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Fibonacci

Fibonacci. The Fibonacci Sequence The 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 12 th century

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Fibonacci

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  1. Fibonacci The Fibonacci Sequence The Golden Ratio

  2. He Loves Me? • After picking off those petals, what do you have left? • Now try counting the number of spirals

  3. 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

  4. 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

  5. Applications • Choose any two numbers between 1 and 10. • Add these numbers like you would a Fibonacci sequence. • The sum is…

  6. 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….

  7. 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

  8. Binet’s Formula

  9. The Most Beautiful

  10. The United Nations

  11. Le Corbusier (France)

  12. In the Arts

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

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