Lecture No. 6

Fibonacci Sequences

(Natural Models)

Dr Nazir A. Zafar Advanced Algorithms Analysis and Design

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In this lecture we will cover the following:

• Fibonacci Problem and its Sequence

• Construction of Mathematical Model

• Explicit Formula Computing Fibonacci

Numbers

• Recursive Algorithms

• Generalizations of Rabbits Problem and

Constructing its Mathematical Models

• Applications of Fibonacci Sequences

Dr Nazir A. Zafar Advanced Algorithms Analysis and Design

Today Covered

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• By studying Fibonacci numbers and constructing

Fibonacci sequence we can imagine how

mathematics is connected to apparently unrelated

things in this universe.

• Even though these numbers were introduced in

1202 in Fibonacci’s book Liber abaci, but these

numbers and sequence are still fascinating and

mysterious to people of today.

• Fibonacci, who was born Leonardo da Pisa gave a

problem in his book whose solution was the

Fibonacci sequence as we will discuss it today.

Fibonacci Sequence

Dr Nazir A. Zafar Advanced Algorithms Analysis and Design

docsity.com

Statement:

• Start with a pair of rabbits, one male and one female,

born on January 1.

• Assume that all months are of equal length and that

rabbits begin to produce two months after their own birth.

• After reaching age of two months, each pair produces

another mixed pair, one male and one female, and then

another mixed pair each month, and no rabbit dies.

How many pairs of rabbits will there be after one year?

Answer: The Fibonacci Sequence!

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .

Fibonacci’s Problem

Dr Nazir A. Zafar Advanced Algorithms Analysis and Design

docsity.com

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University:
Bengal Engineering & Science University

Subject:
Advance Analysis Design

Upload date:
06/08/2012