\begin{frame} \frametitle{Motivation and Overview} How to compute the area of a polygon? \begin{center} \begin{tikzpicture}[default,scale=.5] \begin{scope}[inner sep=0,outer sep=0] \draw (0,0) -- node[at start] (1) {} ++(-3,-1) -- node[at start] (2) {} ++(-1,-2) -- node[at start] (3) {} ++ (1,-2) -- node[at start] (4) {} ++(3,-1) -- node[at start] (5) {} node[at end] (6) {} ++ (2,3) -- cycle; \end{scope} \begin{scope}[cred,dashed] \mpause[2]{ \draw (6) -- node[pos=.7] (m1) {} node[pos=.5] (m1') {} (2); \draw (6) -- node[pos=.7] (m2) {} (3); \draw (6) -- node[pos=.7] (m3) {} node[pos=.5] (m3') {} (4); } \mpause[3]{ \node at ($(1)!.5!(m1')$) {$A_1$}; \node at ($(m1)!.5!(m2)$) {$A_2$}; \node at ($(m2)!.5!(m3)$) {$A_3$}; \node at ($(m3')!.5!(5)$) {$A_4$}; } \end{scope} \end{tikzpicture} \end{center} \pause The ancient Greek did it as follows: \begin{itemize} \pause \item divide the polygon into triangles \pause \item compute the area of the triangles (and sum them up) \end{itemize} \end{frame}