1. 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.

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Presentation transcript:

1

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 Italy

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 …

5

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 The Greek Alphabet

8 This is  to 20 decimal places

This is  to 1000 decimal places

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

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

12

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 Rectangle Width (cm) Length (cm)   Width (cm) Golden rectangle? A  3.0 = Yes B  3.5 = No C  2.0 = Yes D  3.5 = Yes E  2.2 = No F  5.0 = 8.09 Yes

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

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

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

18

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.

20

21

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.

23

24

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

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.