\documentclass[12pt]{article}
\usepackage[Mickael]{ammaths}
\begin{document}
\module{The number $\varphi$}{02}{10}{2 periods}
\en
\prereq{Sequences, arithmetic and geometric sequences}
\object{\begin{itemize}
\item Work on listening skills.
\item Cultural introduction to the Golden Ratio.
\end{itemize}}
\mater{\begin{itemize}
\item Audio recording of the program ``Five numbers'' by Simon Singh.
\item Structure of the radio program (for the teacher)
\item Questions : on separated papers and on one global answer sheet.
\item Beamer with the answers illustrated. Elements of correction of the test or added.
\end{itemize}}
\modpart{Listening to a radio program}{30 mins}
Students listen to a radio program three times. First, the teacher introduces the people appearing in the program :
\begin{itemize}
\item Simon Singh, author who has specialised in writing about mathematical and scientific topics in an accessible manner.
\item Ian Stewart, professor of mathematics at the University of Warwick, England, and a widely known popular-science writer.
\item Robin Wilson, Math historian at the Open University
\item Adam Spencer, Australian radio DJ with a penchant for pure mathematics.
\item Ron Knott, University of Surey, specialist of the Fibonacci numbers.
\end{itemize}
\begin{description}
\item[First time :] They listen to the program, with some small breaks, without knowing what questions are going to be asked. They may take notes.
\item[Second time :] A list of four or three questions is given to each student, to focus on for the second time. They are given time to write down their answers precisely.
\item[Third time :] The complete list of questions is given to the students before the last time they listen to the program. But they're not allowed to write anything down during this last part.
\end{description}
\pagebreak
\moddocdis{The number $\varphi$}{02}{10}{Answer sheet}
\newcommand{\anscell}{\smallskip\\
\hspace*{-1.2cm}
\begin{tabular}{|p{15.6cm}|}
\hline
\rule{0pt}{15pt}\\[5pt]
\hline
\end{tabular}
}
\begin{enumerate}
\item What does Ian Stewart call the Platonist concept of the ideal world ?
\anscell
\item How did the Ancient Greek define the number $\pi$ ?
\anscell
\item What was the preferred way of the Ancient Greek to talk about ``strange'' numbers such as $\pi$ or $\varphi$ ?
\anscell
\item What is an irrational number ?
\anscell
\item What approximate value to 6DP of $\varphi$ is given by Ian Stewart ?
\anscell
\item What are the other names of the Golden Ratio ?
\anscell
\item What did the Ancient Greek regard as the perfect rectangle ?
\anscell
\item Why was the rectangle built using the Golden Ratio considered perfect ?
\anscell
\item Where did Leonardo Da Vinci see the Golden Ratio ?
\anscell
\item Which modern painter used repeatedly the Golden Ratio ?
\anscell
\item What famous Greek building is referred to in this program ? Why ?
\anscell
\item What is the danger of looking for the Golden Ratio everywhere ?
\anscell
\item Which famous modern architect used the Golden Ratio extensively ?
\anscell
\item Why can we hear a heartbeat in the program ?
\anscell
\item How is the DNA spiral involving the Golden Ratio ?
\anscell
\item What figure is created by the rectangles introduced by Adam Spencer ?
\anscell
\item Where is this figure appearing in nature ?
\anscell
\item What do you get if you square the Golden Ratio ? What if you take its reciprocal ?
\anscell
\item Why does the Golden Ratio have this property ?
\anscell
\item What process described by Ron Knott ends up with the Golden Ratio ?
\anscell
\item Who was Fibonacci ?
\anscell
\item How is the Fibonacci sequence built ?
\anscell
\item Initially, what phenomenon were the Fibonacci numbers modelled on ?
\anscell
\item Why are the Fibonacci numbers so important in mathematics ?
\anscell
\item What is the link between Fibonacci numbers and car-parks ?
\anscell
\item What is the link between Fibonacci numbers and sunflowers ?
\anscell
\item What is the link between Fibonacci numbers and pineapples ?
\anscell
\item What is the relation between Fibonacci numbers and the Golden Ratio ?
\anscell
\end{enumerate}
\pagebreak
\moddoc{Groups of four questions}
{\large
\hrule
\bigskip
\begin{enumerate}
\item What does Ian Stewart call the Platonist concept of the ideal world ?
\item What approximate value to 6DP of $\varphi$ is given by Ian Stewart ?
\item Where did Leonardo Da Vinci see the Golden Ratio ?
\item Which famous modern architect used the Golden Ratio extensively ?
\end{enumerate}
\bigskip
\hrule
\bigskip
\begin{enumerate}
\item Where is the spiral appearing in nature ?
\item Who was Fibonacci ?
\item What is the link between Fibonacci numbers and car-parks ?
\item How did the Ancient Greek define the number $\pi$ ?
\end{enumerate}
\bigskip
\hrule
\bigskip
\begin{enumerate}
\item What are the other names of the Golden Ratio ?
\item Which modern painter used repeatedly the Golden Ratio ?
\item Why can we hear a heartbeat in the program ?
\item What do you get if you square the Golden Ratio ?\\ What if you take its reciprocal ?
\end{enumerate}
\bigskip
\hrule
\bigskip
\begin{enumerate}
\item How is the Fibonacci sequence built ?
\item What is the link between Fibonacci numbers and sunflowers ?
\item What was the preferred way of the Ancient Greek to talk about ``strange'' numbers such as $\pi$ or $\varphi$ ?
\item What did the Ancient Greek regard as the perfect rectangle ?
\end{enumerate}
\bigskip
\hrule
\bigskip
\begin{enumerate}
\item What famous Greek building is referred to in this program ? Why ?
\item How is the DNA spiral involving the Golden Ratio ?
\item Why does the Golden Ratio have this property ?
\item Initially, what phenomenon were the Fibonacci numbers modelled on ?
\end{enumerate}
\pagebreak
\hrule
\bigskip
\begin{enumerate}
\item What is the link between Fibonacci numbers and pineapples ?
\item What is an irrational number ?
\item Why was the rectangle built using the Golden Ratio considered perfect ?
\item What is the danger of looking for the Golden Ratio everywhere ?
\end{enumerate}
\bigskip
\hrule
\bigskip
\begin{enumerate}
\item What figure is created by the rectangles introduced by Adam Spencer ?
\item What process described by Ron Knott ends up with the Golden Ratio ?
\item Why are the Fibonacci numbers so important in mathematics ?
\item What is the relation between Fibonacci numbers and the Golden Ratio ?
\end{enumerate}
\bigskip
\hrule
}
\pagebreak
\moddoc{Plan of the radio program}
\begin{description}
\item{Part I --} The Golden Ratio (Simon Singh, author who has specialised in writing about mathematical and scientific topics in an accessible manner,
Ian Stewart, professor of mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer.
Robin Wilson, Math historian at the Open University)
\item{Part II -- } Places where the Golden Ratio can be found (Simon Singh, Ian Stewart, Adam Spencer, Australian radio DJ with a penchant for pure mathematics).
\item{Part III --} Properties of the number (Simon Singh, Robin Wilson, Ron Knott, University of Surey, specialist about the Fibonacci numbers).
\item{Part IV --} The Fibonacci numbers (Adam Spencer)
\item{Part V -- } Fibonacci numbers in parking meters (Simon Singh and Ron Knott)\\
Fibonacci numbers in sunflowers (Ian Stewart)\\
Fibonacci numbers in pineaples (Simon Singh)
\item{Part VI --} Fibonacci numbers and the Golden Ratio (Simon Singh)
\end{description}
\end{document}