\documentclass[10pt,envcountsect]{beamer}
\mode<presentation> {\usetheme{Warsaw}}
\usepackage[english]{babel}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{pstricks,pstricks-add,pst-math}
\usepackage{tkz-tab}



\begin{document}

\title{Episode 09\\ Using variations to order numbers}
\subtitle{European section, season 1}
\date{}

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

%THE RULES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The rules}

{\large
\begin{center}
\begin{itemize}
\item Each of you has been given a number. 
\item Rank you on the first line according to your number.
\item Hey look at this ! What a beautiful variation table.
\item Return your card and rank you according to your new number.
\end{itemize}
\end{center}}
\end{frame}


%TABLE 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Move 1}

{\large
\begin{center}
{\small
\begin{tikzpicture}
\tkzTabInit[lgt=2,espcl=8]{$x$/1,$f(x)$/2}{$-10$,$10$}
\tkzTabVar{-//,+//}
\end{tikzpicture}
}
\end{center}}
\end{frame}

%TABLE 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Move 2}

{\large
\begin{center}
{\small
\begin{tikzpicture}
\tkzTabInit[lgt=2,espcl=8]{$x$/1,$f(x)$/2}{$-10$,$10$}
\tkzTabVar{+//,-//}
\end{tikzpicture}}
\end{center}}
\end{frame}


%TABLE 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Move 3}

{\large
\begin{center}
{\small
\begin{tikzpicture}
\tkzTabInit[lgt=2,espcl=4]{$x$/1,$f(x)$/2}{$-10$,$0$,$10$}
\tkzTabVar{+//,-//,+//}
\end{tikzpicture}}
\end{center}}
\end{frame}



%TABLE 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Move 4}

{\large
\begin{center}
{\small
\begin{tikzpicture}
\tkzTabInit[lgt=2,espcl=2]{$x$/1,$f(x)$/2}{$-10$,$-5$,$0$,$5$,$10$}
\tkzTabVar{-//,+//,-//,+//,-//}
\end{tikzpicture}}
\end{center}}
\end{frame}



%TABLE 5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Move 5}

{\large
\begin{center}
{\small
\begin{tikzpicture}
\tkzTabInit[lgt=2,espcl=1.3]{$x$/1,$f(x)$/2}{$-10$,$-7$, $-3$, $1$, $4$, $5$, $10$}
\tkzTabVar{+//,-//,+//,-D+//,-//,+//,-//}
\end{tikzpicture}}
\end{center}}
\end{frame}


%THE QUIZZ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The quizz : an example}

\Large
Compare the numbers $\cos(1)$ and $\cos(2)$.
\end{frame}

\begin{frame}{An example (continued)}
\Large
What function do we need  ?
$$x\mapsto \cos x$$
The graph of this function :
\begin{center}
\psset{xunit=1.0cm,yunit=2.0cm,dotstyle=*,algebraic=true,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
\begin{pspicture*}(-3.24,-1.2)(3.32,1.2)
\psaxes[xAxis=true,yAxis=false,Dx=1,Dy=1,ticksize=-2pt 0,subticks=2]{->}(0,0)(-3.24,-1.38)(3.32,1.82)
\psplot[plotpoints=200]{-3.24}{3.3200000000000003}{cos(x)}
\end{pspicture*}
\end{center}
\end{frame}

\begin{frame}{An example (continued)}

\Large
What interval do we need ?
\begin{center}
\psset{xunit=1.0cm,yunit=2.0cm,dotstyle=*,algebraic=true,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
\begin{pspicture*}(-3.24,-1.2)(3.32,1.2)
\psaxes[xAxis=true,yAxis=false,Dx=1,Dy=1,ticksize=-2pt 0,subticks=2]{->}(0,0)(-3.24,-1.38)(3.32,1.82)
\psplot[plotpoints=200]{-3.24}{3.3200000000000003}{cos(x)}
\psline[linestyle=dashed](1,0)(1,0.5403)
\psline[linestyle=dashed](2,0)(2,-0.4161)
\end{pspicture*}
\end{center}
The interval $[0,\pi]$.
\end{frame}

\begin{frame}{An example (continued)}

\Large
Over the interval $[0,\pi]$, the functions $x\mapsto\cos x$ is {\bf decreasing}.\\
So, as $1<2$, 
$$\cos(1)\geq \cos(2).$$
\end{frame}

\begin{frame}
\begin{center}
{\Huge The Quizz}
\end{center}
\end{frame}



\begin{frame}\begin{center}
\Huge $\pi^2$ and $9$
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge $\sin(2.3)$ and $\sin(2.7)$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge $\left(\displaystyle\frac{3}{4}\right)^2$ and $\left(\displaystyle\frac{5}{4}\right)^2$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\left(\displaystyle\frac{1}{4}\right)^3-\displaystyle\frac{1}{4}$ and $\left(\displaystyle\frac{4}{17}\right)^3-\displaystyle\frac{4}{17}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$0.98^3-0.98$ and $1.02^3-1.02$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\displaystyle\frac{1}{2.17}$ and $-\displaystyle\frac{1}{2.17}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\left(-2.5\right)^3+2.5$ and $\left(-\pi\right)^3\pi$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\displaystyle\frac{1}{\left(-2.01\right)^2}$ and $\displaystyle\frac{1}{\left(-1.99\right)^2}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\displaystyle\frac{1}{\pi}$ and $\displaystyle\frac{1}{4}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\sqrt{7}$ and $\sqrt{10}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\sin(0)$ and $\sin(-\pi)$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\sqrt{5.17}$ and $\sqrt{5.71}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\left(-2.17\right)^2$ and $\left(-1.5\right)^2$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\sin(-3)$ and $\sin(-2)$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$-\displaystyle\frac{1}{\sqrt{7}}$ and $-\displaystyle\frac{1}{\sqrt{10}}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\sin(-1)$ and $\sin(1)$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\displaystyle\frac{1}{\pi^2}$ and $\displaystyle\frac{1}{3.15^2}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$1.1^2$ and $\left(-1.1\right)^2$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\sqrt{\pi+2}$ and $\sqrt{6}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge$\displaystyle\frac{1}{0.75^2}$ and $\displaystyle\frac{1}{0.66^2}$.
\end{center}\end{frame}


\begin{frame}
\begin{center}
{\Huge The answers\\}
\bigskip
{\LARGE Mark 1 point for every good answer.}
\end{center}
\end{frame}

\begin{frame}\begin{center}
\Huge
$\pi^2\geq 9$
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\sin(2.3)\geq\sin(2.7)$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\left(\displaystyle\frac{3}{4}\right)^2\leq\left(\displaystyle\frac{5}{4}\right)^2$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\left(\displaystyle\frac{1}{4}\right)^3-\displaystyle\frac{1}{4}\leq\left(\displaystyle\frac{4}{17}\right)^3-\displaystyle\frac{4}{17}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$0.98^3-0.98\leq 1.02^3-1.02$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\displaystyle\frac{1}{2.17}\geq-\displaystyle\frac{1}{2.17}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\left(-2.5\right)^3+2.5\geq\left(-\pi\right)^3\pi$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\displaystyle\frac{1}{\left(-2.01\right)^2}\leq\displaystyle\frac{1}{\left(-1.99\right)^2}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\displaystyle\frac{1}{\pi}\geq\displaystyle\frac{1}{4}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\sqrt{7}\leq\sqrt{10}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\sin(0)=\sin(-\pi)$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\sqrt{5.17}\leq\sqrt{5.71}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\left(-2.17\right)^2\geq\left(-1.5\right)^2$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\sin(-3)\geq\sin(-2)$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$-\displaystyle\frac{1}{\sqrt{7}}\leq-\displaystyle\frac{1}{\sqrt{10}}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\sin(-1)\leq\sin(1)$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\displaystyle\frac{1}{\pi^2}\geq\displaystyle\frac{1}{3.15^2}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$1.1^2=\left(-1.1\right)^2$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\sqrt{\pi+2}\leq\sqrt{6}$.
\end{center}\end{frame}

\begin{frame}\begin{center}
\Huge
$\displaystyle\frac{1}{0.75^2}\leq\displaystyle\frac{1}{0.66^2}$.
\end{center}\end{frame}




\end{document}
