Fibonacci Numbers and The Golden Section Thomas J. Hill Kristi Selkirk Melissa Zale Amber Ballance

Who was Fibonacci? Born: 1170 in (probably) Pisa (now in Italy) Died: 1250 in (possibly) Pisa (now in Italy)

The four works from this period which have come down to us are: Fibonacci’s Four Famous Works Liber quadratorum (1225) Flos (1225) Practica geometriae (1220/1221) Liber abbaci (1202, 1228).

Fibonacci's Mathematical Contributions and 0 Roman Numerals I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1000 For instance, 13 would be written as XIII or perhaps IIIX would be MMIII or IIIMM. 99 would be LXXXXVIIII and 1998 is MDCCCCLXXXXVIII For example, XI means 10+1=1 but IX means 1 less than 10 or 9. 8 is still written as VIII (not IIX) Hindu-Arabic Number System (Positional System)

The Fibonacci Series Hindu-Arabic Number System. Fibonacci Number Sequence Fib(n): … n:

Patterns in the Fibonacci Numbers & Cycles in the Fibonacci Numbers Here are some patterns people have already noticed: Pattern Number 1 0,1,1,2,3,5,8,13,21,34,55,... Pattern Number 2 00, 01, 01, 02, 03, 05, 08, 13,... For the last three digits, the cycle length is 1,500 For the last four digits,the cycle length is 15,000 For the last five digits the cycle length is 150,000 and so on....

Fibonacci's Rabbits The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5, 8, 13, 21, 34,...

Fibonacci Puzzles Making a bee-line with Fibonacci numbers …

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What is the Golden Section (or Phi)? (Also called The Divine Proportion) Golden Section, in mathematics, a geometric proportion in which a line is divided so that the ratio of the length of the longer line segment to the length of the entire line is equal to the ratio of the length of the shorter line segment to the length of the longer line segment....

The Golden Section in Architecture The Parthenon and Greek Architecture Even from the time of the Greeks, a rectangle whose sides are in the "golden proportion" (1 : which is the same as : 1)....

Golden Section in Art A B C D AC = CD AD AC AND DB = BA DA DB

. Golden Section In Nature

Nature Continued…

BIBLIOGRAPHY Huntley, H.E. The Divine Proportion: A Study in Mathematical Beauty. New York: Dover Publications, Inc.,