The number ϕ

Season 02 • Episode 10 • The number ϕ

⁰

The number ϕ

Season 02

Episode 10 Time frame 2 periods

Prerequisites :

^{Sequenes,arithmetiandgeometrisequenes}

Objectives :

•

^{Workon listeningskills.}

•

^Culturalintrodution tothe Golden Ratio.

Materials :

•

^{Audio reording of the program Fivenumbers by SimonSingh.}

•

^{Struture of the radio program(for the teaher)}

•

^{Questions : onseparated papers and onone global answer sheet.}

•

^{Beamer with the answers} illustrated. Elementsof orretion of the test oradded.

1 – Listening to a radio program 30 mins

Students listen to a radio program three times. First, the teaher introdues the people

appearing inthe program :

•

^{Simon Singh, author who has speialised in writingabout} mathematialand sienti topis inan aessible manner.

•

^{Ian Stewart, professor of mathematis at the University of Warwik, England, and a}

widely known popular-siene writer.

•

^{Robin Wilson, Math historian atthe Open University}

•

^{Adam Spener,Australian radio DJ with a penhant for pure} mathematis.

•

^{Ron Knott, University of Surey, speialist of the Fibonainumbers.}

First time : Theylistentotheprogram,withsomesmallbreaks,withoutknowingwhat

questions are going to beasked. They may take notes.

Seond time : A list of fourorthree questions is given to eah student, tofous on for

the seond time. They are given time to write down their answers preisely.

Third time : Theomplete listof questionsisgiven tothestudentsbeforethe lasttime

they listen tothe program. But they're not allowed to writeanything down during

this last part.

Document Answer sheet

1

^{. What doesIan Stewart allthe Platonist onept of the ideal world?}

2

^{. Howdid the Anient Greek dene the number}

π

^?

3

^{. What wasthe preferred way of the Anient Greek totalk about strange numbers}

suh as

π

^or

ϕ

^?

4

^{. What is an irrationalnumber?}

5

^{. What} approximate value to 6DP of

ϕ

^{is given by Ian Stewart?}

6

^{. What are the other names of the GoldenRatio?}

7

^{. What did the Anient Greek regardas the perfet retangle?}

8

^{. Why wasthe retangle built using the GoldenRatio onsidered perfet?}

9

^{. Where did Leonardo Da Vinisee the GoldenRatio?}

10

^{. Whih modern painter used repeatedly the GoldenRatio?}

11

^{. What famous Greek buildingis referred toin this program? Why?}

12

^{. What is the danger of lookingfor the Golden Ratio everywhere?}

13

^{. Whih famous modern arhitetused the GoldenRatio} extensively?

Season 02 • Episode 10 • The number ϕ

²

15

^{. Howis the DNA spiral involving the Golden Ratio?}

16

^{. What gure is reated by the retangles introdued by Adam Spener?}

17

^{. Where is this gure appearingin nature?}

18

^{. What doyouget ifyousquare theGolden Ratio?What if youtakeitsreiproal?}

19

^{. Why doesthe Golden Ratio havethis property?}

20

^{. What proess desribed by RonKnott ends up with the Golden Ratio?}

21

^{. Who wasFibonai?}

22

^{. Howis the Fibonaisequene built?}

23

^{. Initially,what phenomenon were the Fibonainumbers modelled on?}

24

^{. Why are the Fibonainumbers so important inmathematis?}

25

^{. What is the link between Fibonainumbers and ar-parks?}

26

^{. What is the link between Fibonainumbers and sunowers?}

27

^{. What is the link between Fibonainumbers and pineapples?}

28

^{. What is the relation between Fibonai numbers and the GoldenRatio?}

Document 1

^{Groups of fourquestions}

1

^{. What does Ian Stewart all the Platonist onept of the ideal world?}

2

^{. What} approximate value to 6DP of

ϕ

^{is given by Ian Stewart?}

3

^{. Where did Leonardo Da Vini see the Golden Ratio?}

4

^{. Whih famous modern arhitet used the Golden Ratio} extensively?

1

^{. Where is the spiral appearing in nature?}

2

^{. Who was Fibonai?}

3

^{. What is the link between Fibonai numbers and ar-parks?}

4

^{. How did the Anient Greek dene the number}

π

^?

1

^{. What are the other names of the Golden Ratio?}

2

^{. Whih modern painter used repeatedly the Golden Ratio?}

3

^{. Why an we hear a heartbeat in the program?}

4

^{. What do you get if you square the Golden Ratio?}

What if you take its reiproal?

1

^{. How is the Fibonai sequene built?}

2

^{. What is the link between Fibonai numbers and sunowers?}

3

^{. WhatwasthepreferredwayoftheAnientGreektotalkaboutstrange}

numbers suh as

π

^or

ϕ

^?

4

^{. What did the Anient Greek regard as the perfet retangle?}

1

^{. What famous Greek building is referred to in this program? Why?}

2

^{. How is the DNA spiral involving the Golden Ratio?}

3

^{. Why does the Golden Ratio have this property?}

4

Season 02 • Episode 10 • The number ϕ

⁴

1

^{. What is the link between Fibonai numbers and pineapples?}

2

^{. What is an irrational number?}

3

^{. Whywas the retanglebuilt usingtheGolden Ratioonsideredperfet?}

4

^{. What is the danger of looking for the Golden Ratio everywhere?}

1

^{. What gure is reated by the retangles introdued by Adam Spener?}

2

^{. What proess desribed by Ron Knott ends up with the Golden Ratio?}

3

^{. Why are the Fibonai numbers so important in mathematis?}

4

^{. Whatisthe relationbetweenFibonainumbersandthe GoldenRatio?}

Document 2

^{Plan of the radio program}

Part I The Golden Ratio (Simon Singh, author who has speialised in writing about

mathematialand sientitopisinanaessiblemanner,IanStewart, professorof

mathematis atthe University of Warwik, England, and a widely known popular-

siene and siene-tion writer. Robin Wilson, Math historianat the Open Uni-

versity)

PartII PlaeswheretheGoldenRatioanbefound(SimonSingh,IanStewart, Adam

Spener, Australianradio DJ witha penhant forpure mathematis).

PartIIIPropertiesofthe number(SimonSingh,RobinWilson, RonKnott,University

of Surey, speialist about the Fibonainumbers).

Part IV The Fibonainumbers (Adam Spener)

Part V  Fibonainumbers in parking meters(Simon Singh and RonKnott)

Fibonainumbers in sunowers (IanStewart)

Fibonainumbers in pineaples (SimonSingh)

Part VI Fibonainumbers and the Golden Ratio (SimonSingh)