Fibonacci NumbersFibonacci Numbers

By: Anthony ChuBy: Anthony ChuKegan DsouzaKegan Dsouza

Thomas FerranolaThomas FerranolaPaulPaul

Vincent RoeschVincent Roesch

Aim: What are Fibonacci Numbers? Aim: What are Fibonacci Numbers? And how do they apply. And how do they apply.

Do Now: Write out what you think Fibonacci Do Now: Write out what you think Fibonacci numbers are in your own words. If you numbers are in your own words. If you can, include a few Fibonacci numbers that can, include a few Fibonacci numbers that you may know. you may know.

What did you get?What did you get?

Fibonacci numbers are numbers that take Fibonacci numbers are numbers that take the previous two terms and use their sum the previous two terms and use their sum as the next number. This is the Fibonacci as the next number. This is the Fibonacci number sequence:number sequence:

0,1,1,2,3,4,8,13,21…0,1,1,2,3,4,8,13,21…

As you can see, 1+0=1 so the term after 0,1 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. is 1 and 1+1 =2, so the term after 1,1 is 2.

A Fibonacci spiral A Fibonacci spiral created by drawing created by drawing circular arcs circular arcs connecting the connecting the opposite corners of opposite corners of squares in the squares in the Fibonacci tiling; this Fibonacci tiling; this one uses squares of one uses squares of sizes 1, 1, 2, 3, 5, 8, sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34.13, 21, and 34.

Why does this matter?Why does this matter?

Fibonacci numbers have numerous applications in Fibonacci numbers have numerous applications in the world of math and can be seen in the the world of math and can be seen in the Fibonacci Square. Fibonacci Square.

You can see that the numbers in the Square are representing terms In the Fibonacci numbers.

These Boxes work in a counter-clockWise spin, started with the 1 on the left.

Miles to Kilometers. Miles to Kilometers.

Another great application of Fibonacci Another great application of Fibonacci numbers is the conversion of miles to numbers is the conversion of miles to kilometers. The preceding term to the next kilometers. The preceding term to the next term is the mile form of a kilometer term is the mile form of a kilometer measurement. For example:measurement. For example:

8 and 13 are consecutive Fibonacci 8 and 13 are consecutive Fibonacci numbers and 8 miles = 13 kilometers. numbers and 8 miles = 13 kilometers.

Complete SetComplete Set

-Fibbonaci numbers are a complete set.-Fibbonaci numbers are a complete set.-This means that you can form any integer with -This means that you can form any integer with them in existence, like binary or decimal them in existence, like binary or decimal systems.systems.-Try these:-Try these:7777

100100

610610

Fibonacci RulesFibonacci Rules

Fibonacci numbers have created trends like:Fibonacci numbers have created trends like:

-Fibonacci numbers are usually about 1.618 -Fibonacci numbers are usually about 1.618 of the previous number and about .618 of of the previous number and about .618 of the following numberthe following number

-The GCF of two Fibonacci numbers is a -The GCF of two Fibonacci numbers is a Fibonacci number.Fibonacci number.

More practical applications of More practical applications of Fibonacci numbersFibonacci numbers

Although Fibonacci numbers are cool in Although Fibonacci numbers are cool in math, they are even cooler in real life math, they are even cooler in real life applications such as :applications such as :

-Predicting breeding rates among animals-Predicting breeding rates among animals

-Stock analysts use Fibonacci numbers to -Stock analysts use Fibonacci numbers to make bank and…make bank and…

-In music, Fibonacci numbers are used to -In music, Fibonacci numbers are used to determining tunings. determining tunings.

ApplicationsApplications

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

Fibonacci Nature.Fibonacci Nature.

Fibonacci numbers also have a recurring Fibonacci numbers also have a recurring presence in nature.presence in nature.

Flowers often have a petal number of a Flowers often have a petal number of a Fibonacci number. Daisies are known to Fibonacci number. Daisies are known to have 34,55 and 89 flower petals, all have 34,55 and 89 flower petals, all Fibonacci Numbers. Fibonacci Numbers.

Quiz time!Quiz time!

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