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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.

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Fibonacci numbers

Fibonacci Numbers

By: Anthony Chu

Kegan Dsouza

Thomas Ferranola

Paul

Vincent Roesch


Aim what are fibonacci numbers and how do they apply
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
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.



Why does this matter
Why does this matter? 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.

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
Miles to Kilometers. 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.

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
Complete Set 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.

  • -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:77100610


Fibonacci rules
Fibonacci Rules 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.

Fibonacci numbers have created trends like:

-Fibonacci numbers are usually about 1.618 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
More practical applications of Fibonacci numbers 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.

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
Applications 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.

-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 Nature. 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.

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
Quiz time! 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.

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


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