Those Fascinating Fibonaccis! 

Patterns in numbers have intrigued mathematicians for years.  Early in the thirteenth century, Leonardo Fibonacci (fee-buh-nah'-chee) discovered a fascinating sequence of numbers.

These much studied Fibonacci numbers retain their magic and mystery to this day and are ubiquitous in both natural and manufactured products—pine cones and pineapples, poetry and computers, art and music, the heavens and the sea—and in the numerical patterns within the sequence itself.  The Fibonacci sequence is a prime example of how mathematics seemingly unrelated things.

Try this!  Start with a pair of rabbits (one female, one male) born on 1 January. Assume that all months are of equal length and that—
  • Rabbits begin to produce young two months after their own birth;
  • After reaching the age of two months, each pair produces a mixed pair (one female, one male) and then another mixed pair each month thereafter; and
  • No rabbit dies--see diagram (click here)

Fibonacci asked, “How many pairs of rabbits will there be after one year?”  

Click here to continue...

1

1

2

3

5

8

13

21

34

55

89

.

.

.

Fibonacci Numbers in Nature

Fibonacci numbers abound in nature.  Cutting a bell pepper crosswise reveals 3 chambers.  An apple has a 5 point-star cross-section, and a lemon has an 8-chambered cross section.  A daisy almost always has 13, 21, or 34 petals.  Sunflowers adore Fibonacci numbers!  Their seeds spiral out from the center with 21 spirals in the one direction and 34 n the other.  The giant sunflower has 89 and 144 spirals, and the whopper sunflower has 144 and 233 spirals.  Each set of spirals contains adjacent Fibonacci numbers.

The genealogy of a drone, a male bee, follows the Fibonacci sequence.  A drone comes from an unfertilized egg; it has a mother but no father.  A female bee has both a mother and a father.  Can you figure out the sequence?

Male Female Total
? ? ?
? ? ?
2 3 5
1 2 3
1 1 2
0 1 1
1 0 1

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