n] are successive Fibonacci numbers
and they seem never to have common factors.
Jane's and my euphoria had a small setback when we found that the objects we were counting were just a little different-looking from a long-known example of Fibonacci numbers
, but we were still quite happy that the sequence had occurred unexpectedly within the context of knot theory.
The more interesting challenge beyond Fibonacci numbers
was to experiment with fractals.
The book has more information on the Divine Proportion and Fibonacci numbers
To understand why Fibonacci numbers
predominate in spiral plants, Gole and Atela started with the theories of 19th-century botanist Wilhelm Hofmeister, who observed that a plant's leaves emerge at the least-crowded spot around a circular meristem, or growing tip.
On the downward movements of the markets, the application of the Fibonacci numbers
can be used to trace retracement moves.
Other explorations are encouraged with Fibonacci numbers
, the Konigsberg Bridge problem, and Venn diagrams.
Some have found Fibonacci numbers
even in such unpredictable occurrences as stock market fluctuations and the ways bees migrate in a honeycomb.
For the price of a tramway ticket, the Strasbourg commuter purchases not only a ride through the city in a transparent, state-of-the-art streetcar, but also a series of encounters with contemporary artworks: Barbara Kruger's monumental anti-advertising campaign covering the lone underground station, Mario Merz's redneon Fibonacci numbers
in translucent glass boxes embedded between the rails over nearly a mile of the surface line, and Jonathan Borofsky's Woman Walking to the Sky, on an eighty-two-foot pole that rises diagonally over a public square (a pendant to his Man Walking to the Sky in Kassel).
Lahr, "Fibonacci and Lucas Numbers and the Morgan-Voyce Polynomials in Ladder Network and in Electric Line Theory," Fibonacci Numbers
and Their Appl.
6) Another method is to use the Fibonacci numbers
, a summation series in which each number is the sum of the two which precede it:
This procedure describes the characteristics of the Fibonacci numbers