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Background

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.

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Background

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  1. 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.

  2. Fibonacci’s Works • Liber Abaci (The Book of Calculating) • Liber Quadratorum (The Book of Squares) • Practica Geometriae (Book on Geometry) • Flos • Letter to Master Theodorus

  3. Liber Abaci • Written in 1202 • Responsible for introduction of Hindu-Arabic system to Western Europe, thus doing away with the Roman numeral system • Taught mathematics and applied it to accounting, money transfer, etc. • Introduced the rabbit problem and consequently the Fibonacci Sequence

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

  5. Fibonacci’s rabbitsHow fast can rabbits breed in ideal circumstances? • One male, one female • Rabbits are able to mate at the age of one month • After the second month, a female can produce another pair of rabbits • A female always produces 1 new pair every month following the second month

  6. 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

  7. Month 1 A1 A3 A A2 A2 A1 A A A B A A1 Month 2 Month 3 Month 4 Month 5 Fibonacci’s Rabbits A

  8. Fibonacci Sequence Month 1 1 Month 2 1 Month 3 2 Month 4 3 Month 5 5 Month 6 8 Can you see the pattern appearing?

  9. Fibonacci Sequence By adding the current month to the previous month you get the next month 0 1 + + 1 + 2 + 3 + 5 + 8 ?

  10. Fibonacci Sequence 34 55 89 144 233 377 610 987 1567 2584 4181 6765

  11. Fibonacci Sequences • Begins with zero • Add the last two numbers to get the next • 0,1,1,2,3,5,8,13,21,34,55,89,144,……… The recursion formula F1=1 F2=2 Fn=Fn-1 + Fn-2 If n > or = 3

  12. Fibonacci Squares 5 8 3 1 1 2

  13. Fibonacci Spirals

  14. The Fibonacci Spiral • A spiral that grows at the rate of the Fibonacci sequence • The spiral consists of quarter-circles inside of squares • This concept is closely related to the golden rectangle used in art and architecture

  15. 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

  16. Fibonacci in NatureHoney Bees • Males bees have only 1 parent (unfertilized) • Female bees have 2 parents (fertilized) • Examine the genealogy

  17. Fibonacci in Nature Plants and seeds http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#rabeecow

  18. Fibonacci in Nature Human Anatomy 2 hands 5 fingers 3 joints per finger Fibonacci Spirals http://goldennumber.net/face.htm

  19. Look! It’s a Fibonacci sock!

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