Paper III: Typed Transfer, Nonlinear Packets, and Obstruction Theory

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round,line join=round]
2 \draw[fill=black!10,draw=black!40,line width=.35pt,] (0.00000,0.50000) rectangle ++(1.30000,1.25000);
3 \node[] at (0.65000,1.12500) {$ac=10$};
4 \draw[fill=black!25,draw=black!40,line width=.35pt,] (0.00000,1.75000) rectangle ++(1.30000,1.75000);
5 \node[] at (0.65000,2.62500) {$ad=14$};
6 \draw[fill=black!25,draw=black!40,line width=.35pt,] (1.30000,0.50000) rectangle ++(1.95000,1.25000);
7 \node[] at (2.27500,1.12500) {$bc=15$};
8 \draw[fill=black!10,draw=black!40,line width=.35pt,] (1.30000,1.75000) rectangle ++(1.95000,1.75000);
9 \node[] at (2.27500,2.62500) {$bd=21$};
10 \node[font=\sffamily\bfseries] at (1.62000,4.25000) {$(2+3)(5+7)=60$};
11 \node[] at (0.65000,0.15000) {$a=2$};
12 \node[] at (2.27000,0.15000) {$b=3$};
13 \node[anchor=east] at (-0.25000,1.10000) {$c=5$};
14 \node[anchor=east] at (-0.25000,2.62000) {$d=7$};
15 \draw[black!25] (4.10000,-0.30000) -- (4.10000,4.65000);
16 \node[font=\sffamily\bfseries] at (8.00000,4.10000) {Diagonal pieces are not the whole product};
17 \node[] at (8.00000,3.10000) {$ac+bd=10+21=31$};
18 \node[] at (8.00000,2.25000) {$ad+bc=14+15=29$};
19 \node[] at (8.00000,1.10000) {$(2+3)^2=25\ne2^2+3^2=13$};
20 \node[] at (8.00000,0.15000) {missing square term: $2\cdot2\cdot3=12$};
21 \end{tikzpicture}

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