Fibonacci Numbers By: Anthony Chu Kegan Dsouza Thomas Ferranola Paul Vincent Roesch

Aim: What are Fibonacci Numbers? And how do they apply. Do Now: Write out what you think Fibonacci numbers are in your own words. If you can, include a few Fibonacci numbers that you may know.

What did you get? Fibonacci numbers are numbers that take the previous two terms and use their sum as the next number. This is the Fibonacci number sequence: 0,1,1,2,3,4,8,13,21… As you can see, 1+0=1 so the term after 0,1 is 1 and 1+1 =2, so the term after 1,1 is 2.

A Fibonacci spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling; this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34.

Why does this matter? Fibonacci numbers have numerous applications in the world of math and can be seen in the Fibonacci Square. You can see that the numbers in the Square are representing terms In the Fibonacci numbers. These Boxes work in a counter-clock Wise spin, started with the 1 on the left.

Miles to Kilometers. Another great application of Fibonacci numbers is the conversion of miles to kilometers. The preceding term to the next term is the mile form of a kilometer measurement. For example: 8 and 13 are consecutive Fibonacci numbers and 8 miles = 13 kilometers.

Complete Set -Fibbonaci numbers are a complete set. -This means that you can form any integer with them in existence, like binary or decimal systems. -Try these:

Fibonacci Rules Fibonacci numbers have created trends like: -Fibonacci numbers are usually about of the previous number and about.618 of the following number -The GCF of two Fibonacci numbers is a Fibonacci number.

More practical applications of Fibonacci numbers Although Fibonacci numbers are cool in math, they are even cooler in real life applications such as : -Predicting breeding rates among animals -Stock analysts use Fibonacci numbers to make bank and… -In music, Fibonacci numbers are used to determining tunings.

Applications -Fibonacci numbers are seen in nature, on the linings of various pinecones, the petals on flowers, and the seeds on a sunflower. -Male drone bee lineage follows Fibbonacci numbers (each 1 drone bee has one parent, 2 grandparents, 3 great grandparents, and so forth), which is sometimes used by sophisticated bee keepers who want a rough population estimate. -As stated it was rarely used for primitive computing systems as there are binary/decimal/etc. computing systems. -Used by random number generators occasionally.

Fibonacci Nature. Fibonacci numbers also have a recurring presence in nature. Flowers often have a petal number of a Fibonacci number. Daisies are known to have 34,55 and 89 flower petals, all Fibonacci Numbers.

Quiz time! Complete the quiz that Kegan made, to the best of your ability.