misc

documents/GeoTopo/Kapitel1.tex

@@ -838,8 +838,6 @@ $\qed$
     $A_1 \cup A_2 = X$. Sei $x \in A_1, y \in A_2, \gamma:[0,1] \rightarrow X$
     ein Weg von $x$ nach $y$.
 
-    \todo[inline]{Bild eines topologischen Raumes, der in zwei Teile $A_1, A_2$ geteilt wird}
-
     Dann ist $C:= \gamma([0,1]) \subseteq X$ zusammenhängend, weil 
     $\gamma$ stetig ist.
     \[C = \underbrace{(C \cap A_1)}_{\ni x} \cup \underbrace{(C \cap A_2)}_{\ni y}\]

documents/GeoTopo/Makefile

@@ -8,5 +8,10 @@ make:
 	pdflatex $(DOKUMENT).tex -output-format=pdf # Stichwortverzeichnis einbinden
 	pdflatex $(DOKUMENT).tex -output-format=pdf # Symbolverzeichnis einbinden
 
+ebook:
+	latexml --dest=$(DOKUMENT).xml $(DOKUMENT).tex
+	latexmlpost -dest=$(DOKUMENT).html $(DOKUMENT).xml
+	ebook-convert $(DOKUMENT).html $(DOKUMENT).epub --language de --no-default-epub-cover
+
 clean:
 	rm -rf  $(TARGET) *.class *.html *.log *.aux *.out *.thm *.idx *.toc *.ind *.ilg figures/torus.tex *.glg *.glo *.gls *.ist *.xdy

tikz/knot-trefoil/Makefile

@@ -0,0 +1,31 @@
+SOURCE = knot-trefoil
+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 *.hd *.glo *.ins *.out *.idx
+
+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/knot-trefoil/README.txt

@@ -0,0 +1,12 @@
+----------------------------------------------------------------
+brunnian --- a style file for drawing link diagrams with TikZ/PGF
+E-mail: stacey@math.ntnu.no
+Released under the LaTeX Project Public License v1.3c or later
+See http://www.latex-project.org/lppl.txt
+----------------------------------------------------------------
+
+This package defines some commands and styles useful for drawing knot and link diagrams with TikZ/PGF.
+Some are geared towards drawing very specific links (the iterated Hopf and Brunnian links) whilst others will be more generally useful for arbitrary knots and links.
+
+
+

tikz/knot-trefoil/Readme.md

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

tikz/knot-trefoil/knot-trefoil.tex

@@ -0,0 +1,25 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{brunnian}
+\usetikzlibrary{arrows}
+
+\begin{document}
+\tikzset{%
+    every path/.style={red,line width=2pt},%
+    every node/.style={transform shape,knot crossing,inner sep=1.5pt},%
+    >=triangle 60,%
+    text node/.style={rectangle,transform shape=false,black}%
+}
+
+\begin{tikzpicture}
+\foreach \brk in {0,1,2} {
+    \begin{scope}[rotate=\brk * 120]
+        \node (k\brk) at (0,-1) {};
+    \end{scope}
+}
+\draw (0,0) \foreach \brk in {0,1,2} {
+    let 
+    \n0=\brk, 
+    \n1={int(Mod(\brk+1,3))}, 
+    \n2={int(Mod(\brk+2,3))} in (k\n0) .. controls (k\n0.16 south east) and (k\n1.16 south west) .. (k\n1.center) .. controls (k\n1.4 north east) and (k\n2.4 north west) .. (k\n2)} (k2);
+\end{tikzpicture}
+\end{document}

tikz/sin(1divx)/Makefile

@@ -1,4 +1,4 @@
-SOURCE = 'sin(1:x)'
+SOURCE = 'sin(1divx)'
 DELAY = 80
 DENSITY = 300
 WIDTH = 500

tikz/sin(1divx)/Readme.md

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

tikz/sin(1divx)/sin(1divx).tex

@@ -24,8 +24,8 @@
         ymin=-1,      % start the diagram at this y-coordinate
         ymax= 1,      % end   the diagram at this y-coordinate
         axis background/.style={fill=white},
-        ylabel=y,
-        xlabel=x,
+        ylabel=$y$,
+        xlabel=$x$,
         legend style={at={(0.9,0.95)}, anchor=north}
      ]
       \addplot[domain=0.01:1, red, thick,samples=2000] {-sin(deg(1/(x)))};

tikz/topology-jordan/Makefile

@@ -0,0 +1,31 @@
+SOURCE = topology-jordan
+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/topology-jordan/Readme.md

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

tikz/topology-jordan/topology-jordan.tex

@@ -0,0 +1,54 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usetikzlibrary{patterns,calc}
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.7}
+
+\begin{document}
+% Code from Christian Feuersänger
+% http://tex.stackexchange.com/questions/54794/using-a-pgfplots-style-legend-in-a-plain-old-tikzpicture#54834
+% argument #1: any options
+\newenvironment{customlegend}[1][]{%
+    \begingroup
+    % inits/clears the lists (which might be populated from previous
+    % axes):
+    \csname pgfplots@init@cleared@structures\endcsname
+    \pgfplotsset{#1}%
+}{%
+    % draws the legend:
+    \csname pgfplots@createlegend\endcsname
+    \endgroup
+}%
+
+% makes \addlegendimage available (typically only available within an
+% axis environment):
+\def\addlegendimage{\csname pgfplots@addlegendimage\endcsname}
+
+%%--------------------------------
+
+% definition to insert numbers
+\pgfkeys{/pgfplots/number in legend/.style={%
+        /pgfplots/legend image code/.code={%
+            \node at (0.295,-0.0225){#1};
+        },%
+    },
+}
+\begin{tikzpicture}
+    \draw[draw=white,pattern=north west lines, pattern color=blue] (-1.5,-1.5) rectangle (1.5,1.5);
+    \draw[fill=white] (0cm,0cm) circle(1cm);
+    \draw[fill=white,thick,pattern=dots, pattern color=red] (0cm,0cm) circle(1cm);
+
+    \begin{customlegend}[
+    legend entries={ % <= in the following there are the entries
+    au{\ss}en,
+    innen,
+    Jordankurve
+    },
+    legend style={at={(4.5,1.5)},font=\footnotesize}] % <= to define position and font legend
+    % the following are the "images" and numbers in the legend
+        \addlegendimage{area legend,pattern=north west lines, pattern color=blue,draw=white}
+        \addlegendimage{area legend,pattern=dots, pattern color=red,draw=white}
+        \addlegendimage{thick}
+    \end{customlegend}
+\end{tikzpicture}
+\end{document}

tikz/topology-sinx/Makefile

@@ -0,0 +1,31 @@
+SOURCE = topology-sinx
+DELAY = 80
+DENSITY = 300
+WIDTH = 500
+
+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/topology-sinx/Readme.md

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

tikz/topology-sinx/topology-sinx.tex

@@ -0,0 +1,40 @@
+\documentclass{article}
+\usepackage[pdftex,active,tightpage]{preview}
+\setlength\PreviewBorder{2mm}
+
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.9}
+\usepackage{tikz}
+\usetikzlibrary{arrows, positioning, calc}
+
+\begin{document}
+\begin{preview}
+
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=left,
+        enlarge y limits=true,
+        xmode=log, % Logarithmic x axis
+        xmin=0.01, xmax=1, % Positive domain...
+        xticklabel=\pgfmathparse{exp(\tick)}\pgfmathprintnumber{\pgfmathresult},
+        xticklabel style={/pgf/number format/.cd,fixed}, % Use fixed point notation
+        width=15cm, height=8cm,     % size of the image
+        grid = major,
+        grid style={dashed, gray!30},
+        ymin=-1,      % start the diagram at this y-coordinate
+        ymax= 1,      % end   the diagram at this y-coordinate
+        axis background/.style={fill=white},
+        ylabel=$Y$,
+        xlabel=$X$,
+        legend style={at={(0.9,0.95)}, anchor=north}
+     ]
+      \addplot[domain=0.0105:1, red, thick,samples=2000] {-sin(deg(1/(x)))};
+      \addplot[domain=0.0105:0.011, blue, thick,samples=20] {10};
+      \addlegendentry{$\{(x, \sin(\frac{1}{x})) \in X \times Y\}$}
+      \addlegendentry{$(-1,1) \subseteq Y$}
+    \end{axis} 
+      \draw[ultra thick,blue] (0,0.5) -- (0,5.9);
+\end{tikzpicture}
+\end{preview}
+\end{document}