The Fibonacci sequence is a series of numbers generated by adding the two previous numbers, resulting in patterns that appear in nature, such as the arrangement of petals in flowers and the spiral of seashells. Its history traces back to 200 BC with early contributions from Indian mathematicians, and it was introduced to Western mathematics by Leonardo of Pisa in 1202. The sequence is closely associated with the golden ratio, which influences various natural phenomena and mathematical concepts.

1. THE FIBONACCI SEQUENCE
It’s as easy as 1, 1, 2, 3….
De Leon N, Gabriel R,Valdez K

2. WHAT IS FIBONACCI SEQUENCE?
• 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 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. THE HISTORY OF 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 toWestern 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. F I B O N AC C I S E Q U E N C E I N S U N F L OW E R
• 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 degreesThis 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. REVIEW
• What are the Fibonacci numbers and how are they obtained?
• Where did the study of the sequence begin?Who introduced
the numbers toWestern 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?

10. THANKYOU FOR LISTENING BEED 1B