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2. 2 Leonardo of Pisa (1170 – 1250 AD) was an Italian mathematician. He is sometimes called Fibonacci. Fibonacci is famous for helping to spread the use of Hindu Arabic numbers in Europe. These numbers replaced the Roman number system.

3. 3 Italy

4. 4 There is a special sequence of numbers called the Fibonacci sequence because Fibonacci wrote about this sequence. 0, 1, 1, 2, 3, 5,5, 8,13,21 …

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6. 6 The Fibonacci numbers can be used to calculate the value of a special number called the golden number. The golden number cannot be written down exactly because it is a decimal number that goes on for ever without any recurring pattern. Because the golden number cannot be written down exactly we use the 21 st letter of the Greek alphabet,  or phi to represent the golden number.  to 20 decimal places

7. 7 The Greek Alphabet

8. 8 This is  to 20 decimal places 1.618 033 988 749 894 848 20

9. 9 1. 618033988749894848204586834365638117720309179805762862 135448622705260462818902449707207204189391137484754088075 386891752126633862223536931793180060766726354433389086595 939582905638322661319928290267880675208766892501711696207 032221043216269548626296313614438149758701220340805887954 454749246185695364864449241044320771344947049565846788509 874339442212544877066478091588460749988712400765217057517 978834166256249407589069704000281210427621771117778053153 171410117046665991466979873176135600670874807101317952368 942752194843530567830022878569978297783478458782289110976 250030269615617002504643382437764861028383126833037242926 7526311653392473167111211588186385133162038400522216579128 667529465490681131715993432359734949850904094762132229810 172610705961164562990981629055520852479035240602017279974 717534277759277862561943208275051312181562855122248093947 123414517022373580577278616008688382952304592647878017889 921990270776903895321968198615143780314997411069260886742 96226757560523172777520353613936 This is  to 1000 decimal places

10. 10 Egypt It is thought that the Egyptians may have known about  over 2500 years

11. 11 Some people think that the Egyptians used  in the design of the Great pyramid of Giza which was completed about 2500 years ago.

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13. 13 Any rectangle that has a length that is  times the width is called a golden rectangle w l This is a golden rectangle because l =   w

14. 14 Rectangle Width (cm) Length (cm)   Width (cm) Golden rectangle? A3.04.9 1.618  3.0 = 4.854 Yes B3.56.7 1.618  3.5 = 5.663 No C2.03.2 1.618  2.0 = 3.236 Yes D3.55.7 1.618  3.5 = 5.663 Yes E2.27.0 1.618  2.2 = 3.5596 No F5.08.1 1.618  5.0 = 8.09 Yes

15. 15 Greece People in Greece knew about golden rectangles about 2500 years ago.

16. 16 The Parthenon is a temple that was built about 2500 years ago on the Acropolis in Athens, Greece.

17. 17 Many golden rectangles can be found in the design of the Parthenon.

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19. 19 France The west face of the cathedral of Notre Dame in Paris which was completed in the 13 th century contains many golden rectangles.

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22. 22 India The Taj Mahal In Agra in India was completed in around 1648 AD. Many golden rectangles can be found in the Taj Mahal.

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25. 25 Honduras The Mayan people have lived in the countries that are now Mexico, Guatemala and Honduras for thousands of years. Guatemala Mexico

26. 26 It is thought that the Mayan people used golden rectangles in their architecture. This is part of the Maya ruins of Copan in Honduras.