Leo of Pisa

LEONARDO OF PISA (~1175- 1240) By: Beth Jarvis MATH 123 Geometry 11/25/08

Fibonacci (1175-1240) ,[object Object],[object Object],[object Object],[object Object]

Fibonacci’s 4 Major Works ,[object Object],[object Object],[object Object],[object Object]

Liber Abaci ,[object Object],[object Object],[object Object]

“ How many pairs of rabbits can be bred from a single pair in one year?” ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Answer: 144 Pairs of Rabbits Month Rabbit pairs 1 1 2 1 3 2 4 3 5 5 6 8 7 13 8 21 9 34 10 55 11 89 12 144

Fibonacci Sequence is born ,[object Object],[object Object],[object Object],[object Object]

Geometric Formula ,[object Object],[object Object],[object Object],Jacques Binet’s Formula (1843) allows us to have a geometric formula so we can get any value of Fibonacci’s sequence without the previous two terms. If n = 6, plug into the calculator and it does equal 8.

Fibonacci Numbers Divided ,[object Object],[object Object]

Fibonacci Spiral ,[object Object],The box below draws squares the size corresponding with the order of Fibonacci sequence.

Fibonacci Sequence in Nature ,[object Object],[object Object],[object Object]

Pythagorean Triples ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Use Fibonacci Sequence to create Pythagorean Triples. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Fibonacci in the Arts ,[object Object],[object Object],[object Object],[object Object],[object Object]

Neat facts about Fibonacci Sequence ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Fibonacci Groups ,[object Object],[object Object],[object Object]

THANK YOU! Sources upon request 1 1 2 3 5 8 13 21…

Leo of Pisa

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Leo of Pisa