The columns are the Pascal triangle numbers, while adding the diagonals from left to right produces the Fibonacci numbers
n] is the n-th Fibonacci number
, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.
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.
And with its stunning range of topics (early Greek fascination with flowery perfumes, the intriguing number patterns found in nature known as Fibonacci numbers
, the relationship between colors and emotion) it offers many interdisciplinary tie-ins between science and other classes such as world studies, math and health.
A number sequence named after him known as the Fibonacci numbers
, which he did not discover but used as an example in the Liber Abaci.
Two sequences are of great importance: the Fibonacci numbers
F = [f.
Any college-level collection strong in science and nature--and many a public lending library--will find this a fascinating review of the history of the Fibonacci numbers
and their applications to everything from nature to art and the stock market.
A function which returns a stream of the Fibonacci numbers
in linear time:
These are called Fibonacci numbers
and are generated by adding the previous two numbers in the list together to form the next and so on.
The appearance here of the Fibonacci numbers
may well be a simple coincidence; or this may be one of those "redundant" convergences of diverse planning methods seen elsewhere in Florentine planning (Trachtenberg, 1997, 62; 1980).
Noting the pervasiveness of Fibonacci numbers
in nature, Penrose even suggests that information processing advantages may be conferred by the Fibonacci number
structure of the microtubules within the neuron cytoskeletons.
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).
The author explains the relationship of the Fibonacci numbers
to compositions and palindromes, tilings, graph theory, and the Lucas numbers.
From the repetition on the florets of a flower to the scales of a pineapple's skin, Fibonacci numbers
are found in the pattern of growth of every living thing in nature.
For the Fibonacci numbers
, applications are discussed in relation to set theory, the composition of integers, graph theory, matrix theory, trigonometry, botany, chemistry, physics, probability, and computational complexity.