelPoint[above](a1) {$m+\iu r$}
+    \tkzLabelPoint[above](a2) {$\lambda^2 m+\iu \lambda^2 r$}
+    \node[red] at ($(m1)+(1.5,-0.2)$)  {$m+1$};
+\end{tikzpicture}

documents/GeoTopo/figures/hyberbolische-geometrie-2.tex

@@ -0,0 +1,18 @@
+\begin{tikzpicture}
+    \tkzSetUpPoint[shape=circle,size=3,color=black,fill=black]
+    \tkzSetUpLine[line width=0.5]
+    \tkzInit[xmax=4.5,ymax=3,xmin=-1,ymin=0]
+    \tkzDefPoints{0/0/O, 3/3/lz, 2/2/z, 3/0/lzx, 2/0/zx}
+    \tkzDrawLines(O,lz zx,z)
+    \tkzDrawLine[add=0 and 0.2](lzx,lz)
+    \tkzAxeXY[ticks=false]
+
+    %\tkzDrawArc[R,line width=1pt,color=red](m1,1.5 cm)(0,180)
+    %\tkzDrawArc[R,line width=1pt](m2,2.5 cm)(0,180)
+    \tkzDrawPoints(z,lz)
+    \tkzLabelPoint[left](z) {$z$}
+    \tkzLabelPoint[above right](zx) {$x$}
+    \tkzLabelPoint[right](lz) {$\lambda^2 z$}
+    \tkzLabelPoint[above right](lzx) {$\lambda^2 x$}
+    %\node[red] at ($(m1)+(1.5,-0.2)$)  {$m+1$};
+\end{tikzpicture}

documents/GeoTopo/figures/hyperbolische-geometrie-axiom-1-1.tex

@@ -0,0 +1,13 @@
+\begin{tikzpicture}
+    \tkzSetUpPoint[shape=circle,size=3,color=black,fill=black]
+    \tkzSetUpLine[line width=1]
+    \tkzInit[xmax=5,ymax=4,xmin=-1,ymin=0]
+    \tkzDefPoints{2/2/Z1,2/3/Z2,2/0/A}
+    \tkzAxeXY
+
+    \tkzDrawLine[add=2 and 1, color=orange](Z1,Z2)
+    \tkzDrawPoints(Z1, Z2)
+    \tkzLabelPoint[right](Z1){$Z_1$}
+    \tkzLabelPoint[right](Z2){$Z_2$}
+    \node[orange] at ($(A)+(0.5,0.3)$)  {$\Re(Z_1)$};
+\end{tikzpicture}

documents/GeoTopo/figures/hyperbolische-geometrie-axiom-1-2.tex

@@ -0,0 +1,17 @@
+\begin{tikzpicture}
+    \tkzSetUpPoint[shape=circle,size=3,color=black,fill=black]
+    \tkzSetUpLine[line width=1]
+    \tkzInit[xmax=5,ymax=4,xmin=-1,ymin=0]
+    \tkzDefPoints{1/1/Z1,2/2/Z2,3/0/A}
+    \tkzAxeXY
+
+    \tkzDrawPoints(Z1, Z2)
+    \tkzLabelPoint[right](Z1){$Z_1$}
+    \tkzLabelPoint[below](Z2){$Z_2$}
+    \node (m) at ($(Z1)!0.5!(Z2)$) {};
+    \tkzDrawSegments[dashed](Z1,Z2 A,Z1 A,Z2)
+
+    \tkzDefLine[perpendicular=through m](Z1,Z2)\tkzGetPoint{c}
+    \tkzDrawLine[add=2 and 1,dashed,thick](m, c)
+    \tkzDrawArc[R,line width=1pt,color=orange](A,2.24 cm)(0,180)
+\end{tikzpicture}

documents/GeoTopo/figures/inversion-am-kreis.tex

@@ -0,0 +1,15 @@
+\begin{tikzpicture}[scale=3]
+    \tkzSetUpPoint[shape=circle,size=3,color=black,fill=black]
+    \tkzSetUpLine[line width=1]
+    \tkzInit[xmax=1.2,ymax=1,xmin=-1.2,ymin=0]
+    \tkzDefPoints{1/1/Z,0.5/0.5/dZ,-0.5/0.5/ndZ,0/0/O}
+    \tkzDrawArc[R,line width=1pt,color=orange](O,1 cm)(0,180)
+    \tkzAxeXY
+
+    \tkzDrawPoints(Z, dZ, ndZ)
+    \tkzLabelPoint[right](Z){$Z = r \cdot e^{\iu \varphi}$}
+    \tkzLabelPoint[below right](dZ){$\frac{1}{z} = \frac{1}{r} \cdot e^{-\iu \varphi}$}
+    \tkzLabelPoint[below left](ndZ){$-\frac{1}{z}$}
+    \tkzDrawSegments[dashed](O,Z)
+    \tkzDrawSegments[dashed](O,ndZ)
+\end{tikzpicture}

documents/GeoTopo/shortcuts.sty

@@ -86,6 +86,7 @@
 \DeclareMathOperator{\Diffeo}{Diffeo}
 \DeclareMathOperator{\conv}{conv}
 \DeclareMathOperator{\IWS}{IWS}
+\newcommand{\iu}{{i\mkern1mu}} % imaginary unit
 %\DeclareMathOperator{\Re}{Re}
 %\DeclareMathOperator{\Im}{Im}
 

tikz/hyberbolische-geometrie-1/Makefile

@@ -0,0 +1,31 @@
+SOURCE  = hyberbolische-geometrie-1
+DELAY   = 80
+DENSITY = 300
+WIDTH   = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/hyberbolische-geometrie-1/Readme.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](hyberbolische-geometrie-1.png)

tikz/hyberbolische-geometrie-1/hyberbolische-geometrie-1.tex

@@ -0,0 +1,25 @@
+\documentclass[varwidth=true, border=10pt]{standalone}
+\usepackage{tkz-euclide}
+\usepackage{tkz-fct} 
+\newcommand{\iu}{{i\mkern1mu}} % imaginary unit
+
+\begin{document}
+\usetkzobj{all}
+\begin{tikzpicture}
+    \tkzSetUpPoint[shape=circle,size=3,color=black,fill=black]
+    \tkzSetUpLine[line width=1]
+    \tkzInit[xmax=7,ymax=3,xmin=-1,ymin=0]
+    \tkzDefPoints{2/0/m1,4/0/m2,1/1.1/a1,1/0/a1x, 2.5/2.0/a2,2.5/0/a2x}
+    \tkzDrawSegments(a1x,a1 a2x,a2)
+    \tkzAxeXY[ticks=false]
+
+    \tkzDrawArc[R,line width=1pt,color=red](m1,1.5 cm)(0,180)
+    \tkzDrawArc[R,line width=1pt](m2,2.5 cm)(0,180)
+    \tkzDrawPoints(m1,m2,a1,a2)
+    \tkzLabelPoint[above](m1) {$m$}
+    \tkzLabelPoint[above](m2) {$\lambda^2 m$}
+    \tkzLabelPoint[above](a1) {$m+\iu r$}
+    \tkzLabelPoint[above](a2) {$\lambda^2 m+\iu \lambda^2 r$}
+    \node[red] at ($(m1)+(1.5,-0.2)$)  {$m+1$};
+\end{tikzpicture}
+\end{document}

tikz/hyberbolische-geometrie-2/Makefile

@@ -0,0 +1,31 @@
+SOURCE  = hyberbolische-geometrie-2
+DELAY   = 80
+DENSITY = 300
+WIDTH   = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/hyberbolische-geometrie-2/Readme.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](hyberbolische-geometrie-2.png)

tikz/hyberbolische-geometrie-2/hyberbolische-geometrie-2.tex

@@ -0,0 +1,26 @@
+\documentclass[varwidth=true, border=10pt]{standalone}
+\usepackage{tkz-euclide}
+\usepackage{tkz-fct} 
+\newcommand{\iu}{{i\mkern1mu}} % imaginary unit
+
+\begin{document}
+\usetkzobj{all}
+\begin{tikzpicture}
+    \tkzSetUpPoint[shape=circle,size=3,color=black,fill=black]
+    \tkzSetUpLine[line width=0.5]
+    \tkzInit[xmax=4.5,ymax=3,xmin=-1,ymin=0]
+    \tkzDefPoints{0/0/O, 3/3/lz, 2/2/z, 3/0/lzx, 2/0/zx}
+    \tkzDrawLines(O,lz zx,z)
+    \tkzDrawLine[add=0 and 0.2](lzx,lz)
+    \tkzAxeXY[ticks=false]
+
+    %\tkzDrawArc[R,line width=1pt,color=red](m1,1.5 cm)(0,180)
+    %\tkzDrawArc[R,line width=1pt](m2,2.5 cm)(0,180)
+    \tkzDrawPoints(z,lz)
+    \tkzLabelPoint[left](z) {$z$}
+    \tkzLabelPoint[above right](zx) {$x$}
+    \tkzLabelPoint[right](lz) {$\lambda^2 z$}
+    \tkzLabelPoint[above right](lzx) {$\lambda^2 x$}
+    %\node[red] at ($(m1)+(1.5,-0.2)$)  {$m+1$};
+\end{tikzpicture}
+\end{document}

tikz/hyperbolische-geometrie-axiom-1-1/Makefile

@@ -0,0 +1,31 @@
+SOURCE  = hyperbolische-geometrie-axiom-1-1
+DELAY   = 80
+DENSITY = 300
+WIDTH   = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/hyperbolische-geometrie-axiom-1-1/Readme.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](hyperbolische-geometrie-axiom-1-1.png)

tikz/hyperbolische-geometrie-axiom-1-1/hyperbolische-geometrie-axiom-1-1.tex

@@ -0,0 +1,21 @@
+\documentclass[varwidth=true, border=10pt]{standalone}
+\usepackage{tkz-euclide}
+\usepackage{tikz}
+\usetikzlibrary{patterns}
+
+\begin{document}
+\usetkzobj{all}
+\begin{tikzpicture}
+    \tkzSetUpPoint[shape=circle,size=3,color=black,fill=black]
+    \tkzSetUpLine[line width=1]
+    \tkzInit[xmax=5,ymax=4,xmin=-1,ymin=0]
+    \tkzDefPoints{2/2/Z1,2/3/Z2,2/0/A}
+    \tkzAxeXY
+
+    \tkzDrawLine[add=2 and 1, color=orange](Z1,Z2)
+    \tkzDrawPoints(Z1, Z2)
+    \tkzLabelPoint[right](Z1){$Z_1$}
+    \tkzLabelPoint[right](Z2){$Z_2$}
+    \node[orange] at ($(A)+(0.5,0.3)$)  {$\Re(Z_1)$};
+\end{tikzpicture}
+\end{document}

tikz/hyperbolische-geometrie-axiom-1-2/Makefile

@@ -0,0 +1,31 @@
+SOURCE  = hyperbolische-geometrie-axiom-1-2
+DELAY   = 80
+DENSITY = 300
+WIDTH   = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/hyperbolische-geometrie-axiom-1-2/Readme.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](hyperbolische-geometrie-axiom-1-2.png)

tikz/hyperbolische-geometrie-axiom-1-2/hyperbolische-geometrie-axiom-1-2.tex

@@ -0,0 +1,25 @@
+\documentclass[varwidth=true, border=10pt]{standalone}
+\usepackage{tkz-euclide}
+\usepackage{tikz}
+\usetikzlibrary{patterns}
+
+\begin{document}
+\usetkzobj{all}
+\begin{tikzpicture}
+    \tkzSetUpPoint[shape=circle,size=3,color=black,fill=black]
+    \tkzSetUpLine[line width=1]
+    \tkzInit[xmax=5,ymax=4,xmin=-1,ymin=0]
+    \tkzDefPoints{1/1/Z1,2/2/Z2,3/0/A}
+    \tkzAxeXY
+
+    \tkzDrawPoints(Z1, Z2)
+    \tkzLabelPoint[right](Z1){$Z_1$}
+    \tkzLabelPoint[below](Z2){$Z_2$}
+    \node (m) at ($(Z1)!0.5!(Z2)$) {};
+    \tkzDrawSegments[dashed](Z1,Z2 A,Z1 A,Z2)
+
+    \tkzDefLine[perpendicular=through m](Z1,Z2)\tkzGetPoint{c}
+    \tkzDrawLine[add=2 and 1,dashed,thick](m, c)
+    \tkzDrawArc[R,line width=1pt,color=orange](A,2.24 cm)(0,180)
+\end{tikzpicture}
+\end{document}

tikz/inversion-am-kreis/Makefile

@@ -0,0 +1,31 @@
+SOURCE  = inversion-am-kreis
+DELAY   = 80
+DENSITY = 300
+WIDTH   = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/inversion-am-kreis/Readme.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](inversion-am-kreis.png)

tikz/inversion-am-kreis/inversion-am-kreis.tex

@@ -0,0 +1,22 @@
+\documentclass[varwidth=true, border=10pt]{standalone}
+\usepackage{tkz-euclide}
+\newcommand{\iu}{{i\mkern1mu}} % imaginary unit
+
+\begin{document}
+\usetkzobj{all}
+\begin{tikzpicture}[scale=3]
+    \tkzSetUpPoint[shape=circle,size=3,color=black,fill=black]
+    \tkzSetUpLine[line width=1]
+    \tkzInit[xmax=1.2,ymax=1,xmin=-1.2,ymin=0]
+    \tkzDefPoints{1/1/Z,0.5/0.5/dZ,-0.5/0.5/ndZ,0/0/O}
+    \tkzDrawArc[R,line width=1pt,color=orange](O,1 cm)(0,180)
+    \tkzAxeXY
+
+    \tkzDrawPoints(Z, dZ, ndZ)
+    \tkzLabelPoint[right](Z){$Z = r \cdot e^{\iu \varphi}$}
+    \tkzLabelPoint[below right](dZ){$\frac{1}{z} = \frac{1}{r} \cdot e^{-\iu \varphi}$}
+    \tkzLabelPoint[below left](ndZ){$-\frac{1}{z}$}
+    \tkzDrawSegments[dashed](O,Z)
+    \tkzDrawSegments[dashed](O,ndZ)
+\end{tikzpicture}
+\end{document}