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# Fibonacci

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### Fibonacci

1. 1. Iván Alarcón Quintana 2 º A E.S.O. “La Inmaculada"
2. 2. Index • Life • Mathematical work – Liber Abaci – Sequence Fibonacci – Reflection in nature • Contribution to mathematics • Legacy
3. 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. 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. 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. 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. 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. 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. 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. 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