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1.
A sequence of numbers, created by Leonardo of Pisa (also known as Fibonacci). The sequence starts out with the first two numbers being 0 and 1, and after that you add the previous two numbers to get the next number in the sequence. Often used in proofs.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765
The fibonacci sequence starts with 0, 1....

0+1=1, so the next number must be 1.

1+1=2, so the next number is 2.

2+1=3, and so the next number is 3, and so on.
by poetamatrice May 17, 2009
 
2.
A mathematical sequence starting with zero and one. To find the next number in the sequence, add the last two numbers in the sequence.
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987. These are the Fibonacci sequence numbers before 1000.
by Matt11111 November 25, 2011