From 23eed4cd2463bcb4e2829321c422a75ed267fc6b Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Sun, 2 Feb 2014 18:42:22 +0100 Subject: [PATCH] TikZ'en von Bildern --- documents/GeoTopo/Arbeitszeit.md | 1 + documents/GeoTopo/GeoTopo.pdf | Bin 4711569 -> 4712097 bytes documents/GeoTopo/Kapitel2.tex | 2 +- documents/GeoTopo/Kapitel3.tex | 13 ++++---- documents/GeoTopo/Kapitel4.tex | 14 ++++---- documents/GeoTopo/figures/topology-paths.tex | 8 +++++ documents/GeoTopo/figures/triangle-4.tex | 25 ++++++++++++++ tikz/topology-paths/Makefile | 31 +++++++++++++++++ tikz/topology-paths/Readme.md | 3 ++ tikz/topology-paths/topology-paths.png | Bin 0 -> 15644 bytes tikz/topology-paths/topology-paths.tex | 15 +++++++++ tikz/triangle-4/Makefile | 31 +++++++++++++++++ tikz/triangle-4/Readme.md | 3 ++ tikz/triangle-4/triangle-4.png | Bin 0 -> 12004 bytes tikz/triangle-4/triangle-4.tex | 33 +++++++++++++++++++ 15 files changed, 163 insertions(+), 16 deletions(-) create mode 100644 documents/GeoTopo/figures/topology-paths.tex create mode 100644 documents/GeoTopo/figures/triangle-4.tex create mode 100644 tikz/topology-paths/Makefile create mode 100644 tikz/topology-paths/Readme.md create mode 100644 tikz/topology-paths/topology-paths.png create mode 100644 tikz/topology-paths/topology-paths.tex create mode 100644 tikz/triangle-4/Makefile create mode 100644 tikz/triangle-4/Readme.md create mode 100644 tikz/triangle-4/triangle-4.png create mode 100644 tikz/triangle-4/triangle-4.tex diff --git a/documents/GeoTopo/Arbeitszeit.md b/documents/GeoTopo/Arbeitszeit.md index f8fd136..3066b9c 100644 --- a/documents/GeoTopo/Arbeitszeit.md +++ b/documents/GeoTopo/Arbeitszeit.md @@ -56,3 +56,4 @@ in dem Erstellen dieses Skripts steckt: |30.01.2014 | 15:45 - 17:00 | Digitalisieren der Vorlesung von 30.01.2014 |30.01.2014 | 19:30 - 21:30 | Textsetzung |01.02.2014 | 15:40 - 15:50 | Beweis "Möbiustransformation ist Gruppenoperation" hinzugefügt +|02.02.2014 | 17:00 - 18:00 | 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zxnWM3?c$C{uty}9whun0)_WXQPcw&WSS&mKT)PY0x@7E!TLN8ghM0?|v9M$HsYH1ffP1M)JP<5+=%EXLw&Hi_*bNTnWY<05N zeV=s|S@uniq`g(|cb_HK|2u#D$3iIVKUPBjib?+WA<3E|&K{N(lKvcS?L&1Q6$!?` z9{i`DnTay+VY0-a9^?dLk1A4W!!^O6@OZNo$FH*Osz2>aH!LCtSye z^3O8g3heJZeo(-N{&Q4>4-NwcLLzfZerS2qFLO%=A%XXfBl!Oz!2Unj_&=EVX-)pa zl(}E+_!9Rg)8HoiRTvhm0qXbqA*Xl95i0o?j@mtTr|h7Q>MZyolA`#WoT_?i`2Pzf C*xsZ7 diff --git a/documents/GeoTopo/Kapitel2.tex b/documents/GeoTopo/Kapitel2.tex index 060310d..9814e70 100644 --- a/documents/GeoTopo/Kapitel2.tex +++ b/documents/GeoTopo/Kapitel2.tex @@ -879,7 +879,7 @@ $\partial X$ ist eine Mannigfaltigkeit der Dimension $n-1$. \begin{figure}[h!] \centering \input{figures/topology-oriented-triangle.tex} - \caption{TODO} + \caption{Simplizialkomplex mit Totalordnung} \end{figure} $a < b < c$ diff --git a/documents/GeoTopo/Kapitel3.tex b/documents/GeoTopo/Kapitel3.tex index 6b66f0b..8769799 100644 --- a/documents/GeoTopo/Kapitel3.tex +++ b/documents/GeoTopo/Kapitel3.tex @@ -269,7 +269,7 @@ Für einen Weg $\gamma$ sei $[\gamma]$ seine \textbf{Homotopieklasse}\xindex{Hom \begin{figure}[htp] \centering - \input{figures/todo.tex} + \input{figures/topology-paths.tex} \caption{Situation aus \cref{kor:gruppenisomorphismus-wege}}. \label{fig:situation-gruppenisomorphismus-wege} \end{figure} @@ -826,12 +826,11 @@ $p|V_j: V_j \rightarrow U$ Homöomorphismus. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Mitschrieb vom 19.12.2013 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{bemerkung}%Vorlesung: Folgerung 12.12 - \todo{Hier stimmt was mit den Tilden nicht} - Sind $p:X \rightarrow X$ und $y: \tilde{Y} \rightarrow X$ +\begin{folgerung}%Vorlesung: Folgerung 12.12 + Sind $p:\tilde{X} \rightarrow X$ und $q: \tilde{Y} \rightarrow X$ universelle Überlagerungen, so sind $\tilde{X}$ und $\tilde{Y}$ homöomorph. -\end{bemerkung} +\end{folgerung} \begin{beweis} Seien $x_0 \in X, \tilde{x_0} \in \tilde{X}$ mit @@ -848,8 +847,8 @@ $p|V_j: V_j \rightarrow U$ Homöomorphismus. $p:\tilde{X} \rightarrow X$ mit $(g \circ f) (\tilde{x_0}) = \tilde{x_0}$. Da auch $\id_{\tilde{x}}$ diese Eigenschaft hat, folgt mit - \cref{kor:12.4}: $g \circ f = \id_{\tilde{X}}$. - Analog $f \circ g = \id_{\tilde{Y}}$. $\qed$ + \cref{kor:12.4}: $g \circ f = \id_{\tilde{X}}$.\\ + Analog gilt $f \circ g = \id_{\tilde{Y}}$. $\qed$ \end{beweis} Die Frage, wann es eine universelle Überlagerung gibt, beantwortet diff --git a/documents/GeoTopo/Kapitel4.tex b/documents/GeoTopo/Kapitel4.tex index 3da241f..237f477 100644 --- a/documents/GeoTopo/Kapitel4.tex +++ b/documents/GeoTopo/Kapitel4.tex @@ -600,8 +600,7 @@ Sei im Folgenden \enquote{IWS} die \enquote{Innenwinkelsumme}. \end{beweis} \section{Weitere Eigenschaften einer euklidischen Ebene} -\subsection{Strahlensatz} -\begin{satz} +\begin{satz}[Strahlensatz] In ähnlichen Dreiecken sind Verhältnisse entsprechender Seiten gleich. \end{satz} @@ -612,9 +611,8 @@ Sei im Folgenden \enquote{IWS} die \enquote{Innenwinkelsumme}. \label{fig:bild-2} \end{figure} -\begin{beweis} - TODO -\end{beweis} +Der Beweis wird hier nicht geführt. Für Beweisvorschläge wäre ich +dankbar. \begin{figure}[htp] \centering @@ -632,11 +630,11 @@ Sei im Folgenden \enquote{IWS} die \enquote{Innenwinkelsumme}. \begin{figure}[ht] \centering - \subfloat[TODO]{ + \subfloat[Zwei kongruente Dreiecke]{ \input{figures/rectangle-2.1.tex} \label{fig:bild-4} }% - \subfloat[TODO]{ + \subfloat[Zwei weitere kongruente Dreiecke]{ \input{figures/rectangle-2.2.tex} \label{fig:bild-5} }% @@ -648,7 +646,7 @@ Der Flächeninhalt eines Dreiecks ist $\nicefrac{1}{2} \cdot \text{Grundseite} \ \begin{figure}[htp] \centering - \input{figures/todo.tex} + \input{figures/triangle-4.tex} \caption{Flächenberechnung im Dreiecks} \label{fig:flaechenberechnung-dreieck} \end{figure} diff --git a/documents/GeoTopo/figures/topology-paths.tex b/documents/GeoTopo/figures/topology-paths.tex new file mode 100644 index 0000000..8554242 --- /dev/null +++ b/documents/GeoTopo/figures/topology-paths.tex @@ -0,0 +1,8 @@ +\begin{tikzpicture} + \tikzstyle{point}=[circle,thick,draw=black,fill=black,inner sep=0pt,minimum width=4pt,minimum height=4pt] + \node (a)[point,label=180:$a$] at (0,0) {}; + \node (b)[point,label=0:$b$] at (3, 0) {}; + \draw [rounded corners,->, thick, red] (a) .. controls (0.5,2) .. (2,1) .. controls (2,0.5) .. (a); + \draw [rounded corners,->, thick, blue] (a) .. controls (1,-1) .. (2,-0.5) .. controls (2.2,-1) .. (b); + \node at (1,1.2) [red] {$\gamma$}; +\end{tikzpicture} diff --git a/documents/GeoTopo/figures/triangle-4.tex b/documents/GeoTopo/figures/triangle-4.tex new file mode 100644 index 0000000..48a7c76 --- /dev/null +++ b/documents/GeoTopo/figures/triangle-4.tex @@ -0,0 +1,25 @@ +\begin{tikzpicture} + \tkzSetUpPoint[shape=circle,size=10,color=black,fill=black] + \tkzSetUpLine[line width=1] + \tkzDefPoints{0/0/A, 4/0/B, -2/3/C} + + \tkzDefLine[orthogonal=through A,/tikz/overlay](B,C) \tkzGetPoint{helper} + \tkzInterLL(B,C)(A,helper) \tkzGetPoint{La} + + \tkzMarkAngle[arc=l,size=0.4cm,color=red,fill=red!20](A,La,B) + \tkzLabelAngle[pos=0.25](A,La,B){$\cdot$} + + \tkzDrawPolygon(A,B,C) + + \node at ($(A)+(-0.47,-0.2)$){$A$}; + \node at ($(B)+(0.35,-0.2)$) {$B$}; % \tkzLabelPoint[below](B){$B$} is not accurate enough + \node at ($(C)+(0.05,0.3)$) {$C$}; + \node[green] at ($(La)+(-0.4,-0.1)$) {$L_A$}; + + \tkzDrawSegments[red](A,La) + \tkzDrawSegments[blue](B,C) + \tkzLabelSegment[right,red](A,La){$h_a$} + \tkzLabelSegment[above,blue](B,C){$c$} + \tkzDrawPoints(A,B,C) + \tkzDrawPoints[color=green,fill=green](La) +\end{tikzpicture} diff --git a/tikz/topology-paths/Makefile b/tikz/topology-paths/Makefile new file mode 100644 index 0000000..e24d93d --- /dev/null +++ b/tikz/topology-paths/Makefile @@ -0,0 +1,31 @@ +SOURCE = topology-paths +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/topology-paths/Readme.md b/tikz/topology-paths/Readme.md new file mode 100644 index 0000000..1ca7912 --- /dev/null +++ b/tikz/topology-paths/Readme.md @@ -0,0 +1,3 @@ +Compiled example +---------------- +![Example](topology-paths.png) diff --git a/tikz/topology-paths/topology-paths.png b/tikz/topology-paths/topology-paths.png new file mode 100644 index 0000000000000000000000000000000000000000..6deb1057b100a50539e5432353a1dca4d36fde9c GIT binary patch literal 15644 zcmd_Ri96Ka7dZZ!v5tKZ*}_C**9h6u$d+A^l#z^VA!~`5DYBD&%U0G9Wlu3FysJSG zAHbZDJO)27sfzCQ+rnMcaQZ(EclG@H@O@LK`OTo|6#hxGo#>3p&%p2AUi)?P^jx| zcPKP8RLS#}cc7cAzq^v(ZI67ajxYpCK&F_p_F<1#CPOnsyPJB~SD8}LhS=N8se$}w zZxCUr>6|Byh7nYIr1%Q?gxo|ne4f0;h;TIjCxpcC#B!WqL1HXV@fL?oi=Y0~KSEya z@81gAzChPoSaxlBvJpw}YuyoE z;?oY8QXcYTL-N`2)UigAHN_w6MzY=cTF3f<vZQl7`Y08txDni025= 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(2,1) .. controls (2,0.5) .. (a); + \draw [rounded corners,->, thick, blue] (a) .. controls (1,-1) .. (2,-0.5) .. controls (2.2,-1) .. (b); + \node at (1,1.2) [red] {$\gamma$}; +\end{tikzpicture} +\end{document} diff --git a/tikz/triangle-4/Makefile b/tikz/triangle-4/Makefile new file mode 100644 index 0000000..7e857bd --- /dev/null +++ b/tikz/triangle-4/Makefile @@ -0,0 +1,31 @@ +SOURCE = triangle-4 +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/triangle-4/Readme.md b/tikz/triangle-4/Readme.md new file mode 100644 index 0000000..7311200 --- /dev/null +++ b/tikz/triangle-4/Readme.md @@ -0,0 +1,3 @@ +Compiled example +---------------- +![Example](triangle-4.png) diff --git a/tikz/triangle-4/triangle-4.png b/tikz/triangle-4/triangle-4.png new file mode 100644 index 0000000000000000000000000000000000000000..82e2f8a72606cc942aff2c5d1e8a83b9c04d5053 GIT binary patch literal 12004 zcmbt)i$Bxv`~Pc4Gv~vQL$q{2p%#+UIG6$v?&$SH9L`44`-9*-XL+H3c9J+JF}Ue|ryhg5gB9dcMrECfMvt}c!q z5CjK*!b~t|@Ig3v?gIEgMs9cY#DIUXn4>A+S(@TR4Uc@L|8~fmK2-2Fx`Ln7!#gg4BzdQayJjeC*{r|RDN-l5CljKRXBwjuUTcLX>(7FI~JS1>%lxnK%X6nJL8?GsHAl5>F4`!idGLS`({^q{8!oK#Y@0_{@yr%z< zNjFYGi}=_*Mo{*UG5PGtTT^O4pX@O$=u1-N^us^T=UD{@^L&Az&6%g5Xv^4H&PS8% zA%E5pYQXi$dM6N1haqExpKdg65E^Xd*o6g(Pto%ctE1jAfw!WbltOhvb(R4V#=XVQ zfedmEhI2K!e*Y|RG@7=8H3;qKK@1N4VrOVp@^EL_rJTbucd)Wlf%sUAn*^_0e>Z%Q zM|kf5YT={n4y@s?rDQeQ-Mpca3Uu^Gs6p4|L;GKG20l-6flb$MHlZLe)WE+! zS`(m1$<&ZMU(@h_fHPB9{qNyq?xn=+p;}fT(Jo;P-2~AM7o1olA>{m<^Ei6W6*Ntz zEceJyKW+!FdHtgslGwW)6KF~W&w$x{flsP9hbOw0g;9T>wn)I zD1vbjdYnsAwrswi#F(HJD2OVCN3VV!eq~$FOljO^%Y4aDZy`2(Svt>yLJa5fjp`Taw zgx{8dJ)(!19@CgHlRjVR(^7(tj$O4udy@8X{|W{0L&x{mFZsfrNv%b!gAXU^Rw73c z4HxEgBLof!%azU0LLMegIgtgA4$2f}Kdjcw0N|dkpN4wAlE}GmUr0up_CXi6pkR?6 zCCL3Qc>Z_$ps=map4)ki_t5r6HA51@)s}LQtCYpCeD+>SH@%zT&ucE5xAoa`A+wk#$eB=1 z|GZq;gjuk%v&2~c(TxttjHyYGg!k5ul@Rj`cs;j7-aI2#Dc-Gw99{8^_M_$J)}w$W zPrNfA$hDl_(kQ%FE*uRvmQQ4D`<>qp?R}2^&$%IgtHo3z4v;G{Nft^irz`Pjk<%^0 zN0-KTOg+HBe~v%D#_O=lo!$geH1kmc3e@ar*`}SE<@5`4T7IXcwWGtn>+#1if_vSQ zQ9U5Q$BLOSXmdD9U%Q=~mfr@O+CFymx9>^%!+<0OXG09|=9Z0VP{wH^z2A>%^MtMZ z8Q{DECEgCZ{Ml@fe{c7+BA~)h)XZnz9Qm|$V!)EN{5Bawl|+^i{|!b^s{TatDKL9Q zsy;*vI|MVhdJvYitSxUV^S9z~%L8=u7u;gu$GDzLLwP$u?do${0m(+I4w@{jpYSH8 z1^KYLO%ff}>Ps==I}^K0IqA^`>Ql_{aXmF|+zU27<`uYS}BB zJ9hy&mcwX!E`Pqq#7S}SY@JY4`8h^gQsBII!iI0WA-VF@5sXu}Ipzjx~UGMlUrWWnb6_9&MLn&tctqkWR+zLsw|Ci>fDo%|7F>61f*XBw?&+H z8j?tw9d9!V@Bz$bgwe+QbtdsQSuh9>3Uyhe(l{$;yR=^xD9J6A!f zr;PNj<(#4aj0bPqBrsprSGm;)-70td1LFQp3R*AnCf+y2EZNG!XTLw|gG@wP{VV>V z*k_muK@a|CN&C5$i$TtSKUpHVX`e=FfZ`D3RbJ4hVwHz>$u z2s`+OGj=Ir_mFAznM6I)UmZPmn=sa>+$-*iib~h~4Bz}O{3FZ!^&K~4>=n0$V6~|p z+ZFjteASs6q1vSat$QHVFL}sA=p~gwi>2bDzOYnws7r{tq7o$SFJ!eqmt7uEm9NGG!10l;>V%xVC| zg?%#!N&#T^_1ZIEjsNZ-b?hG*Hc6FeQoi{_24YHFFs%A&&qZAYh6o4howk}anjGS*il^JS*G3H;3Y*|11cxMUJSBI2R_c^mZfAU7=&^z0 zI}Aahd)&fF!nt*b6Ml)};?&MIzxcQ}Fxo4^i8O8(c=25+Fevlc6FG=~*of;z(&@vx z93hX%B(j*Q_S|=-m?D?7MCNp#j!l=(tu0Gjm1mO0xX#hK=fm+RHPm>-vm6%&gO z9;xN7szEzC?)2GUDA8ih4h_+;K{#vQiha!e6i-aw^v|$cgGk8bBq|pB%fpEIn;ojP z^|ylQ5BIO(65o!-YBZ#K0X`eZJw6WWbFH)QaW2MXs8IvH&}PR?Nmd%mkhNA(M=hG8 zAb$vPX{Bcf(XnvxWhopQtAUFYG&E?1-o#{fnaZ8b2xpz^eo6;^D9%LRHU#ir8k~he z9<}hZ5duMhj@P%%)wA48J63Vx^+eYDi_BaJ9j>K%$uQm0yoqJ`xQva|_~GRS2NKa| z>*T#x<&3b4$a2O@g<>;3yodFXgD`q#IbF9=s9T`5?+?as!)h_~aAk&{QuMU_U|^F( zR5UjI!B$TyDej9px~kYfJl3dcapv z?6R01&8=tjWRF)pcs1T4uvhm2LL$Iq1gnAHKSs7;o=0C^nXQey#gVzYPBH;}PCf+5 z72^~)QUkcO-sUQyoBJ}-S}W{CNY9^QrWt=>1EKa(6ccm|L>wInfG7}#rIWkqk7Mk` zXi1QtOV#FbyM`sjt?+^YR0s??y{X!t@_QMV-FINt|%u`j28`o#Om z2_KR{&%oRB!$vf}dg7jX8?7KRARgrlyCN!p25`)hD z&~ayqNsK>`bN?v0u`NBARi_Keydb#UToQ{t?lR03yk=w#JndFvcVx@&i>6FvHxV^1 zgt-S5O3>)vuqj4hEFt#w5_nI7YB~MJ$nxHIS6pr%A>X9DkJ7NytH<-lHw=E)mN*WM zh01|FCpJ|#2P%He$79$R%DVuguhs3BVdC1nS*Y>hD|9=@t=cCTjV)Z-Fr-nXb?2Ag zL_f=Whg3O3AS&vor@Y89gvvp507*rZ_ggf^OzQDfOJRdQtbq>wFjeTiLRQjxwbqg(<@*3D^yNKaF8c?u(XxZ< zmR!o|%E!od7gQd$eT%zp1lQ%Dd?oZcwhN|*FgOIW;VdT}-?1iVbF~fkLJ7rr4g{yg zD)8q|z_Y@UVpIl0wH)H;6rfjFGn;@3mR8+ z+W&{YO@j_|ow-shh&rlZCtk(h#a&AcOFa^b_t5l&z23gvh!oU^U2nt_)d^=CiQ;AM z;-4!<@Z2OEBVDY$&xw18OW{^E=!$!iSpKYFrOU34J5vmygF7D^aviBHHf^h1^RkC% zrlHt7HTxr+xVVvj z55W=>dsZqm;-1wUXzVw@8(_lvp9h+|R^uo4Y@}GdN zM<1x}n~9Hq+kyK-4t3*Ch+(Gd20GNQExM!hcJyIWObAwrR~t3Ec-Q=t7MDz_=3jW? 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