Page 16 - Module 1_Chapter 1_Mathematics in the Modern World

Mathematics in our World
6

The sequence 1, 1, 2, 3, 5, 8, 13, 21, 34,
The Fibonacci Sequence 55, 89, 144, 233, 377, … is called the

Fibonacci sequence and its terms the
Around 1,200 AD, Fibonacci also Fibonacci numbers.
known as Leonardo Pisano (1,170 -

1,250) from Pisa, Italy published the Example 1
Liber Abaci, or “Book of Calculation”, an Let f1 and f2 both equal to 1, find the 7th term

arithmetic text on financial
of the Fibonacci sequence using the
computations and promoted the use of recursion formula.
Hindu-Arabic numerals.

One of the exercises in Fibonacci’s Solution: Let f1 and f2 = 1, then
book is written like this: f3 = f3–1 + f3–2

f3 = f2 + f1 = 1 + 1 = 2
“A man put a pair of rabbits in a place surrounded f4 = f3 + f2 = 2 + 1 = 3
on all sides by a wall. How many pairs of rabbits
f5 = f4 + f3 = 3 + 2 = 5
are produced from that pair in a year, if it is
f6 = f5 + f4 = 5 + 3 = 8
supposed that every month each pair produces
a new pair, which from the second month f7 = f6 + f5 = 8 + 5 = 13

onwards becomes productive?”
Example 2

What is the 8 term of Fibonacci sequence?
th

Solution: Let f6 = 8 and f7 = 13, then

f8 = f7 + f6 = 13 + 8 = 21

The Golden Rectangle
The Rabbit Habit

A golden rectangle can be broken into
What is Fibonacci smaller squares based from Fibonacci
Sequence?
sequence and divide each with an arc, the
The Fibonacci sequence is the pattern begins to take shapes called the

sequence f1, f2, f3, f4, … which has its Fibonacci spiral in which we can see in
first two terms f1 and f2 both equal to 1 nature.
and satisfies thereafter the recursion

formula fn = fn–1 + fn–2.

ZANNIE I. GAMUYAO, MSM
Assistant Professor 1 UNIT 1.2 The Fibonacci Sequence
Department of Arts and Sciences