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Aim: Fibonacci Numbers

Aim: Fibonacci Numbers. Jason Iannelli Jessica Zukhovich Patrick Blancero Dennis Lytkine. Fibonacci Series.

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Aim: Fibonacci Numbers

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  1. Aim: Fibonacci Numbers Jason Iannelli Jessica Zukhovich Patrick Blancero Dennis Lytkine

  2. Fibonacci Series The first two numbers in the series are one and one. To obtain each number of the series, you simply add the two numbers that came before it. In other words, each number of the series is the sum of the two numbers preceding it. 1,1,2,3,5,8,etc.

  3. Golden Ratio Taking any two consecutive Fibonacci numbers and placing them in a ratio , you end up wit a ratio very close to the golden ratio

  4. Golden Rectangle The Golden Rectangle, alleged to be the most aesthetically pleasing rectangular shape possible, when squared, leaves another Golden Rectangle behind.

  5. Fibonacci Spiral The Fibonacci Spiral is a geometric spiral whose growth is regulated by the Fibonacci Series. Its sudden, almost exponential growth parallels the rapid growth of the series itself.

  6. Applications

  7. Solve Find the missing number(s) in each sequence: 1.) 0, 1, 1, 2, 3, 5, 8, ___, 21, 34,... 2.) ...55, 89, ___, 233, ___, 610,... 3.) ...610, 987, ___, ___, 4181,... 4.) …10946, ___, 28657, ___, 75025, ___...

  8. Solve this too 3 ÷ 2 =   5 ÷ 3 =               8 ÷ 5 =             13 ÷ 8 =                 21 ÷ 13= 

  9. What is a real life application of Fibonacci's numbers? …………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………----------------------------------------------------------------------------------------------------------

  10. Answer What are other types of functions of the Fibonacci Series that apply to other math topics?

  11. Solve this! If you do, you get a cookie. A man puts a pair of baby rabbits into an enclosed garden. Assuming each pair of rabbits bears two new rabbits every month and that it takes a month for the rabbits to reach maturity, how many rabbits will there be in the garden after one year?

  12. Solution At the end of the first month, they mate, but there is still one only 1 pair.  At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.  At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.         At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs. And so on…

  13. Where’s my cookie? 268!

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