1031 \label{fig:horizontal-composition} |
1031 \label{fig:horizontal-composition} |
1032 \end{figure} |
1032 \end{figure} |
1033 \begin{figure}[t] |
1033 \begin{figure}[t] |
1034 \begin{align*} |
1034 \begin{align*} |
1035 \mathfig{0.4}{triangle/triangle4f} \\ |
1035 \mathfig{0.4}{triangle/triangle4f} \\ |
1036 \mathfig{0.4}{triangle/triangle4f_i} |
1036 \begin{tikzpicture} |
|
1037 \node[circle,fill=black,inner sep=1pt] (A) at (1.73,0) {}; |
|
1038 \node[circle,fill=black,inner sep=1pt] (B) at (-1.73,0) {}; |
|
1039 \draw[dashed] (A) -- (B); |
|
1040 \node[circle,fill=black,inner sep=1pt] (C) at (0,0) {}; |
|
1041 \node[circle,fill=black,inner sep=1pt] (D) at (0.8,0) {}; |
|
1042 \begin{scope}[yshift=-1cm] |
|
1043 \path[clip] (0,0) circle (2); |
|
1044 \begin{scope}[yshift=2cm] |
|
1045 \draw (0,0) circle (2); |
|
1046 \node[circle,fill=black,inner sep=1pt] (L2) at (-90:2) {}; |
|
1047 \node[circle,fill=black,inner sep=1pt] (L1) at (-120:2) {}; |
|
1048 \end{scope} |
|
1049 \end{scope} |
|
1050 \begin{scope}[yshift=1cm] |
|
1051 \path[clip] (0,0) circle (2); |
|
1052 \begin{scope}[yshift=-2cm] |
|
1053 \draw (0,0) circle (2); |
|
1054 \node[circle,fill=black,inner sep=1pt] (U) at (90:2) {}; |
|
1055 \end{scope} |
|
1056 \end{scope} |
|
1057 \begin{scope} |
|
1058 \path[clip] (0,1) circle (2); |
|
1059 \path[clip] (0,-1) circle (2); |
|
1060 \foreach \n in {1,...,6} { |
|
1061 \path (B) to[out=0,in=-180] node[coordinate,pos=\n/6] (BC\n) {} (C); |
|
1062 \draw[green!50!brown] (BC\n) -- +(0,1); |
|
1063 \draw[green!50!brown] (BC\n) -- +(-1.5,-1); |
|
1064 } |
|
1065 \foreach \n in {0,...,5} { |
|
1066 \path (C) to[out=0,in=-180] node[coordinate,pos=\n/5] (CD\n) {} (D); |
|
1067 \path (L1) to[out=-30,in=-180] node[coordinate,pos=\n/5] (L1L2\n) {} (L2); |
|
1068 \draw[blue] (CD\n) -- (L1L2\n); |
|
1069 } |
|
1070 \foreach \n in {0,...,5} { |
|
1071 \path (L1) to[out=40,in=-140] node[coordinate,pos=\n/5] (L1C\n) {} (C); |
|
1072 \path (L2) to[out=50,in=-130] node[coordinate,pos=\n/5] (L2D\n) {} (D); |
|
1073 \draw[blue] (L1C\n) -- (L2D\n); |
|
1074 } |
|
1075 \foreach \n in {1,3,...,9} { |
|
1076 \path(C) to[out=30,in=150] node[coordinate,pos=\n/10] (CA\n) {} (A); |
|
1077 \path(D) to[out=0,in=180] node[coordinate,pos=\n/10] (DA\n) {} (A); |
|
1078 \path(L2) to[out=0,in=-120] node[coordinate,pos=\n/10] (L2A\n) {} (A); |
|
1079 \draw[brown] (CA\n) -- +(0,1); |
|
1080 \draw[brown] (CA\n) to[out=0] (DA\n) -- (L2A\n); |
|
1081 } |
|
1082 \draw[dashed] (U) -- (C) -- (L1) (L2) -- (D); |
|
1083 \end{scope} |
|
1084 \end{tikzpicture} |
1037 \end{align*} |
1085 \end{align*} |
1038 \caption{Vertical composition in the triangle axiom.} |
1086 \caption{Vertical composition in the triangle axiom.} |
1039 \label{fig:vertical-composition} |
1087 \label{fig:vertical-composition} |
1040 \end{figure} |
1088 \end{figure} |
1041 \begin{figure}[t] |
1089 \begin{figure}[t] |