Background

Born 1170, Died 1250 in Pisa (now in Italy).

Real name is Leonardo Pisano, Fibonacci is his nickname.

Studied in North Africa in mathematics.

Wrote many books on Mathematics: Liber abaci, Practica geometriae, Flos, and Liber quadratorum.

There are other text of his that were lost.

Fibonacci’s WorksFibonacci’s Works

Liber Abaci (The Book Liber Abaci (The Book of Calculating)of Calculating)

Liber Quadratorum Liber Quadratorum (The Book of Squares)(The Book of Squares)

Practica Geometriae Practica Geometriae (Book on Geometry)(Book on Geometry)

FlosFlos Letter to Master Letter to Master

Theodorus Theodorus

Liber AbaciLiber Abaci

Written in 1202Written in 1202 Responsible for Responsible for

introduction of Hindu-introduction of Hindu-Arabic system to Arabic system to Western Europe, thus Western Europe, thus doing away with the doing away with the Roman numeral systemRoman numeral system

Taught mathematics and Taught mathematics and applied it to accounting, applied it to accounting, money transfer, etc.money transfer, etc.

Introduced the rabbit Introduced the rabbit problem and problem and consequently the consequently the Fibonacci SequenceFibonacci Sequence

Fibonacci’s QuestionFibonacci’s Question

“ “A man has one pair of rabbits at a certain place entirely A man has one pair of rabbits at a certain place entirely surrounded by a wall. We wish to know how many pairs surrounded by a wall. We wish to know how many pairs will be bred from it in one year, if the nature of these will be bred from it in one year, if the nature of these rabbits is such that they breed every month one other pair rabbits is such that they breed every month one other pair and begin to breed in the second month after their birth.” and begin to breed in the second month after their birth.” -Liber Abaci, 1202-Liber Abaci, 1202

Fibonacci’s rabbitsFibonacci’s rabbitsHow fast can rabbits breed in ideal How fast can rabbits breed in ideal

circumstances?circumstances? One male, one femaleOne male, one female Rabbits are able to mate Rabbits are able to mate

at the age of one monthat the age of one month After the second month, After the second month,

a female can produce a female can produce another pair of rabbitsanother pair of rabbits

A female A female alwaysalways produces 1 new pair produces 1 new pair every month following every month following the second monththe second month

Fibonacci’s Rabbits

Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month

on. The puzzle that Fibonacci posed was…. How many pairs will there be in one year? http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#rabeecow

Fibonacci’s Rabbits

AA

Month 1

AMonth 2

A A1

Month 3

A A2

A1

Month 4

A A3

A1

B A2

Month 5

Fibonacci Sequence

Month 1

Month 2

Month 6

Month 3

Month 4

Month 5

1

1

8

2

3

5

Can you see the pattern appearing?

Fibonacci Sequence

By adding the current month to the previous month you get the next month

1

1

8

2

3

5

+

+

+

+

+

?

0

+

Fibonacci Sequence

F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15

0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610

F16 F17 F18 F19 F20

987 1567 2584 4181 6765

Fibonacci SequencesFibonacci Sequences

Begins with zeroBegins with zero Add the last two numbers to get the Add the last two numbers to get the

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

……………… The recursion formulaF1=1F2=2

Fn=Fn-1 + Fn-2

If n > or = 3

Fibonacci Squares

1 1

23

5

8

Fibonacci Spirals

The Fibonacci SpiralThe Fibonacci Spiral

A spiral that grows at A spiral that grows at the rate of the the rate of the Fibonacci sequenceFibonacci sequence

The spiral consists of The spiral consists of quarter-circles inside quarter-circles inside of squaresof squares

This concept is This concept is closely related to the closely related to the golden rectangle golden rectangle used in art and used in art and architecturearchitecture

Fibonacci in NatureHoney Bees

In a typical hive, there is 1 queen who can lay eggs

There are many worker bees who are female, but they cannot lay eggs

There are several male bees who do not work. They are drones.

Male bees are produced by unfertilized female eggs

Females are produced from fertilized female eggs

Fibonacci in NatureHoney Bees

Males bees have only 1 parent (unfertilized)

Female bees have 2 parents (fertilized) Examine the genealogy

Parents Grand Parents

Great Gr Parents

Grt GrtGrd

Parents

Male 1 2 3 5

Female

2 3 5 8

Fibonacci in Nature Plants and seeds

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#rabeecow

Fibonacci in Nature Human Anatomy

2 hands

5 fingers

3 joints per finger

Fibonacci Spirals

http://goldennumber.net/face.htm

Look!Look!

It’s a Fibonacci sock!It’s a Fibonacci sock!