1. Fibonacci Numbers By: Darrin Goldberg Sai Palati Alaina Lynch Allan Fridlikh

2. Background Info Fibonacci numbers were popularized by Leonardo Fibonacci. (1200 AD) The sequence of numbers was created in India, centuries before Fibonacci ever discovered them.

3. Aim- What are Fibonacci numbers ? Do now- How do you find Fibonacci numbers ?

4. The Basics Fibonacci numbers are a sequence of numbers that start off at 0 and 1. The sum of the previous two numbers is equal to the following number. Ex: 0,1,1,2,3,5,8,13,21,34,55. What are the next three numbers after 55 ? The formula for Fibonacci numbers is: F n = F n – 1 + F n - 2

5. Golden Ratio O The golden ratio is the number encountered when you are taking the ratio of distances in geometric figures such as the pentagon, the pentagram, decagon, and dodecahedron. O The formula for the golden ratio is ½(1+√5) The golden ratio is 1.618033988749895

6. Relationship to the Golden Ratio. O When you divide two consecutive numbers in the Fibonacci sequence you will get a number that is close to the Golden Ratio O As you keep on dividing the numbers in the Fibonacci sequence the numbers you get will get more and more closer to the Fibonacci sequence. O Ex. 21/13 = 1.615, 34/21 = 1.619

7. Fibonacci Numbers in nature O Fibonacci numbers are frequent in nature. O One example is the number of petals on a flower. O Some flowers have 1 petal. Some have 2 petals, some have 3, some have 5, some have 8 and so on. O This shows that the Fibonacci sequence is also in nature.

8. Recap Video O http://video.google.com/videoplay?docid=7 179950432887640376# http://video.google.com/videoplay?docid=7 179950432887640376#