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The Fibonacci Sequence

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Page 1: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time

The Fibonacci Sequence

Page 2: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time

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

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

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

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

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

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
Page 9: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time
Page 10: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time

The Golden Rectangle

Page 11: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time
Page 12: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time
Page 13: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time

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
Page 15: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time
Page 16: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time
Page 17: The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time

And many other places…


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