The Man Who Brought Numbers to Europe

ORIGINAL TOPIC TITLE:
FIBONACCI NUMBERS
&
Hindu–Arabic numeral system to
EUROPE
PRESENTATION BY:
CHARLENE GRACE A. MILLANO
II – 18 BME

NEW TOPIC TITLE:
FIBONACCI
The Man of Numbers

THROUGH OUT THE PRESENTATION,
WE’LL TALK ABOUT THE FOLLOWING

CHOPPER’S ADVICE
MUST:
• LISTEN CAREFULLY & TAKE SOME
NOTES
MAY:
• ASK QUESTIONS AT THE END OF THE
DISCUSSION

LET’S GO STRAIGHT TO THE
CONTENT! 

WHAT DO WE NEED TO KNOW
ABOUT THE LIFE OF
LEONARDO?

Little is known of his
life, and no portrait
exists.
However, a statue of
Fibonacci was
erected by the
citizens of Pisa.
SOURCE: http://faculty.evansville.edu/ck6/bstud/fibo.html

his life is written in this
story book,
Blockhead.
Did you notice
that in the book,
he’s called a
block head?

ACTUALLY HE HAS LOTS OF
NAMES 
Fibonacci
Leonardo of Pisa
Leonardo Pisano Bigollo,
Leonardo Fibonacci
Leonardo Bonacci
BUT WHEN HE
WAS YOUNG,
EVERYONE IN
PISA (INCLUDING
HIM) CALLED HIM
AS “BLOCKHEAD”
BIGOLLO – GOOD
FOR NOTHING

Leonardo Fibonacci
MATHEMATICIAN
Born: c. 1170
Died: c. 1240
Birthplace:
Pisa, Italy
Best known as: The guy
who brought the Hindu-
Arabic number system to
Europe
SOURCE: http://www.infoplease.com/biography/var/leonardofibonacci.html
TYPICAL BIOGRAPHY OF LEO

TYPICAL BIOGRAPHY OF
LEO
The mathematical writings of Fibonacci known to us and
their dates are:
Liber Abbaci (The Book of Calculation), 1202 (1228);
Practica Geometriae (The Practice of Geometry), 1220;
Liber Quadratorum (The Book of Square Numbers), 1225;
Flos (The Flower), 1225;
Letter to Master Theodore (cf. §3).
SOURCE: EIGHT HUNDRED YEARS YOUNG A. F. HORADAM
Department of Mathematics University of New England

A GLIMPSE TO LEO’S LIFE
THROUGH LIBER ABBACI
“I joined my father after his assignment by
his homeland Pisa as an officer in the customhouse
located at Bugia for the Pisan merchants who were
often there. He had me marvelously instructed in the
Arabic-Hindu numerals and calculation. I enjoyed so
much the instruction that I later continued to study
mathematics while on business trips to Egypt, Syria,
Greece, Sicily, and Provence and there enjoyed
discussions and disputations with the scholars of
those places. Returning to Pisa I composed this book
of fifteen chapters which comprises what I feel is the
best of the Hindu, Arabic, and Greek methods. I have
included proofs to further the understanding of the
reader and Italian people. If by chance I have omitted
anything more or less proper or necessary, I beg
forgiveness, since there is no one who is without fault
and circumspect in all matters.”
1. He was
educated in
Bugia Africa
(he had an Arab
master)
2. He continued
studying math
around the world
3. He wrote in one
book the best
mathematical
methods of
different
places/people

FROM THAT WE SAW:
• personality
• mathematical quality of his mind.
• the intellectual curiosity and excitement
• they leave us with a respect and warmth of
feeling for the modest humility of the man.
• "Leonardo's humility graces his genius"

WHAT ARE HIS MAJOR
CONTRIBUTIONS TO
MATHEMATICS?

THE BOOKS 
Liber Abbaci
The Book of Calculation
1202 (1228)
Practica Geometriae
(The Practice of Geometry)
1220
Liber Quadratorum
(The Book of Square
Numbers)
1225
Flos
(The Flower)
1225
Letter to Master Theodore

LIBER ABACI
(BOOK OF CALCULATION) 1202
1. INTRODUCED HINDU-ARABIC NUMERAL
SYSTEM TO EUROPE
– A FEW INTELLECTUALS KNOW THE HINDU-
ARABIC NUMERALS. (VIA al-Khwarizmi)
• He started the second page of liber abaci
with these words:
“The nine Indian figures are :9 8 7 6 5 4 3 2 1,
with these nine figures, and with the sign 0 ...
any number may be written”

CONTENTS OF LIBER ABACCI
A - 1, 2, 3, 4, 5, 6, 7, 8, 9, 0
B -PLACE VALUE
C -USE OF NUMERALS IN ARITHMETIC
OPERATIONS
D -PRACTICAL APPLICATIONS
Profit Margin, Barter, Money, Changing,
Conversion of weights and measures,
Partnerships, and interest.

E. PROPORTIONS
- Rule of Three
- Rule of Five
- FINDING PROPORTIONS
F. RULE OF FALSE POSITION
G. EXTRACTION OF ROOTS
H. PROPERTIES OF NUMBERS
I. A LITTLE BIT OF GEOMTRY AND ALGEBRA

(HINDU-ARABIC NUMERAL
SYSTEM)
FACTS
1. Fibonacci writes out these operations in
words or else illustrates his calculations with
diagrams.
2. There being no algebraic symbolism
available to him, Fibonacci uses res (thing)
for the unknown x, and for x2 he write
squadratus numerus (square number).

SYSTEM)
FACTS:
3. in 1299, Florentine merchants issued
an ordinance prohibiting the use of
Hindu-Arabic numerals

SYSTEM)
4. We owe him the use of BAR on fractions.
before Fibonacci Now
2 2 2
3 3 3
64 64 64
257 257 257
5 5 5

SYSTEM)
5. HE USES THE FOLLOWING:
UNITS
COMMON FRACTIONS
SEXAGISIMAL FRACTIONS
X Decimal Fractions

SYSTEM)
6. APPROXIMATION OF SQUARE ROOTS

(THE FIBONACCI SEQUENCE)
“If two new born
rabbits are placed
in a pen, how
many rabbits will
be there in one
year?”

(THE FIBONACCI SEQUENCE)
Assume that rabbits...
-Can produce one male
and one female.
-Can produce once a
month.
-Can produce when they
are one month old.
-rabbits never die.

RABBIT
PROBLEM
Month 1
Pairs 1

RABBIT
PROBLEM
Month 1 2
Pairs 1 1

RABBIT
PROBLEM
Month 1 2 3
Pairs 1 1 2

RABBIT
PROBLEM
Month 1 2 3 4
Pairs 1 1 2 3

RABBIT
PROBLEM
Month 1 2 3 4 5
Pairs 1 1 2 3 5

RABBIT
PROBLEM
Month 1 2 3 4 5 6 7 8 9 10
Pairs 1 1 2 3 5 8 ? ? ? ?

FIBONACCI
SEQUENCEThis lead to the number sequence which French
number theorist Edouard Lucas named in 1870, the
Fibonacci Sequence.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…
Definition:
The Fibonacci Sequence is the series ofnumbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The nextnumber is
found by adding up the two numbersbefore it.

FIBONACCI
SEQUENCE
Since Fibonacci's time his sequence (which
was not important to him) has generated nearly
as many research papers as it has hypothetical
rabbits!

RESEARCHES ON THE
FIBONACCI SEQUENCE
1. FIBONACCI NUMBERS IN NATURE

RESEARCHES ON THE
FIBONACCI SEQUENCE
2. FIBONACCI NUMBERS IN PASCAL’S TRIANGLE

RESEARCHES ON THE
FIBONACCI SEQUENCE
2. FIBONACCI SEQUENCE & GOLDEN
RATIO1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377…
1/1 1
2/1 2
3/2 1.5
5/3 1.666666667
13/8 1.6
21/13 1.625
34/21 1.615384615
55/34 1.619047619
89/55 1.617647059
144/89 1.618181818
233/144 1.617977528
377/233 1.618055556
DID YOU
NOTICE WHERE
THE QUOTIENT
APPROACHES
TO?

RESEARCHES ON THE
FIBONACCI SEQUENCE
3. FIBONACCI SQUARES

RESEARCHES ON THE
FIBONACCI SEQUENCE
4. GOLDEN SPIRAL

RESEARCHES ON THE
FIBONACCI SEQUENCE
INTRIGUING PROPERTIES OF THE
FIBONACI NUMBERS
•Any 2 consecutive Fibonacci numbers are relatively
prime.
•Summing together any 10 consecutive Fibonacci
numbers will be divisible by 11
•Every third Fibonacci number is an even number
•Many more.

HOW CAN WE INTEGRATE HIS
CONTRIBUTIONS TO LEARNING
& TEACHING MATHEMATICS?

INTEGRATION
• BECED
(Make a fictional story of
numbers w/ are partly
related to history.
• GRADE 1-3
BRING
THEM TO THE
GARDEN, AND
LET COUNT
THE PETALS
OF FLOWERS.

INTEGRATION
• GRADE 4
Story telling :
• GRADE 5 - 6
Photography with
Fibonacci

INTEGRATION
• GET PROBLEMS FROM FIBONACCI’S
BOOK AND HAVE THE GRADES 7 – 12
ANSWER THEM FOR ASSIGNMENT /
BONUS QUESTIONS.

WHAT ARE HIS PHILOSOPHIES
THAT WE NEED TO LEARN SO
THAT WE’LL FELL (MORE) IN
LOVE TO MATHEMATICS??

THERE ARE THREE
PHILOSOPHIES,
WHOEVER EXPLAINS THE
PHILOSPHY RIGHT (of course
with relation to fibonacci), WILL
GET A PRIZE.

1. Be Curious and go out of your
comfort zone
SAIL AWAY FROM
THE SAFE
HARBOR,
CATCH THE TRADE
WINDS IN YOUR
SAILS,
EXPLORE, DREAM,
DISCOVER

2. Don’t keep the knowledge to
yourself.
“I have included
proofs to further
the
understanding
of the reader
and Italian
people.” –
Leonardo ,
Liber Abaci

4. Today You may think that you are
a nobody, but one day you’ll just
see yourself, as a hero saving the
day.
LEONARDO
CALLED HIMSELF
AS A GOOD-FOR-
NOTHING PERSON
WHEN HE WAS
YOUNG.

5. Never let the persuit for
knowlege come to an end.
LEONARDO
CALLED HIMSELF
AS A GOOD-FOR-
NOTHING PERSON
WHEN HE WAS
YOUNG.

LEONARDO DESERVE AN
OSCAR FOR THESE!!!

REFERENCES:
(to be pasted on the description box soon)

The Man Who Brought Numbers to Europe

The Man Who Brought Numbers to Europe

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