The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence...
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The Fibonacci Sequence
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Transcript of The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence...
![Page 1: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/1.jpg)
The Fibonacci Sequence
![Page 2: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/2.jpg)
The Fibonacci Sequence
Leonardo Fibonacci(1170 – 1250)
First from the West, but lots of evidence from before his time
![Page 3: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/3.jpg)
The Fibonacci Sequence
1, 1, 2, 3, 5, 8, 13, …
The current term is found by adding the previous two
![Page 4: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/4.jpg)
The Fibonacci Sequence
Originated from a question he had about rabbit population
![Page 5: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/5.jpg)
The Fibonacci Sequence
What’s special about it?
If we continue the sequence… and take the limit of the ratio to infinity…
![Page 6: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/6.jpg)
The Fibonacci Sequence
We find a ratio that is approximately 1.61803399
This is known as the GOLDEN Ratio
![Page 7: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/7.jpg)
The Fibonacci Sequence
This ratio can be found in nature…
![Page 8: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/8.jpg)
![Page 9: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/9.jpg)
![Page 10: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/10.jpg)
The Golden Rectangle
![Page 11: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/11.jpg)
![Page 12: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/12.jpg)
![Page 13: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/13.jpg)
The Fibonacci Sequence
This ratio can be found in art…
![Page 14: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/14.jpg)
![Page 15: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/15.jpg)
![Page 16: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/16.jpg)
![Page 17: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.](https://reader036.fdocuments.in/reader036/viewer/2022081417/56649f515503460f94c74b5a/html5/thumbnails/17.jpg)
And many other places…