Page 21 - Math 21 Module_Chapter One

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Module 2: The Fibonacci Sequence

and the Golden Ratio

Objectives:

At the end of the lesson, the students should be able to:

1. Discuss various applications of Fibonacci sequence and the golden
ratio.
2. Examine Fibonacci sequence in nature and in art.
3. Calculate golden ratio in objects.

The Fibonacci Sequence

As introduced in the module 1, the Fibonacci
sequence is a series of numbers where a number is
found by adding up the two numbers before it.
Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3,
5, 8, 13, 21, 34, and so forth. Written as a rule, the
expression is

= − + −

Leonardo Fibonacci (1170 –
1250)
The sequence was named after Leonardo
Fibonacci, also known as Leonardo of Pisa or
Leonardo Pisano. It was first introduced in his Liber Abbaci (Book of
Calculation) in 1202. This book contains the problem created by Fibonacci
that concerns the birth rate of rabbits. Here is the Fibonacci’s rabbit problem:

At the beginning of a month, you are given a pair of newborn rabbits.
After a month, the rabbits produced no offspring; however, every month
thereafter, the pair of rabbits produces another pair of rabbits. The offspring
reproduce in exactly the same manner. If none of the rabbits dies, how many
pairs of rabbits will there be at the start of each succeeding month?