The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. This integer sequence can be found throughout nature, such as the spiral patterns of seashells and seed arrangements in sunflowers that are based on the golden ratio of 1.618. The Fibonacci sequence was first studied by Indian mathematicians around 200 BC and introduced to Western Europe in 1202 by Leonardo Fibonacci, who discovered the sequence in the patterns of breeding rabbits.

1. The Fibonacci Sequence
It's as easy as 1, 1, 2, 3...

2. What is the Fibonacci Sequence?
The Fibonacci sequence is a series of numbers that follow a
unique integer sequence.
These numbers generate mathematical patterns that can be
found in all aspects of life.
The patterns can be seen in everything from the human body to
the physiology of plants and animals.

3. How does the Fibonacci Sequence Work?
The Fibonacci sequence is derived from the Fibonacci numbers. The Fibonacci
numbers are as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...and so on.
These numbers are obtained by adding the two previous numbers in the
sequence to obtain the next higher number.
Example: 1+1= 2, 2+3= 5, 5+8= 13...
The formula is: Fn = Fn-1 + Fn-2
Every third number is even and the difference between each number is .618
with the reciprocal of 1.618. These numbers are know as the “golden ratio”
or “golden mean.”

4. What is the History of the Fibonacci Sequence?
The exact origination of the Fibonacci sequence is unknown.
It is believed that contributions to the theory began in 200 BC by Indian
mathematicians whose studies were based on Sanskirt prosody.
The sequence was introduced to Western European mathematics in 1202
by Leonardo of Pisa, aka “Fibonacci”
His study of the sequence began with the breeding patterns of rabbits. In
which he found rabbit generations duplicated in
accordance with the Fibonacci numbers.

5. Fibonacci in Nature
Patterns created by the Fibonacci sequence can be found throughout
nature...

6. Fibonacci Sequence in Petal Patterns
The Fibonacci sequence can be seen in most petal patterns.
For instance most daisies have 34, 55, or 89 petals. (The 9th, 10th, and 11th
Fibonacci numbers)

7. Fibonacci Sequence in Sunflowers
The Fibonacci sequence can be found in a sunflower heads seed arrangement.
The arrangement of seed is based upon the golden mean which corresponds to
the “golden angle” of 137.5 degrees.
The seeds are arranged in consistent patterns of 137.5 degrees
This gives the flower the optimal filling ratio for its seeds.

8. Fibonacci Sequence in Seashells
The Fibonacci numbers directly correspond to the spiral found in seashells.
The numbers form what are called Fibonacci rectangles or “golden rectangles”
The rectangles are unique because each rectangle has sides equal to the length
of the Fibonacci numbers.
Within these rectangles we can create a spiral with
cross sections equal to exactly 1.618 (the “golden
mean” with the corresponding angle of 137.5 degrees

9. Fibonacci Review
What are the Fibonacci numbers and how are they obtained?
Where did the study of the sequence begin?
Who introduced the numbers to Western European mathematics?
What is the golden ratio/golden mean and how is it related to the Fibonacci
sequence?
Where can the Fibonacci sequence be found?
What are some natural phenomena created by using the Fibonacci sequence?