From 5ada0a42edd417c5b232de78477d0db2209264bd Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Sat, 25 Jan 2014 12:40:32 +0100 Subject: [PATCH] Vorlesung vom 23.01.2014 geTeXt --- documents/GeoTopo/Arbeitszeit.md | 1 + .../figures/hyberbolische-geometrie-1.tex | 17 ++++++++++ .../figures/hyberbolische-geometrie-2.tex | 18 ++++++++++ .../hyperbolische-geometrie-axiom-1-1.tex | 13 ++++++++ .../hyperbolische-geometrie-axiom-1-2.tex | 17 ++++++++++ .../GeoTopo/figures/inversion-am-kreis.tex | 15 +++++++++ documents/GeoTopo/shortcuts.sty | 1 + tikz/hyberbolische-geometrie-1/Makefile | 31 ++++++++++++++++++ tikz/hyberbolische-geometrie-1/Readme.md | 3 ++ .../hyberbolische-geometrie-1.png | Bin 0 -> 16734 bytes .../hyberbolische-geometrie-1.tex | 25 ++++++++++++++ tikz/hyberbolische-geometrie-2/Makefile | 31 ++++++++++++++++++ tikz/hyberbolische-geometrie-2/Readme.md | 3 ++ .../hyberbolische-geometrie-2.png | Bin 0 -> 12708 bytes .../hyberbolische-geometrie-2.tex | 26 +++++++++++++++ .../Makefile | 31 ++++++++++++++++++ .../Readme.md | 3 ++ .../hyperbolische-geometrie-axiom-1-1.png | Bin 0 -> 11631 bytes .../hyperbolische-geometrie-axiom-1-1.tex | 21 ++++++++++++ .../Makefile | 31 ++++++++++++++++++ .../Readme.md | 3 ++ .../hyperbolische-geometrie-axiom-1-2.png | Bin 0 -> 18782 bytes .../hyperbolische-geometrie-axiom-1-2.tex | 25 ++++++++++++++ tikz/inversion-am-kreis/Makefile | 31 ++++++++++++++++++ tikz/inversion-am-kreis/Readme.md | 3 ++ .../inversion-am-kreis/inversion-am-kreis.png | Bin 0 -> 12845 bytes .../inversion-am-kreis/inversion-am-kreis.tex | 22 +++++++++++++ 27 files changed, 371 insertions(+) create mode 100644 documents/GeoTopo/figures/hyberbolische-geometrie-1.tex create mode 100644 documents/GeoTopo/figures/hyberbolische-geometrie-2.tex create mode 100644 documents/GeoTopo/figures/hyperbolische-geometrie-axiom-1-1.tex create mode 100644 documents/GeoTopo/figures/hyperbolische-geometrie-axiom-1-2.tex create mode 100644 documents/GeoTopo/figures/inversion-am-kreis.tex create mode 100644 tikz/hyberbolische-geometrie-1/Makefile create mode 100644 tikz/hyberbolische-geometrie-1/Readme.md create mode 100644 tikz/hyberbolische-geometrie-1/hyberbolische-geometrie-1.png create mode 100644 tikz/hyberbolische-geometrie-1/hyberbolische-geometrie-1.tex create mode 100644 tikz/hyberbolische-geometrie-2/Makefile create mode 100644 tikz/hyberbolische-geometrie-2/Readme.md create mode 100644 tikz/hyberbolische-geometrie-2/hyberbolische-geometrie-2.png create mode 100644 tikz/hyberbolische-geometrie-2/hyberbolische-geometrie-2.tex create mode 100644 tikz/hyperbolische-geometrie-axiom-1-1/Makefile create mode 100644 tikz/hyperbolische-geometrie-axiom-1-1/Readme.md create mode 100644 tikz/hyperbolische-geometrie-axiom-1-1/hyperbolische-geometrie-axiom-1-1.png create mode 100644 tikz/hyperbolische-geometrie-axiom-1-1/hyperbolische-geometrie-axiom-1-1.tex create mode 100644 tikz/hyperbolische-geometrie-axiom-1-2/Makefile create mode 100644 tikz/hyperbolische-geometrie-axiom-1-2/Readme.md create mode 100644 tikz/hyperbolische-geometrie-axiom-1-2/hyperbolische-geometrie-axiom-1-2.png create mode 100644 tikz/hyperbolische-geometrie-axiom-1-2/hyperbolische-geometrie-axiom-1-2.tex create mode 100644 tikz/inversion-am-kreis/Makefile create mode 100644 tikz/inversion-am-kreis/Readme.md create mode 100644 tikz/inversion-am-kreis/inversion-am-kreis.png create mode 100644 tikz/inversion-am-kreis/inversion-am-kreis.tex diff --git a/documents/GeoTopo/Arbeitszeit.md b/documents/GeoTopo/Arbeitszeit.md index 4c7879a..f3614d4 100644 --- a/documents/GeoTopo/Arbeitszeit.md +++ b/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 diff --git a/documents/GeoTopo/figures/hyberbolische-geometrie-1.tex b/documents/GeoTopo/figures/hyberbolische-geometrie-1.tex new file mode 100644 index 0000000..b85de93 --- /dev/null +++ b/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} diff --git a/documents/GeoTopo/figures/hyberbolische-geometrie-2.tex b/documents/GeoTopo/figures/hyberbolische-geometrie-2.tex new file mode 100644 index 0000000..360289d --- /dev/null +++ b/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} diff --git a/documents/GeoTopo/figures/hyperbolische-geometrie-axiom-1-1.tex b/documents/GeoTopo/figures/hyperbolische-geometrie-axiom-1-1.tex new file mode 100644 index 0000000..82b6101 --- /dev/null +++ b/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} diff --git a/documents/GeoTopo/figures/hyperbolische-geometrie-axiom-1-2.tex b/documents/GeoTopo/figures/hyperbolische-geometrie-axiom-1-2.tex new file mode 100644 index 0000000..523f923 --- /dev/null +++ b/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} diff --git a/documents/GeoTopo/figures/inversion-am-kreis.tex b/documents/GeoTopo/figures/inversion-am-kreis.tex new file mode 100644 index 0000000..42a2243 --- /dev/null +++ b/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} diff --git a/documents/GeoTopo/shortcuts.sty b/documents/GeoTopo/shortcuts.sty index 5d18fbd..5a2bef7 100644 --- a/documents/GeoTopo/shortcuts.sty +++ b/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} diff --git a/tikz/hyberbolische-geometrie-1/Makefile b/tikz/hyberbolische-geometrie-1/Makefile new file mode 100644 index 0000000..75bc2b4 --- /dev/null +++ b/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 diff --git a/tikz/hyberbolische-geometrie-1/Readme.md 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+ \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} diff --git a/tikz/hyberbolische-geometrie-2/Makefile b/tikz/hyberbolische-geometrie-2/Makefile new file mode 100644 index 0000000..d42def9 --- /dev/null +++ b/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 diff --git a/tikz/hyberbolische-geometrie-2/Readme.md b/tikz/hyberbolische-geometrie-2/Readme.md new file mode 100644 index 0000000..510b902 --- /dev/null +++ b/tikz/hyberbolische-geometrie-2/Readme.md @@ -0,0 +1,3 @@ +Compiled example +---------------- +![Example](hyberbolische-geometrie-2.png) diff --git a/tikz/hyberbolische-geometrie-2/hyberbolische-geometrie-2.png b/tikz/hyberbolische-geometrie-2/hyberbolische-geometrie-2.png new file mode 100644 index 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+\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} diff --git a/tikz/inversion-am-kreis/Makefile b/tikz/inversion-am-kreis/Makefile new file mode 100644 index 0000000..d77f49e --- /dev/null +++ b/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 diff --git a/tikz/inversion-am-kreis/Readme.md b/tikz/inversion-am-kreis/Readme.md new file mode 100644 index 0000000..7b00b51 --- /dev/null +++ b/tikz/inversion-am-kreis/Readme.md @@ -0,0 +1,3 @@ +Compiled example +---------------- +![Example](inversion-am-kreis.png) diff --git a/tikz/inversion-am-kreis/inversion-am-kreis.png 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\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}