\documentclass[xcolor={hyperref,table},hyperef={naturalnames,pdfpagelabels},french,envcountsect
]{beamer}
\usepackage{etex}
\usepackage[beamer,utf8,grec]{preambule}


\usepackage[encapsulated]{CJK}
\usepackage{ucs}
\usepackage{athnum}
\usepackage{fancyhdr,bclogo}
\usepackage{linknodes}

\let\Cross\undefined
\usepackage{bbding,picins}




\newcommand\ath[1]{\foreignlanguage{greek}{\athnum{#1}}}



\let\vert\undefined
\usepackage{mathabx}
\newcommand{\mathbfont}{\usefont{U}{mathb}{m}{n}}


\usepackage{akkadian}
\newcommand{\babun}{{\AKK\dish}}
\newcommand{\babdeux}{{\AKK\min}}
\newcommand{\babtrois}{{\AKK\eshV}}
\newcommand{\babquatre}{{\AKK\shaII}}
\newcommand{\babcinq}{{\AKK\iaII}}
\newcommand{\babsix}{{\AKK\ashIII}}
\newcommand{\babsept}{{\AKK\imin}}
\newcommand{\babhuit}{{\AKK\ussu}}
\newcommand{\babneuf}{{\AKK\geshilimmu}}
\newcommand{\babdix}{{\AKK\AKKu}}
\newcommand{\babvingt}{{\AKK\man}}
\newcommand{\babtrente}{{\AKK\esh}}
\newcommand{\babquarante}{{\AKK\ninV}}
\newcommand{\babcinquante}{{\AKK\ninnu}}

\usepackage{hieroglf}
\newcommand{\hun}{{\LARGE\pmglyph{\Hone}}}
\newcommand{\hdix}{{\LARGE\pmglyph{\Hten}}}
\newcommand{\hcent}{{\LARGE\pmglyph{\Hhundred}}}
\newcommand{\hmil}{{\LARGE\pmglyph{\Hthousand}}}
\newcommand{\hdixmil}{{\LARGE\pmglyph{\HXthousand}}}
\newcommand{\hcentmil}{{\LARGE\pmglyph{\HCthousand}}}
\newcommand{\hmillion}{{\LARGE\pmglyph{\Hmillion}}}



\usepackage{CJK}
\newcommand\japonais[1]{\begin{CJK}{UTF8}{song}#1\end{CJK}}
\newcommand{\jzero}{\japonais{〇}}
\newcommand{\jun}{\japonais{一}}
\newcommand{\jdeux}{\japonais{二}}
\newcommand{\jtrois}{\japonais{三}}
\newcommand{\jquatre}{\japonais{四}}
\newcommand{\jcinq}{\japonais{五}}
\newcommand{\jsix}{\japonais{六}}
\newcommand{\jsept}{\japonais{七}}
\newcommand{\jhuit}{\japonais{八}}
\newcommand{\jneuf}{\japonais{九}}
\newcommand{\jdix}{\japonais{十}}
\newcommand{\jcent}{\japonais{百}}
\newcommand{\jmil}{\japonais{千}}
\newcommand{\jdixmil}{\japonais{万}}
\newcommand{\jdixiem}{\japonais{割}}
\newcommand{\jcentiem}{\japonais{分}}
\newcommand{\jmiliem}{\japonais{厘}}
\newcommand{\jcentmillion}{\japonais{おく}}
\newcommand{\jgiga}{\japonais{ちょお}}


%%%% un peu de giac/xcas

\makeatletter
\newcommand{\executGiacmp}[1]{
\immediate\write18{giac  <#1 } }
\makeatother

\begin{VerbatimOut}{XCASjaptex.cxx}
testjap(n):={
ifte(n=="0","zero",
ifte(n=="1","\\jun",ifte(n=="2","\\jdeux",ifte(n=="3","\\jtrois",ifte(n=="4","\\jquatre",ifte(n=="5","\\jcinq",ifte(n=="6","\\jsix",ifte(n=="7","\\jsept",ifte(n=="8","\\jhuit","\\jneuf"))))))))
)
}:;

japtex(n):={
puis:=["","\\jdix","\\jcent","\\jmil","\\jdixmil","\\jcentmil","\\jmillion","\\jdixmillion","\\jcentmillion","\\jmilliard","\\jdixmilliard","\\jcentmilliard","\\jgiga"]
n:=string(n);
N:=NULL;for(j:=0;j<size(n);j++){N:=N,n[j]};N:=[N];
NN:=NULL;for(k:=0;k<size(N);k++){NN:=NN,ifte(testjap(N[k])=="zero","",concat(testjap(N[k]),puis[size(N)-k-1]))};
L:="":;for(k:=0;k<size(NN);k++){L:=concat(L,NN[k])};
return(L);
}:;

japop(L):={
local r,n,m,opp;
n:=L[0];m:=L[1];opp:=L[2];
r:=expr(n+opp+m);
return(japtex(n)+"  "+opp+"  "+japtex(m)+"  =  "+japtex(r));
}

\end{VerbatimOut}



\begin{VerbatimOut}{XCASjaptex.giac}
maple_mode(0);
read("XCASjaptex.cxx");
Sortie:=fopen("XCASjaptex.tex");
donnees:=read("XCASjaptex.user");
donnees:=donnees[0];
Resultat:=cat("japtex(",donnees);
Resultat:=cat(Resultat,");");
Resultat:=expr(Resultat);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}

\newenvironment{japtex}
{\VerbatimEnvironment\begin{VerbatimOut}{XCASjaptex.user}}
{\end{VerbatimOut}
           \executGiacmp{XCASjaptex.giac}

\input{XCASjaptex}
}



\begin{VerbatimOut}{XCASjapop.giac}
maple_mode(0);
read("XCASjaptex.cxx");
Sortie:=fopen("XCASjapop.tex");
donnees:=read("XCASjapop.user");
Resultat:=cat("japop(",donnees);
Resultat:=cat(Resultat,");");
Resultat:=expr(Resultat);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}

\newenvironment{japop}
{\VerbatimEnvironment\begin{VerbatimOut}{XCASjapop.user}}
{\end{VerbatimOut}
           \executGiacmp{XCASjapop.giac}

\input{XCASjapop}
}



%%% liste des nombres en binaires de no a n


\begin{VerbatimOut}{XCASbibeam.cxx}
bibeam(NN):={
n:=NN[0];
L:="0";
for(k:=1;k<=n;k++){
B:=revlist(convert(k,base,2));
nb:=size(B)-1;
LB:="";
for(j:=0;j<=nb;j++){LB:=LB+string(B[j])};
L:=L+"\\uncover<"+k+"->{ - "+LB+"}\\ "; 
}
return(L);
}:;
\end{VerbatimOut}

\begin{VerbatimOut}{XCASbibeam.giac}
maple_mode(0);
read("XCASbibeam.cxx");
Sortie:=fopen("XCASbibeam.tex");
donnees:=read("XCASbibeam.user");
Resultat:=cat("bibeam(",donnees);
Resultat:=cat(Resultat,");");
Resultat:=expr(Resultat);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}



\newenvironment{bibeam}
{\VerbatimEnvironment\begin{VerbatimOut}{XCASbibeam.user}}
{\end{VerbatimOut}
           \executGiacmp{XCASbibeam.giac}

\input{XCASbibeam}
}




%%bibin->dec

\begin{VerbatimOut}{XCASbibine.cxx}
bibine(N):={
n:=N[0];
ib:=convert(n,base,2);
bi:=revlist(ib);
while(size(ib) mod 4!=0){ib:=append(ib,0)};
if(n==0){ib:=[0,0,0,0]};
bibi:=NULL;
for(k:=0;k<size(ib);k:=k+4){
     if(ib[k..k+1]==[0,0]){bibi:=bibi,O}else{
         if(ib[k..k+1]==[1,0]){bibi:=bibi,A}else{
               if(ib[k..k+1]==[0,1]){bibi:=bibi,E}else{
                      bibi:=bibi,I}
}
}
    if(ib[k+2..k+3]==[0,0]){bibi:=bibi,H}else{
       if(ib[k+2..k+3]==[1,0]){bibi:=bibi,B}else{
              if(ib[k+2..k+3]==[0,1]){bibi:=bibi,K}else{
                    bibi:=bibi,D}
}
}
};
nbi:=size(bi)-1;
BI:="";
for(j:=0;j<=nbi;j++){BI:=BI+string(bi[j])};

bibi:=revlist([bibi]);
nbibi:=size(bibi)-1;
BIBI:="";
for(j:=0;j<=nbibi;j++){BIBI:=BIBI+string(bibi[j])};

RE:=[["En decimale",n],["En binaire",BI],["En bibinaire",BIBI]];

return("$"+latex(RE)+"$");
}:;
\end{VerbatimOut}

\begin{VerbatimOut}{XCASbibine.giac}
maple_mode(0);
read("XCASbibine.cxx");
Sortie:=fopen("XCASbibine.tex");
donnees:=read("XCASbibine.user");
Resultat:=cat("bibine(",donnees);
Resultat:=cat(Resultat,");");
Resultat:=expr(Resultat);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}


\newenvironment{bibine}
{\VerbatimEnvironment\begin{VerbatimOut}{XCASbibine.user}}
{\end{VerbatimOut}
           \executGiacmp{XCASbibine.giac}

\input{XCASbibine}
}


%%% dec->bibin

\begin{VerbatimOut}{XCASenibib.cxx}
bibine(n):={
ib:=convert(n,base,2);
while(size(ib) mod 4!=0){ib:=append(ib,0)};
if(n==0){ib:=[0,0,0,0]};
bibi:=NULL;
for(k:=0;k<size(ib);k:=k+4){
     if(ib[k..k+1]==[0,0]){bibi:=bibi,O}else{
         if(ib[k..k+1]==[1,0]){bibi:=bibi,A}else{
               if(ib[k..k+1]==[0,1]){bibi:=bibi,E}else{
                      bibi:=bibi,I}
}
}
    if(ib[k+2..k+3]==[0,0]){bibi:=bibi,H}else{
       if(ib[k+2..k+3]==[1,0]){bibi:=bibi,B}else{
              if(ib[k+2..k+3]==[0,1]){bibi:=bibi,K}else{
                    bibi:=bibi,D}
}
}
};

bibi:=revlist([bibi]);

return(bibi);        
}:;

enibib(L):={
   local N,k;
   decod:=table(seq(bibine(k)=k,k=0..15));
   N:=0;p:=0;
   pour k de size(L)-2 jusque 0 pas -2 faire
   N:=N+decod[L[k..k+1]]*16^p;
   p:=p+1;
   fpour;
   N:=simplifier(N);
   bi:=revlist(convert(N,base,2));
   nbi:=size(bi)-1;
   BI:="";
   for(j:=0;j<=nbi;j++){BI:=BI+string(bi[j])};
   nbibi:=size(L)-1;
   BIBI:="";
   for(j:=0;j<=nbibi;j++){BIBI:=BIBI+string(L[j])};

RE:=[["En bibinaire",BIBI],["En binaire",BI],["En decimale",N]];

return("$"+latex(RE)+"$");
}:;
\end{VerbatimOut}



\begin{VerbatimOut}{XCASenibib.giac}
maple_mode(0);
read("XCASenibib.cxx");
Sortie:=fopen("XCASenibib.tex");
donnees:=read("XCASenibib.user");
Resultat:=cat("enibib(",donnees);
Resultat:=cat(Resultat,");");
Resultat:=expr(Resultat);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}

\newcounter{enib}
\newcommand{\tenib}{\theenib}
\newenvironment{enibib}
{\VerbatimEnvironment\begin{VerbatimOut}{XCASenibib.user}}
{\end{VerbatimOut}
\immediate\write18{rm  XCASenibib.tex}
           \executGiacmp{XCASenibib.giac}
%\immediate\write18{rm -f XCASenibib\tenib.tex}
\immediate\write18{cp XCASenibib.tex  XCASenibib\tenib.tex}
\input{XCASenibib\tenib}
\stepcounter{enib}
}



%% tableau correspondance dec/bin/bibin


\begin{VerbatimOut}{XCAStabib.cxx}
bibine(n):={
local ib,bibi,k;
ib:=convert(n,base,2);
while(size(ib) mod 4!=0){ib:=append(ib,0)};
if(n==0){ib:=[0,0,0,0]};
bibi:=NULL;
for(k:=0;k<size(ib);k:=k+4){
     if(ib[k..k+1]==[0,0]){bibi:=bibi,O}else{
         if(ib[k..k+1]==[1,0]){bibi:=bibi,A}else{
               if(ib[k..k+1]==[0,1]){bibi:=bibi,E}else{
                      bibi:=bibi,I}
}
}
    if(ib[k+2..k+3]==[0,0]){bibi:=bibi,H}else{
       if(ib[k+2..k+3]==[1,0]){bibi:=bibi,B}else{
              if(ib[k+2..k+3]==[0,1]){bibi:=bibi,K}else{
                    bibi:=bibi,D}
}
}
};

bibi:=revlist([bibi]);

return(bibi)        
}:;

tabib(LLL):={
local L,k,j,no,n,bb,nbb,lbb,BB,nBB,lBB;
no:=LLL[0];
n:=LLL[1];
L:=[["En decimale"],["En binaire"],["En bibinaire"]];
L[0]:=append(L[0],seq(k,k=no..n));
for(k:=no;k<=n;k++){
bb:=revlist(convert(k,base,2));
if(k==0){bb:=[0]};
nbb:=size(bb)-1;
lbb:="";
for(j:=0;j<=nbb;j++){lbb:=lbb+string(bb[j])};
L[1]:=append(L[1],lbb);
BB:=bibine(k);
nBB:=size(BB)-1;
lBB:="";
for(j:=0;j<=nBB;j++){lBB:=lBB+string(BB[j])};
L[2]:=append(L[2],lBB);
}
return("$"+latex(L)+"$");
}:;
\end{VerbatimOut}



\begin{VerbatimOut}{XCAStabib.giac}
maple_mode(0);
read("XCAStabib.cxx");
Sortie:=fopen("XCAStabib.tex");
donnees:=read("XCAStabib.user");
Resultat:=cat("tabib(",donnees);
Resultat:=cat(Resultat,");");
Resultat:=expr(Resultat);
fprint(Sortie,Unquoted,Resultat);
fclose(Sortie);
\end{VerbatimOut}




\newcounter{tabi}
\newcommand{\ttabi}{\thetabi}
\newenvironment{tabib}
{\VerbatimEnvironment\begin{VerbatimOut}{XCAStabib.user}}
{\end{VerbatimOut}
\immediate\write18{rm XCAStabib.tex}
           \executGiacmp{XCAStabib.giac}
\immediate\write18{cp XCAStabib.tex  XCAStabib\ttabi.tex}
\input{XCAStabib\ttabi}
\stepcounter{tabi}
}












\newcommand\frbal[3]{\  {\Large{\textifsym{#1}}}\!\!\!
\raisebox{1ex}{\resizebox{8pt}{9pt}{$\frac{{\rm \textifsym{#2}}}{{\rm \textifsym{#3}}}$}}\,}

\usepackage{casio,ti83font,keystroke,xlop} 













\usepackage{tikz}

\usetikzlibrary{calc}
%\usepackage[xcas]{pro-courbes}
\usepackage{numprint}
%\usepackage[french,vlined]{algorithm2e}
\usepackage{cclicenses}
\usepackage{cclicence}
%\usepackage{docacompleter}



% \newcommand{\cacheb}[1]{\dotfill\textcolor{white}{#1}\textcolor{white}{#1}}
% \newcommand{\cacheg}[1]{\dotfill\textcolor{0.9white}{#1}\textcolor{0.9white}{#1}} 

% \newcommand{\cachegg}[1]{\dots\dots\textcolor{0.8white}{#1}\textcolor{0.8white}{#1}} 
\newcolumntype{A}{>{\arraybackslash}X}

\usepackage{textcomp}
\usepackage{mathtools}
%\usepackage[xcas]{pro-statdiv}

\hypersetup{
pdftitle={Activités mathématiques en 1L}, % title
}



\graphicspath{{/home/moi/Figures/figuresTS/}{/home/moi/Photos/Tehessin/}{/home/moi/Figures/FigSTI/}{/home/moi/Alice/figures3/}{/home/moi/Alice/figures3/newcourbes/}{/home/moi/Alice/figures/}{/home/moi/Figures/figuresAlice/}{/home/moi/Photos/Maths/}{/home/moi/Lycee/TS/}{/home/moi/Lycee/TS/2009_10/}{/home/moi/Figures/FigMaple/}{/home/moi/Figures/figuresTS/newcourbes/}{/home/moi/Figures/FigEspace/}}





%\setcounter{tocdepth}{4}







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\setlength{\headheight}{23pt}
\setlength{\parindent}{0pt}



\setlength{\columnseprule}{0pt}

\graphicspath{{/home/moi/Lycee/2nde/2009_10/}{/home/moi/Photos/Maths/}{/home/moi/Figures/FigSTI/}{/home/moi/Figures/FigSeconde/}{/home/moi/Figures/figuresTS/}{/home/moi/Lycee/TDmaple/2007_8/}{/home/moi/IREM/IREM10_06_09/}}


\mode<presentation>
{
  \usetheme[secheader]{Madrid}
  % or ...Warsaw

  \setbeamercovered{highly dynamic}
  % or whatever (possibly just delete it)
}
\usepackage{elephantbird}



\begin{document}


\title[1\up{ère}L] % (optional, use only with long paper titles)
{Maths, histoire, littérature et cinéma}

\subtitle{ }

\author[] % (optional, use only with lots of authors)
{Guillaume CONNAN  }
% - Give the names in the same order as the appear in the paper.
% - Use the inst{?} command only if the authors have different
%   affiliation.

\institute{ Lycée Jean Perrin}% (optional, but mostly needed)

%\logo{\includegraphics[scale=0.15]{big_connan}}

\date[] % (optional, should be abbreviation of conference name)
{\today}
% - Either use conference name or its abbreviation.
% - Not really informative to the audience, more for people (including
%   yourself) who are reading the slides online

\subject{ }


\beamerdefaultoverlayspecification{<+->}

% \AtBeginSubsubsection[]
% {
%   \begin{frame}<beamer>
%     \frametitle{Sommaire}
%  {\scriptsize
% \begin{multicols}{2}
%     \tableofcontents[currentsection,currentsubsection]
%        \end{multicols}
% }

%   \end{frame}
% }




% \AtBeginSubsection[]
% {
%   \begin{frame}<beamer>
%     \frametitle{Sommaire}
%  {\scriptsize
% \begin{multicols}{2}
%     \tableofcontents[currentsection,currentsubsection]
%        \end{multicols}
% }

%   \end{frame}
% }





\AtBeginSection[]
{
  \begin{frame}<beamer>
    \frametitle{Sommaire}
 {\scriptsize
\begin{multicols}{2}
    \tableofcontents[currentsection]
       \end{multicols}
}

  \end{frame}
}


% If you wish to uncover everything in a step-wise fashion, uncomment
% the following command: 

\beamerdefaultoverlayspecification{<+->}







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


\section{L'année dernière à Marienbad}


\begin{frame}
  %\begin{figure}
\begin{center}
  \includegraphics[height=4cm]{resnais2}
\end{center}
%\end{figure}


\href{http://www.dailymotion.com/video/xa92dg\_l-annee-derniere-a-marienbad-1\_music?start=867}{\beamergotobutton{L'EXTRAIT}}



\end{frame}






\section{L'Égypte antique}
\subsection{Le système de numération de l'Égypte antique}





\begin{frame}
\begin{itemize}
\item   \hun :~représente 1

\item \hdix :~représente 10

\item \hcent :~représente 100

\item \hmil :~représente 1000

\item \hdixmil :~représente 10000

\item \hcentmil :~représente 100000

\item \hmillion :~représente 1000000
\end{itemize}
\end{frame}




\begin{frame}[fragile]
\begin{NodesList}
  \hmil \hmil \hmil \AddNode \\
  \hcent \hcent \hcent \hcent \hcent \hcent \hcent \hcent \hcent \AddNode\\
 \hdix \hdix \hdix\hdix \hdix \hdix \hdix \AddNode\\
 \hun \hun\hun\hun\hun\hun\hun \AddNode\\
  \uncover<6->{{\bfseries \textcolor{red}{3977}}} \AddNode%
\uncover<2->{\LinkNodes{\textcolor{white}{3000}}}
\uncover<3->{\LinkNodes{\textcolor{white}{+900}}}
\uncover<4->{\LinkNodes{\textcolor{white}{+70}}}
\uncover<5->{\LinkNodes{\textcolor{white}{+7}}}
\end{NodesList}


\end{frame}





\subsection{L'addition égyptienne}
\begin{frame}
  \hcentmil \hcentmil \hcentmil \hcentmil  \hmil \hmil \hcent \hcent  \hcent \hcent \hcent
\hcent \hcent \hun \hun \hun  \hun \hun \hun \hun \hun \hun
\uncover<2->{$\ \Longrightarrow 402\, 709$}

\uncover<3->{ $+$ \hmillion \hmillion \hmillion \hcentmil \hcentmil \hdixmil \hdixmil \hmil \hmil \hcent \hcent \hdix \hdix \hdix \hdix \hun \hun \hun \hun \hun \hun}
\uncover<4->{$\ \Longrightarrow 3\, 222\, 246$}


\vspace{1cm}

\uncover<5->{\Large $=3\,624\,955$}

\end{frame}



\subsection{La multiplication égyptienne}



\begin{frame}

\hdix \hdix \hdix \hdix \hdix \hun \hun \hun = \hdix \hdix \hdix \hun \hun + \hdix \hun \hun \hun \hun
             \hun \hun + \hun \hun \hun \hun +\hun.

\pause

  \begin{center}
             \begin{tabular}{*{3}{|l}|}
	     \hline
             \XSolidBrush & \hun & \hcent \hcent \hdix \hdix \hdix \hun \hun \hun \hun \hun\\
                   & \hun \hun & \hcent \hcent\hcent \hcent\hdix \hdix \hdix\hdix \hdix \hdix\hdix\\
              \XSolidBrush   &   \hun   \hun\hun   \hun&   \hcent   \hcent\hcent\hcent   \hcent\hcent\hcent
              \hcent\hcent\hdix \hdix \hdix\hdix\\
                   &  \hun \hun\hun  \hun\hun \hun\hun  \hun& \hmil  \hcent \hcent\hcent\hcent\hcent
                   \hcent\hcent\hcent \hdix \hdix \hdix\hdix\hdix \hdix \hdix\hdix\\
              \XSolidBrush & \hdix \hun \hun\hun\hun \hun\hun&\hmil\hmil\hmil \hcent \hcent\hcent\hcent\hcent
                   \hcent\hcent \hdix \hdix \hdix\hdix\hdix \hdix\\
              \XSolidBrush     &    \hdix\hdix\hdix  \hun\hun   &     \hmil\hmil\hmil\hmil\hmil\hmil\hmil    \hcent
              \hcent\hcent\hcent\hcent\hdix\hdix\\

             \hline
             \end{tabular}
             \end{center}

\end{frame}



\subsection{La division égyptienne}

\begin{frame}
  \begin{center}
             \begin{tabular}{*{3}{|l}|}
	     \hline
              & \hdix \hdix\hdix \hdix\hdix \hdix \hun\hun\hun \hun\hun & \hun\hun\hun \hun\hun \\
              \hline
 \XSolidBrush & \hun & \hun\hun\hun \hun\hun \\
              & \hun \hun & \hdix \\
 \XSolidBrush & \hun \hun\hun \hun & \hdix\hdix\\
\XSolidBrush & \hun \hun\hun \hun\hun \hun\hun \hun & \hdix\hdix\hdix\hdix\\

\hline
             \end{tabular}
             \end{center}
\end{frame}



\subsection{les fractions égyptiennes}
\begin{frame}
  \begin{center}
  \includegraphics[height=4.5cm]{oeilhorus.pdf}
\end{center}

\end{frame}


\section{Numération athénienne}



\begin{frame}
  \begin{itemize}
\item 2 se note \ath{2}
\item 5 se note \ath{5}
\item 9 se note \ath{9}
\item 17 se note \ath{17}
\item 43 se note \ath{43}
\item 438 se note \ath{438}
\item 782 se note \ath{782}
\item 1997 se note \ath{1997}
\item 6284 se note \ath{6284}
\end{itemize}
\end{frame}


\section{Babylone}

\subsection{La numération babylonienne}

\begin{frame}
  
Lisez les nombres suivants~:



\begin{itemize}
\item \babtrente\babhuit 

\item \babcinquante\babtrois 

\item \babvingt\babneuf
\end{itemize}

\end{frame}


\begin{frame}
  \begin{itemize}
  \item \babtrois \ \babvingt\babtrois

\item \babdeux\ \babdix\babneuf \ \babtrente\babcinq


\item \babdix\babcinq + \babquarante\babcinq = \babun

\item \babdeux $\times$ \babun\babtrente $=$ \babtrois
  \end{itemize}
\end{frame}


\subsection{Multiplication babylonienne}


\begin{frame}
  
\begin{center}
  \includegraphics[width=.75\linewidth]{tablebab2.pdf}
\end{center}
\end{frame}


\begin{frame}


\begin{center}
  \includegraphics[height=7cm]{numbab.1}
\end{center}

\end{frame}


\section{Les Mayas}

\subsection{Numération}

\begin{frame}
  Essayez  de décrire  leur  système de  numération sachant  que~:  6 s'écrit  $\maya{6}$, 13  s'écrit
$\maya{13}$, 24  s'écrit $\maya{24}$,  30 s'écrit $\maya{30}$,  65 s'écrit $\maya{65}$,  232 s'écrit
$\maya{232}$, 400 s'écrit $\maya{400}$, 512 s'écrit $\maya{512}$, 8600 s'écrit $\maya{8600}$.
\end{frame}










\subsection{La «~cinquième opération~»}
\begin{frame}
  


Regardons comment s'écrit 35 : \emph{  holhucakal}.  On peutle décomposer en ho.lahun ti+u-ca-KAL ce
qui se
traduit mot à mot par : «~15 vers 2\eme vingt~».

\pause


Appelons-la «~mayation~»~:~que donne la mayation de

\begin{itemize}
\item $\maya{5}$ et $\maya{60}$
\item  $\maya{16}$  et $\maya{120}$
\end{itemize}

\end{frame}












\section{La numération sino-japonaise}




\subsection{Comptons}


\begin{frame}
\begin{itemize}
\item 7 s'écrit \jsept
\item 20 s'écrit \jdeux \jdix
\item 24 s'écrit \jdeux \jdix \jquatre
\item 26 s'écrit \jdeux \jdix \jsix
\item 40 s'écrit \jquatre\jdix
\item 75 s'écrit \jsept\jdix \jcinq
\item 11 s'écrit \jdix \jun
\item 98 s'écrit \jneuf\jdix\jhuit
\item 308 s'écrit \jtrois \jcent \jhuit au Japon et \jtrois \jcent \jzero\jhuit en Chine
\item 3008 s'écrit \jtrois \jmil \jhuit au Japon et \jtrois \jmil \jzero\jhuit en Chine
\item 30008 s'écrit \jtrois \jdixmil \jhuit  au Japon et \jtrois \jdixmil \jzero\jhuit en Chine
\item 0,3 s'écrit \jtrois \jdixiem
\item 0,03 s'écrit \jtrois \jcentiem
\item 0,003 s'écrit \jtrois \jmiliem
\end{itemize}
\end{frame}





\begin{frame}
  \begin{center}
             \begin{tabularx}{\textwidth}{Y{9}}
	     \whline
             Ch. & \jzero&\jun&\jdeux&\jtrois&\jquatre&\jcinq&\jsix&\jsept&\jhuit&\jneuf\\
\hline
Ar.&0&&&&&&&7&&\\

             \whline
             \end{tabularx}
             \end{center}

\begin{center}
             \begin{tabularx}{\textwidth}{Y{8}}
	     \whline
             Ch.&\jdix&\jcent&\jmil&\jdixmil&\jcentmillion&\jgiga&\jdixiem&\jcentiem&\jmiliem\\
          \hline
Ar.&&&&&$10^8$&$10^{12}$&&&\\

             \whline
             \end{tabularx}
             \end{center}

\end{frame}




\begin{frame}[fragile]
  

\begin{japop}
8250,7054,"+"
\end{japop}

\uncover<2->{8250}
\uncover<3->{$+$}
\uncover<4->{$7054$}
\uncover<5->{$=$}
\uncover<6->{$15\,304$}

\end{frame}


\begin{frame}[fragile]


\begin{japop}
8,12,"*"
\end{japop}


\uncover<2->{8}
\uncover<3->{$\times$}
\uncover<4->{$ 12$}
\uncover<5->{$=$}
\uncover<6->{$96$}

\end{frame}

\begin{frame}[fragile]


\begin{japop}
128,4,"/"
\end{japop}


\uncover<2->{128}
\uncover<3->{$\div$}
\uncover<4->{$ 4$}
\uncover<5->{$=$}
\uncover<6->{$32$}


\end{frame}









\section{La numération shadock}
\begin{frame}
Les shadoks n'ont que quatre mots pour compter : GA, BU, ZO et MEU. 



\begin{center}
  \includegraphics[height=6cm]{gabuzo.jpg}
\end{center}



Malgré leur faible cerveau, ils
ont réussi à se débrouiller :

\href{http://www.youtube.com/watch?v=fQ8rPlksAu8}{\beamergotobutton{SHADOKS}} 




\end{frame}






\section{La numération... des ordinateurs}



\subsection{Comment compter avec des 0 et des 1~?}

\begin{frame}[fragile]

\begin{bibeam}
28
\end{bibeam}



  
\end{frame}










\subsection{Paquets}


\begin{frame}
  \begin{center}
    
{\LARGE \Bicycle\Bicycle\Bicycle\Bicycle\Bicycle\Bicycle\Bicycle\Bicycle\Bicycle\Bicycle\Bicycle}

  \end{center}
\end{frame}










\subsection{La table des Égyptiens}
\begin{frame}
\begin{center}
             \begin{tabularx}{\textwidth}{Y{9}}
	     \whline
             $2^0$&$2^1$&$2^2$&$2^3$&$2^4$&$2^5$&$2^6$&$2^7$&$2^8$&$2^9$&$2^{10}$\\
\hline
                  & &&&&&&&&&\\
             \whline
             \end{tabularx}
             \end{center}
\end{frame}
\subsection{Une méthode plus générale}

\begin{frame}[fragile]
  
\begin{center}
\opidiv[displayintermediary=all,voperation=top]{37}{4}
\end{center}

\pause

\begin{center}
  \includegraphics{Nombres.pdf}
\end{center}

\pause

\begin{center}
  \opidiv[style=text]{37}{4}
\end{center}


\end{frame}


\begin{frame}[fragile]
  \begin{center}
\textbf<5>{\opidiv[remainderstyle=\bfseries\large\color{gray},resultstyle=\color{blue}]{11}{2}}
\hspace{0.5cm}
\uncover<2->{\textbf<6>{\opidiv[remainderstyle=\bfseries\large\color{gray},resultstyle=\color{blue}]{5}{2}}\hspace{0.5cm}}
\uncover<3->{\textbf<7>{\opidiv[remainderstyle=\bfseries\large\color{gray},resultstyle=\color{blue}]{2}{2}}\hspace{0.5cm}}
\uncover<4->{\opidiv[remainderstyle=\bfseries\large\color{gray},resultstyle=\color{blue}]{1}{2}}
\end{center}

\begin{align*}
\uncover<5->{11 &=\Bigl(2\times5+1\Bigr)}
\uncover<6->{\\ &=\Bigl(2\times\bigl(2\times2+1\bigr)+1\Bigr)}
\uncover<7->{\\ &=\Bigl(2\times\bigl(2\times(2\times 1)+1\bigr)+1\Bigr)}
\uncover<8->{\\ &=\Bigl(2\times 2^2+1\Bigr)}
\uncover<9->{\\ &=2^3+2+1}
\uncover<10->{\\ &=1\times 2^3+0\times 2^2+1\times 2^1+1\times 2^0 }
\end{align*}



\uncover<11->{L'écriture de 11 en base 2 est donc 1011}

\end{frame}



\section{La numération des Mickey}
\begin{frame}
  {\LARGE
  \Football\Football\Football\Football\Football\Football\Football\Football\Football\Football\Football
  \Football\Football\Football\Football\Football\Football\Football\Football\Football\Football\Football }

\end{frame}

\section{Le code bibinaire}






\begin{frame}[fragile]

\tiny

  \begin{tabib}
0,12
  \end{tabib}

\pause

 \begin{tabib}
13,22
  \end{tabib}

\pause

 \begin{tabib}
23,31
  \end{tabib}

\pause

\large

\begin{center}
 \dots 
\end{center}


\pause

\tiny

\begin{tabib}
253,259
  \end{tabib}

\pause

\begin{tabib}
4094,4098
  \end{tabib}




\end{frame}




\normalsize



\begin{frame}[fragile]
  \begin{bibine}
1177
  \end{bibine}

\medskip

\pause

\begin{enibib}
K,E,K,I,D,I,B,I,B,I
\end{enibib}

\medskip

\pause

\begin{enibib}
K,E,B,O,K,A,D,O
\end{enibib}



\end{frame}


\section{Notion de base}

\subsection{On n'est pas des Mickey}


\begin{frame}
  Un nombre s'écrit \textbf<5->{\textcolor{yellow}{5}}\textbf<4->{\textcolor{blue}{7}}\textbf<3->{\textcolor{red}{4}}\textbf<2->{\textcolor{gray}{3}} en base \textcolor{green}{10}, cela signifie qu'il est égal à :

\[
\uncover<2->{\textcolor{gray}{3}\times \textcolor{green}{10}^0}
\uncover<3->{+\textcolor{red}{4}\times \textcolor{green}{10}^1}
\uncover<4->{+\textcolor{blue}{7}\times \textcolor{green}{10}^2}
\uncover<5->{+\textcolor{yellow}{5}\times \textcolor{green}{10}^3}
\]
\end{frame}



\subsection{Les bases à travers les âges}


\begin{frame}
\tiny
\begin{NodesList}[marge=1cm]
  \[
             \begin{array}{lllllll}
	     \hline
            \text{ Décimal}%&Égypte
&\text{Babylone}&\text{Athénien}&\text{Maya}&\text{Japonais}&\text{Binaire}&\text{Bibinaire} \\
\hline
\uncover<2->{\vtab 13%&\hdix\hun\hun\hun
&\text{\babdix\babtrois}&\text{\ath{13}}&\maya{13}&\text{\jdix\jtrois}&1101&DA%  &  \textcolor{white}{.}
\AddNode\AddNode[2]\AddNode[3]\AddNode[4]\AddNode[5]\\}
\uncover<4->{\vtab 130%&\hcent\hdix\hdix\hdix
&\text{\babdeux \ \babdix}& \text{\ath{130}}& \maya{130} & \text{\jcent\jtrois\jdix}
  &10000010&KOHE % & \textcolor{white}{.}
  \AddNode\\}
\uncover<6->{\vtab 26%&\hdix\hdix\hun\hun\hun\hun\hun\hun
&\text{\babvingt\babsix}&\text{\ath{26}}&\maya{26}&\text{\jdeux\jdix\jsix}&11010&HAKE
  % & \textcolor{white}{.} 
  \AddNode[2]\\}
\uncover<8->{\vtab 208%&\hcent\hcent\hun\hun\hun\hun\hun\hun\hun\hun
&\text{\babtrois\
  \babvingt\babsix}&\text{\ath{208}}&\maya{208}&\text{\jdeux\jcent\jhuit}&11010000&DAHO % & \textcolor{white}{.}
\AddNode[3]\\}
\uncover<10->{\vtab 260%&\hcent\hcent\hdix\hdix\hdix\hdix\hdix\hdix
&\text{\babquatre\
  \babvingt}&\text{\ath{260}}&\maya{260}&\text{\jdeux\jcent\jsix\jdix}&100000100&HAHOBO % &  \textcolor{white}{.} 
\AddNode[4]\\}
\uncover<12->{\vtab 780%&\hcent\hcent\hcent\hcent\hcent\hcent\hcent\hdix\hdix\hdix\hdix\hdix\hdix\hdix\hdix
&\text{\babdix\babtrois}&\text{\ath{780}}&\maya{780}&\text{\jsept\jcent\jhuit\jdix}&1100001100&HIHODO
% & \textcolor{white}{.}
\AddNode[5]\\
\hline}


\end{array}
             \]

\tikzstyle{ArrowStyle}+=[<->,blue]

\visible<3-4>{\LinkNodes[]{$\times10$}}
\visible<5-6>{\LinkNodes[]{$\times2$}}
\visible<7-8>{\LinkNodes[]{$\times16$}}
\visible<9-10>{\LinkNodes[]{$\times20$}}
\visible<11-12>{\LinkNodes[]{$\times60$}}

\end{NodesList}

\normalsize

\end{frame}


  

\section{Le jeu de Marienbad}


\begin{frame}
  \href{http://www.crocodilus.org/jeux/allumettes/nim.htm}{\beamergotobutton{Jouons}}
\end{frame}



\section{FLATLAND}



\href{http://www.youtube.com/watch?v=Y9KT4M7kiSw}{\beamergotobutton{Carl Sagan}}



\end{document}

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