We know that

Fibonacci numbers grow exponentially and also [F.sub.n] [greater than or equal to] [[alpha].sup.n].

Much of the time used to prepare this article was spent learning to use Maple through the

Fibonacci number and logistic formula examples.

On the downward movements of the markets, the application of the

Fibonacci numbers can be used to trace retracement moves.

The

Fibonacci numbers are the numbers generated in a sequence when you start with 1, 1, then add the two previous numbers to get the next in the sequence e.g., 1, 1, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, ...

Sun,

Fibonacci numbers and Fermat's last theorem, Acta Arith.

An injective function f: V(G) [right arrow] {[F.sub.0], [F.sub.1],[F.sub.2], ..., [F.sub.q-i], [F.sub.q+i]}, where [F.sub.q+i] is the (q + 1)th

fibonacci number, is said to be almost super fibonacci graceful if the induced edge labeling [f.sup.*](uv) = |f (u) = f (v)| is a bijection onto the set {[F.sub.1], [F.sub.2], ..., [F.sub.q]}.

where [F.sup.n] is the n-th

Fibonacci number, [F.sub.n] = [[psi].sup.n] - (1 - [[psi].sup.n]/[square root of 5].

The number of ways to group n digits into singletons and pairs is [F.sub.n+1], where [F.sub.n] is the nth

Fibonacci number.

Tichy

Fibonacci numbers of graphs, The Fibonacci Quarterly, 20(1982), No.1, 16-21.

After a few weeks of guided exploration, many children can, with just a few minutes of effort, set up a spreadsheet to list the

Fibonacci numbers. They can also program spreadsheets to generate odd and even numbers, a multiplication table, squares, square roots, and exponential growth.

Tichy,

Fibonacci numbers of graphs, The Fibonacci Quarterly 20(1982), N0.1, 16-21.

The hundredth

Fibonacci number, for example, is roughly equal to the hundredth power of the golden ratio.