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}

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\begin{document}

\title{Episode 16 -- Cross sections of a cube}
\subtitle{European section -- Season 2}
\date{}

\begin{frame}
  \titlepage
\end{frame}


\begin{frame}{What is a plane section ?}

\Large

\begin{itemize}
\item A solid (a cube for example).
\item A plane intersecting the solid.
\end{itemize}

The section is :\\ 
The polygon whose sides are the segments intersections of the plane with
each of the polyhedron's faces. \\

\end{frame}


\begin{frame}{Method}
\large

What we must find :
\begin{itemize}
\item The intersection of the plane of section with each face of the cube.
\item The intersection of the plane of section with each edge of the cube.
\end{itemize}

\end{frame}

\begin{frame}{Method}
\large

\begin{center}
An example :\\
\includegraphics[scale=0.8]{images/beamer1.eps}
\end{center}

\end{frame}

\begin{frame}{Method}
\large

\begin{center}
Rule 1 : You can join two points of the section if they are on the same face.\\
\includegraphics[scale=0.8]{images/beamer2.eps}
\end{center}

\end{frame}

\begin{frame}{Method}
\large

\begin{center}
Rule 2 : When a line of the section plane is in a face, and a third point is on a face with an edge in
common, you can draw the intersection of the line with the common edge.\\
\includegraphics[scale=0.8]{images/beamer3.eps}
\end{center}

\end{frame}

\begin{frame}{Method}
\large

\begin{center}
Rule 3 : When a line of the section plane is in a face, you can build its
intersection with an edge of the face.\\
\includegraphics[scale=0.8]{images/beamer4.eps}
\end{center}

\end{frame}

\begin{frame}{Method}
\large

\begin{center}
Rule 1.\\
\includegraphics[scale=0.8]{images/beamer5.eps}
\end{center}

\end{frame}

\begin{frame}{Method}
\large

\begin{center}
Rule 1.\\
\includegraphics[scale=0.8]{images/beamer6.eps}
\end{center}

\end{frame}

\begin{frame}{Method}
\large

\begin{center}
Rule 4 : When a line of the section plane is in a face and a point of the section plane is on a parallel face,
you can draw the parallel to the line passing through that point.\\
\includegraphics[scale=0.8]{images/beamer7.eps}
\end{center}

\end{frame}

\begin{frame}{Method}
\large

\begin{center}
Rule 3 and rule 1.\\
\includegraphics[scale=0.8]{images/beamer8.eps}
\end{center}

\end{frame}

\begin{frame}{Method}
\large

\begin{center}
Rule 1.\\
\includegraphics[scale=0.8]{images/beamer9.eps}
\end{center}

\end{frame}

\begin{frame}{Method}
\large

\begin{center}
The section is done.\\
\includegraphics[scale=0.8]{images/beamer10.eps}
\end{center}

\end{frame}

\begin{frame}{The four rules}
\large
\pause

\begin{description}
\item[Rule 1 :] You can join two points of the section if they are on the same face.\pause
\item[Rule 2 :] When a line of the section plane is in a face, and a third point is on a face with an edge in
common, you can draw the intersection of the line with the common edge.\pause
\item[Rule 3 :] When a line of the section plane is in a face, you can build its
intersection with an edge of the face.\pause
\item[Rule 4 :] When a line of the section plane is in a face and a point of the section plane is on a parallel face,
you can draw the parallel to the line passing through that point.
\end{description}


\end{frame}


\end{document}
