FibonacciThe Fibonacci SequenceThe Golden Ratio

He Loves Me?• After picking off those

petals, what do you have left?

• Now try counting the number of spirals

Who is Fibonacci?• Leonardo of Pisa, or more

commonly, Fibonacci• Italian mathematician who

lived during the 12th century

• Spread the use of the hindu-arabic numbers in Europe

• Used the Fibonacci sequence in his book Liber Abaci

And the Sequence?•The first two terms of the sequence are 1

and 1•Each succeeding term is the sum of the

previous two terms, or (for n>=3)

•1, 1, 2, 3, 5, 8, 13, 21, 34

Applications•Choose any two numbers between 1 and

10.•Add these numbers like you would a

Fibonacci sequence.•The sum is…

The Golden Ratio•Suppose a and b are two consecutive

terms of the FS. Then the next term would be a+b

•Thus we have the ratio

•Solving for phi, we get

•To ten decimal places, this is 1.6180339887….

Interesting Properties•Look at the sum of the first n terms of the

sequence•Look at the sum of alternating terms of

the sequence•Look at multiple intervals•The squares of the Fibonacci Numbers•The PT

Binet’s Formula

The Most Beautiful

The United Nations

Le Corbusier (France)

In the Arts

Your Own Golden Rectangle•Create one using an index card!