diff options
| -rw-r--r-- | buch/papers/punktgruppen/Makefile | 3 | ||||
| -rw-r--r-- | buch/papers/punktgruppen/figures/symmetric-shapes.pdf | bin | 0 -> 12790 bytes | |||
| -rw-r--r-- | buch/papers/punktgruppen/symmetry.tex | 48 | ||||
| -rw-r--r-- | buch/papers/punktgruppen/tikz/symmetric-shapes.tex | 59 |
4 files changed, 63 insertions, 47 deletions
diff --git a/buch/papers/punktgruppen/Makefile b/buch/papers/punktgruppen/Makefile index 3960d76..f92dc95 100644 --- a/buch/papers/punktgruppen/Makefile +++ b/buch/papers/punktgruppen/Makefile @@ -15,7 +15,8 @@ TIKZFIGURES := \ tikz/lattice.tex \ tikz/piezo-atoms.tex \ tikz/piezo.tex \ - tikz/projections.tex + tikz/projections.tex \ + tikz/symmetric-shapes.tex FIGURES := $(patsubst tikz/%.tex, figures/%.pdf, $(TIKZFIGURES)) diff --git a/buch/papers/punktgruppen/figures/symmetric-shapes.pdf b/buch/papers/punktgruppen/figures/symmetric-shapes.pdf Binary files differnew file mode 100644 index 0000000..03a05ce --- /dev/null +++ b/buch/papers/punktgruppen/figures/symmetric-shapes.pdf diff --git a/buch/papers/punktgruppen/symmetry.tex b/buch/papers/punktgruppen/symmetry.tex index aa3f7fb..e173f8e 100644 --- a/buch/papers/punktgruppen/symmetry.tex +++ b/buch/papers/punktgruppen/symmetry.tex @@ -16,50 +16,7 @@ ist das Konzept der Symmetrie eigentlich viel allgemeiner. \begin{figure} \centering - \begin{tikzpicture}[ - node distance = 2cm, - shapetheme/.style = { - very thick, draw = black, fill = magenta!20!white, - minimum size = 2cm, - }, - line/.style = {thick, draw = darkgray}, - axis/.style = {line, dashed}, - dot/.style = { - circle, draw = darkgray, fill = darkgray, - minimum size = 1mm, inner sep = 0, outer sep = 0, - }, - ] - - \node[ - shapetheme, - rectangle - ] (R) {}; - \node[dot] at (R) {}; - \draw[axis] (R) ++(-1.5, 0) to ++(3, 0) node[right] {\(\sigma\)}; - - \node[ - shapetheme, - regular polygon, - regular polygon sides = 5, - right = of R, - ] (Ps) {}; - \node[dot] (P) at (Ps) {}; - \draw[line, dotted] (P) to ++(18:1.5); - \draw[line, dotted] (P) to ++(90:1.5); - \draw[line, ->] (P) ++(18:1.2) - arc (18:90:1.2) node[midway, above right] {\(r, 72^\circ\)}; - - \node[ - shapetheme, - circle, right = of P - ] (Cs) {}; - \node[dot] (C) at (Cs) {}; - \draw[line, dotted] (C) to ++(1.5,0); - \draw[line, dotted] (C) to ++(60:1.5); - \draw[line, ->] (C) ++(1.2,0) - arc (0:60:1.2) node[midway, above right] {\(r, \alpha\)}; - - \end{tikzpicture} + \includegraphics{papers/punktgruppen/figures/symmetric-shapes} \caption{ Beispiele für geometrisch symmetrische Formen. \label{fig:punktgruppen:geometry-example} @@ -91,8 +48,7 @@ Mit dem oben Gesagten können wir das \(n\)-Gon Beispiel formalisieren. Wenn wir \(r\) eine Drehung von \(2\pi/n\) sein lassen, gibt es eine wohlbekannte Symmetriegruppe \[ C_n = \langle r \rangle - = \left\{\mathds{1}, r, r^2, \ldots, r^{n-1}\right\}, -\] + = \left\{\mathds{1}, r, r^2, \ldots, r^{n-1}\right\}, \] die zyklische Gruppe heisst. Hier die Potenzen von \(r\) sind als wiederholte Komposition gemeint, d.h. \(r^n = r\circ r \circ \cdots r\circ r\). Die Schreibweise mit den spitzen Klammern wird als Erzeugendensystem bezeichnet. diff --git a/buch/papers/punktgruppen/tikz/symmetric-shapes.tex b/buch/papers/punktgruppen/tikz/symmetric-shapes.tex new file mode 100644 index 0000000..b2c051f --- /dev/null +++ b/buch/papers/punktgruppen/tikz/symmetric-shapes.tex @@ -0,0 +1,59 @@ +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} + +\usetikzlibrary{arrows} +\usetikzlibrary{shapes.geometric} +\usetikzlibrary{intersections} +\usetikzlibrary{math} +\usetikzlibrary{positioning} +\usetikzlibrary{arrows.meta} +\usetikzlibrary{shapes.misc} +\usetikzlibrary{calc} + +\begin{document} + \begin{tikzpicture}[ + node distance = 2cm, + shapetheme/.style = { + very thick, draw = black, fill = magenta!20!white, + minimum size = 2cm, + }, + line/.style = {thick, draw = darkgray}, + axis/.style = {line, dashed}, + dot/.style = { + circle, draw = darkgray, fill = darkgray, + minimum size = 1mm, inner sep = 0, outer sep = 0, + }, + ] + + \node[ + shapetheme, rectangle + ] (R) {}; + \node[dot] at (R) {}; + \draw[axis] (R) ++(-1.5, 0) to ++(3, 0) node[right] {\(\sigma\)}; + + \node[ + shapetheme, + regular polygon, + regular polygon sides = 5, + right = of R, + ] (Ps) {}; + \node[dot] (P) at (Ps) {}; + \draw[line, dotted] (P) to ++(18:1.5); + \draw[line, dotted] (P) to ++(90:1.5); + \draw[line, ->] (P) ++(18:1.2) + arc (18:90:1.2) node[midway, above right] {\(r, 72^\circ\)}; + + \node[ + shapetheme, + circle, right = of P + ] (Cs) {}; + \node[dot] (C) at (Cs) {}; + \draw[line, dotted] (C) to ++(1.5,0); + \draw[line, dotted] (C) to ++(60:1.5); + \draw[line, ->] (C) ++(1.2,0) + arc (0:60:1.2) node[midway, above right] {\(r, \alpha\)}; + + \end{tikzpicture} +\end{document} |