Niles Johnson

While teaching Geometry for elementary/middle grade teachers, I forced myself to learn TikZ. Here are pictures with code from that class and other endeavors. These are nowhere near as fancy as the examples on TeXample.net, but that makes them a bit easier to read.

If you want, you can download all of these in a single file:
(latex) (pdf).

  \begin{tikzpicture}
    \draw[fill=red!10] (0,6) -- (0,0) -- (2,4) -- cycle;
    \draw[fill=blue!10] (5,0) -- (10,1) -- (10,3) -- cycle;
    \draw[fill=yellow!10] (3,6) -- (3,5) -- (6,1) -- (6,2) -- cycle;
    \draw[fill=green!10] (7,6) -- (12,6) -- (10,4) -- (5,4) -- cycle;
    \draw[fill=orange!10] (12,4) -- (11,0) -- (12,0) -- cycle;
    \draw[color=gray, style=dotted] (0,0) grid[xstep=1cm, ystep=1cm] (12cm,6cm);
  \end{tikzpicture}

  Determine the areas of the indicated shapes.

  \begin{tikzpicture}[scale=.8, z={(-.707,-.3)}]
    \draw (4,0,0) -- (0,0,0) -- (0,5,0);
    \draw (4,0,0) -- (4,0,-3) -- (4,5,-3) -- (4,5,0) -- cycle;
    \draw (4,5,0) -- (0,5,0) -- (0,5,-3) -- (4,5,-3);
    \draw[style=dashed, color=gray] (4,0,-3) -- (0,0,-3) -- (0,5,-3);
    \draw[style=dashed, color=gray] (0,0,0) -- (0,0,-3); 
    \draw (2,-.4,0) node{4 ft};
    \draw (4.6,-.2,-1.5) node{3 ft};
    \draw (4.5,2.5,-3) node{5 ft};
  \end{tikzpicture}
  \hspace{5pc}
  \begin{tikzpicture}[scale=.8, z={(.707,.3)}]
    \draw (2,3,2) -- (0,0,0) -- (4,0,0) -- (4,0,4) -- (2,3,2) --
    (4,0,0);
    \draw[color=gray, style=dashed] (2,3,2) -- (0,0,4) -- (0,0,0);
    \draw[color=gray, style=dashed] (0,0,4) -- (4,0,4);
    \draw (4.6,-.2,2) node{4 ft};
    \draw[|-|] (5.5,3,2) -- node[right] {3 ft} (5.5,0,2);

    % spacer
    \draw (0,-1,0) node {};
  \end{tikzpicture}

  Determine the length of the longest pole that can fit in the box, and
  determine the lengths of the edges of the pyramid.

  \begin{tikzpicture}
    %% background grid
    % \draw[color=gray, help lines, line width=.05pt] (-2,-2)
    % grid[xstep=.25cm, ystep=.25cm] (4,2);
    % \draw[color=black, help lines, line width=.1pt] (-2,-2)
    % grid[xstep=1cm, ystep=1cm] (4,2);
    % \draw[fill=red] (0,0) circle(.05);

    %% horizontal lines
    \draw (-2,-1) -- (3,-1);
    \draw (-2,.5) -- (3,.5);
    
    %% other lines
    \draw (-2,-1.5) -- ++(40:5.5);
    \draw (1.5,2) -- ++(-60:3);
    \draw[very thin] (2.625,.5) arc (0:-60:.25) node[right] {\small
      $60^\circ$};
    \draw[very thin] (1.9,1.77) arc (40:-60:.24) node[anchor=south west]
    {\small \ $100^\circ$};
    \draw[very thin] (-1.14,-1) arc (0:-140:.25) node[anchor=north west]
    {\small $\theta$};
  \end{tikzpicture}
  \hspace{2pc}
  \begin{tikzpicture}
    %% background grid
    \draw[color=gray, help lines, line width=.05pt] (-2,-2)
    grid[xstep=.25cm, ystep=.25cm] (4,2);
    \draw[color=black, help lines, line width=.1pt] (-2,-2)
    grid[xstep=1cm, ystep=1cm] (4,2);
    \draw[fill=red] (0,0) circle(.05);

    %% horizontal lines
    \draw (-2,-1) -- (3,-1);
    \draw (-2,.5) -- (3,.5);
    
    %% other lines
    \draw (-2,-1.5) -- ++(40:5.5);
    \draw (1.5,2) -- ++(-60:3);
    \draw[very thin] (2.625,.5) arc (0:-60:.25) node[right] {\small
      $60^\circ$};
    \draw[very thin] (1.9,1.77) arc (40:-60:.24) node[anchor=south west]
    {\small \ $100^\circ$};
    \draw[very thin] (-1.14,-1) arc (0:-140:.25) node[anchor=north west]
    {\small $\theta$};
  \end{tikzpicture}

  Find the measure of the angle marked $\theta$.\\
  (Use the grid at right while drawing the diagram, to help determine where various things should be placed.)  

  \begin{tikzpicture}
    \draw[thick, fill=white] (0,0) circle(1);
    \draw[thick, fill=white] (0,1.3) circle(.6);
    \draw[thick, fill=white] (0,2.1) circle(.4);
    \draw (0,2.1) ++(-30:.2) arc(-30:-150:.2);
    \draw[very thick] (0,1.3) ++(10:.4) --++(20:.8);
    \draw[very thick] (0,1.3) ++(170:.4) --++(160:.8);
    \draw[fill=black] (0,2.15) +(.1,0) circle(.03) +(-.1,0) circle(.03);
    \draw[|-|] (1.45,1.9) --node[right] {2 ft.} (1.45,.7);
    \draw[|-|] (-1.2,-1.1) --node[below] {3 ft.} (1.2,-1.1);
    \draw[|-|] (-.4,2.65) -- node[above] {1 ft.} (.4,2.65);
    \draw[|-|] (2.4,2.5) -- node[right] {$H$} (2.4,-1);
  \end{tikzpicture}
  \hspace{5pc}
  \begin{tikzpicture}[scale=2/3]
    \draw[thick, fill=white] (0,0) circle(1);
    \draw[thick, fill=white] (0,1.3) circle(.6);
    \draw[thick, fill=white] (0,2.1) circle(.4);
    \draw (0,2.1) ++(-30:.2) arc(-30:-150:.2);
    \draw[very thick] (0,1.3) ++(10:.4) --++(20:.8);
    \draw[very thick] (0,1.3) ++(170:.4) --++(160:.8);
    \draw[fill=black] (0,2.15) +(.1,0) circle(.03) +(-.1,0) circle(.03);
    \draw[|-|] (1.45,1.9) --node[right] {$a$} (1.45,.7);
    \draw[|-|] (-1.2,-1.1) --node[below] {2 ft.} (1.2,-1.1);
    \draw[|-|] (-.4,2.65) -- node[above] {$t$} (.4,2.65);
    \draw[|-|] (2.2,2.5) -- node[right] {4 ft.} (2.2,-1);
  \end{tikzpicture}

  Two similar snowmen.

  \begin{tikzpicture}[rotate=90]
    \draw[violet, fill=violet!10] (4,0) arc(90:-90:4) -- (4,-4) -- node[above, black]{$2$ cm} (4,-2)  -- (4,0);
    \draw[|-|]  (3.6,-4) -- node[below]{$4$ cm} (3.6,0);
    \draw[fill=black] (4,-4) circle(.03);
    \draw[blue, dashed] (4,-2) arc(90:-90:2);
  \end{tikzpicture}

  Pattern for a right circular cone.

\newdimen\R
\R=1cm
\newdimen\S
\S=1.5cm

  \begin{tikzpicture}
    % square
    \draw (0,0) -- (\S,0) -- (\S,\S) -- (0,\S) -- cycle;
    \draw (.5\S,-.5) node {\textbf{A}} 
    ++ (0,-.5) node {square};
    
    % pentagon
    \draw[xshift=3\R, yshift=.814\R] (90:\R) \foreach \x in {162,234,...,449} {
      -- (\x:\R)
    }-- cycle (0:\R);
    \draw[xshift=3\R] (0,-.5) node {\textbf{B}} 
    ++ (0,-.5) node {regular} ++ (0,-.5) node {pentagon};
    
    % parallelogram
    \draw[xshift=4.3\R] (0,0) -- (1.8\S,0) -- (2.3\S,.9\S) -- (.5\S,.9\S) -- cycle;
    \draw[xshift=4.3\R] (.9\S,-.5) node {\textbf{C}} 
    ++ (0,-.5) node {parallelogram};
    
    % octagon
    \draw[xshift=9.3\R, yshift=.925\R, rotate=22.5] (0:\R) \foreach \x in {45,90,...,359} {
      -- (\x:\R)
    } -- cycle (90:\R);
    \draw[xshift=9.3\R] (0,-.5) node {\textbf{D}} 
    ++ (0,-.5) node {regular octagon};
    
    % trapezoid
    \draw[xshift=10.5\R] (0,0) -- (2.8\S,0) -- node[rotate=-52]{$\vert$} (2\S,1.1\S) -- (.8\S,1.1\S)
    -- node[rotate=52]{$\vert$} (0,0);
    \draw[xshift=10.5\R] (1.4\S,-.5) node {\textbf{E}} 
    ++ (0,-.5) node {trapezoid};
  \end{tikzpicture}

  Some shapes.

  \begin{tikzpicture}[scale=.4]
    \draw[fill=none] (0,0) coordinate (o) 
    -- (3,-9) coordinate[pos=.5] (b)  coordinate (top)
    -- (6,0) coordinate[pos=.5] (a)
    -- (0,0);
    \draw[fill=red!08] (b) -- (a) -- (top) -- cycle;
    \draw[|-|] (-4,0) -- node[left] {\small 10 in} (-4,-9);
    \draw[|-|] (-1,-9/2) -- node[left] {\small 5 in} (-1,-9);
  \end{tikzpicture}
  \hspace{2pc}
  \begin{tikzpicture}[scale=.4]
    \draw[fill=none] (0,0) coordinate (o) 
    -- (-3,-8) coordinate[pos=.666] (b)  coordinate (top)
    -- (6,0) coordinate[pos=.333] (a)
    -- (0,0);
    \draw[fill=red!08] (b) -- (a) -- (top) -- cycle;
    \draw[|-|] (-4,0) -- node[left] {\small 6 in} (-4,-16/3);
    \draw[-|] (-4,-16/3) -- node[left] {\small 3 in} (-4,-8);
    \draw (0,-8.7) node {};
  \end{tikzpicture}

  Explain for each triangle what fraction of the total area is shaded.

  \begin{tikzpicture}[x=.5cm,y=.5cm]
    \draw[fill=green!10] (-1,3) -- (-2,3) -- (-3,2) -- (-2,1) -- cycle;
    \draw[fill=green!10] (2,3) -- (1,2) -- (2,2)-- (2,1) -- (4,1) --cycle;
    \draw[thick, ->] (0,-4) -- (0,4) node[above] {y};
    \draw[thick, ->] (-4,0) -- (4,0) node[right] {x};
    \draw[color=gray, help lines, line width=.05pt] (-4,-4)
    grid[xstep=.5cm, ystep=.5cm] (4,4);
    \draw (0,-4.75) node[below] {reflect across $x$-axis};
  \end{tikzpicture}
  \hspace{2pc}
  \begin{tikzpicture}[x=.5cm,y=.5cm]
    \draw[fill=orange!10] (-1,3) -- (-2,3) -- (-3,2) -- (-2,1) -- cycle;
    \draw[fill=orange!10] (2,3) -- (1,2) -- (2,2)-- (2,1) -- (4,1) --cycle;
    \draw[thick, ->] (0,-4) -- (0,4) node[above] {y};
    \draw[thick, ->] (-4,0) -- (4,0) node[right] {x};
    \draw[color=gray, help lines, line width=.05pt] (-4,-4)
    grid[xstep=.5cm, ystep=.5cm] (4,4);
    \draw (0,-4.75) node[below] {rotate around origin $180^\circ$};
  \end{tikzpicture}
  \hspace{2pc}
  \begin{tikzpicture}[x=.5cm,y=.5cm]
    \draw[fill=blue!10] (-3,0) -- (-4,1) -- (-3,3) -- (-2,1) -- (-1,1)
    -- (-1,0) -- cycle;
    \draw[fill=blue!10] (3,1) -- (2,0) -- (2,-2) -- (4,-1) -- (3,-1) -- cycle;
    \draw[thick, ->] (0,-4) -- (0,4) node[above] {y};
    \draw[thick, ->] (-4,0) -- (4,0) node[right] {x};
    \draw[color=gray, help lines, line width=.05pt] (-4,-4)
    grid[xstep=.5cm, ystep=.5cm] (4,4);
    \draw (0,-4) node[below, text width=4cm] {rotate around origin $90^\circ$ counter-clockwise};
  \end{tikzpicture}

  Carry out the indicated transformations.  

  \begin{tikzpicture}[scale=.5]
    \draw (0,0) -- node[above]{$c$} (13,0) -- node[anchor=south west]{$b$} (144/13,60/13) coordinate
    (a) -- node[above]{$a$} (0,0);
    \draw[color=gray, line width=.5pt, dashed] (a) -- (144/13,0);
  \end{tikzpicture}
  \begin{tikzpicture}[scale=.5*12/13]
    \draw (0,0) --  node[above] {$a$} (13,0) -- (144/13,60/13) -- cycle;
  \end{tikzpicture}
  \begin{tikzpicture}[scale=.5*5/13]
    \draw (0,0) --  node[above] {$b$} (13,0) -- (144/13,60/13) -- cycle;
  \end{tikzpicture}

  Use these diagrams to give at least three different proofs of the Pythagorean theorem.  

\begin{tikzpicture}[scale=1.8]
  \draw (-2.5,-.05) node (t) {} 
  arc(-90:0:.6cm) node (h1) {}
  arc(0:180:.6cm) node (h2) {}
  arc(180:270:.6cm);
  \draw[fill=black] (t) circle (.02);
  \draw[very thin] (h1) ++(-.05,0) -- ++(.1,0);
  \draw[very thin] (h2) ++(-.05,0) -- ++(.1,0);

  \draw (t) ++(0,-.3cm) node {$S^n$};

  \draw[->] (t) ++(1cm,.6cm) -- node[above]{$*$}++(.6cm,0);
  \draw[cap=round,join=round] (0,0) 
  arc(-60:260:.4cm) 
  arc(-100:0:.03cm)
  node(x){}
  arc(0:80:.03cm)
  arc(260:-80:.34cm)
  arc(100:270:.03cm)
  arc(-90:0:1.55cm and .65cm)
  arc(0:180:.52cm and .49cm)
  arc(0:-85:.367cm and .602cm)
  --cycle;

  \draw[fill=black] (x) circle(.02);
  \draw (x) ++(.1cm,-.3cm) node{$S^1 \vee S^n$};
\end{tikzpicture}

Map which gives the action of $\pi_1$ on $\pi_n$.

(closeup)

\begin{tikzpicture}
% requires the "matrix" library
\matrix (m) [matrix of math nodes, row sep=2em, column sep=1.7pc, text
width=1pc, text height=1pc, text depth=.5pc] { 
X_0 & X_1 & X_2 & \cdots \\
}; 

% decimals control start and end positions of arrows
\path[<-] 
(m-1-1.15) edge node[above] {\tiny $p$}  (m-1-2.165)
(m-1-1.-15) edge (m-1-2.-165);
\path[<-]
(m-1-2.28) edge node[above] {\tiny $p$} (m-1-3.152)
(m-1-2) edge (m-1-3)
(m-1-2.-28) edge (m-1-3.-152);
\path[<-]
(m-1-3.37) edge node (t) {} node[above] {\tiny $p$} (m-1-4.143)
(m-1-3.-37) edge node (b) {} (m-1-4.-143);

\path[->]
(m-1-1) edge (m-1-2);
\path[->]
(m-1-2.15) edge (m-1-3.165)
(m-1-2.-15) edge (m-1-3.-165);


\path[dotted]
(t) edge (b);
\end{tikzpicture}

A simplicial object.