1. Iván Alarcón Quintana
2 º A E.S.O. “La Inmaculada"

2. Index
• Life
• Mathematical work
– Liber Abaci
– Sequence Fibonacci
– Reflection in nature
• Contribution to mathematics
• Legacy

3. Life
• Born in Pisa (1170)
• Son of Guglielmo, Nicknamed
Bonacci.
• He lived with his father in Bejaia
(Algiers).
• Was there he learned about the
numbering system Arabic.
• Guest of the Emperor Frederick II
• 1240, Pisa granted permanent wage
• He died in Pisa (1250)

4. Mathematical work
• Liber abaci (1202)
– Introduced Indorum
operandi, today known as Arabic
numerals
– Defended numbering digits 0-9 and
placed value
– Applied to accounting, conversion
of weights and
measures, interest, money
exchange, ...
– Well received in Europe, had a
profound impact

5. Mathematical work
• Sequence Fibonacci
– Known for Indian
mathematicians
– It was introduced in the West
(Liber Abaci)
– Starting at 1, each term is the
sum of the two previous
numbers
– But did not mention the
proportion Golden
• Associated with the beauty in
nature according to the Greeks
•1
•1
•1 +1 =2
•1 +2 =3
•2 +3 =5
•3 +5 =8
•5 +8 =13
•8 +13 =21
•13 +21 =34
•21 +34 =55
•34 +55 =89
•...

6. Mathematical work
• Reflection in nature
– In the human body:
• The length of phalanges
(2, 3, 5, 8)
• Ratio between hip height and
knee height
• Ratio between distance from
shoulder to fingers and
distance from elbow to fingers
– The reproduction of rabbits
(1, 1, 2, 3, 5,8, ...)

7. Mathematical work
• Reflection in nature
– Nature uses the same pattern to have the seeds in a
flower, the petals on the edges, and place the leaves in a
stem. They grow in spiral maintaining an angle no matter
how much the plant is going to grow, so a leaf will be
covered the least possible and will receive the necessary
amount of sunlight.
Sunflower : 55 coils in one direction and 89 in the
other, or, 89 and 144 respectively.
Leaves arise following a spiral around the stem

8. Mathematical work
• Reflection in nature
– The galaxies also grow
following the suquence of
Fibonacci.
– The shells of Nautilus are
formed according to this
pattern.

9. Contribution to mathematics
• Liber Abaci (Book of the Abacus)
– 15 chapters
• Practice Geometriae (Practical Geometry)
– 7 chapters
– Geometry Problems
• Letter to Theodore (astrologer of Frederick II)
– Resolution of two problems: algebraic and geometricalgebraic
• Liber quadratorum (Book of square numbers)
– 20 propositions about properties of square numbers

10. Legacy
• S. Century, stands statue in Pisa.
– Today, the historic cemetery Piazza
dei Miracoli.
• Character in the children's book
"Crusade in Jeans" of Thea
Beckman.
• Math Concepts:
– Pisano Period, search Fibonacci, ...
• Asteroid 6765 Fibonacci
• Art rock band The Fibonaccis