\begin{frame}
  \frametitle{Motivation and Overview}

  But what did the ancient Greek do with curved figures?
  \begin{center}
  \begin{tikzpicture}[default,scale=.7]
    \onslide<1,2>{
        \draw (0,0) circle (1cm);
    }

    \foreach \c in {2,3,4,5,6,7} {
      \setcounter{tmpcounter}{\c}
      \addtocounter{tmpcounter}{1}
      \onslide<\arabic{tmpcounter}->{
      \begin{scope}[xshift={(\c-2)*2.5cm}]
        \draw (0,0) circle (1cm);
        \inscribe{\c}
      \end{scope}
      }
    }
  \end{tikzpicture}
  \end{center}
  \pause
  They inscribed polygons into the figure:
  \begin{itemize}
  \foreach \c in {3,4,5} {
    \pause
      \pgfmathparse{1/2*\c*sin(360/\c)}
      \item first a polygon with $\c$ points $\implies$ area $A_\c = \pgfmathresult$,
  }
  \pause\pause\pause\pause
    \item \ldots      
    \foreach \c in {10,100} {
      \pgfmathparse{1/2*\c*sin(360/\c)}
      $A_{\c} = \pgfmathresult$,
    }\ldots
  \end{itemize}
  \pause\medskip
  
  If you continue, you will see:
  \begin{itemize}
  \pause
    \item the values get closer and closer to $\pi = 3.141 592 653 \ldots$
  \end{itemize}
  \pause
  \begin{block}{}
    Area $A$ of the circle is the \emph{limit} of the sequence $A_3,A_4,A_5,\ldots$
    \pause
    \begin{talign}
      \text{A} = \lim_{n\to\infty} A_n 
    \end{talign} 
  \end{block}
\end{frame}