Simply stated, the term Fibonacci numbers refers to a set of numbers
(part of whose sequence includes 3, 5, 8, 13 and 21) that occurs with remarkable
frequency in various dimensions of our existence, including nature, music ... and writing!
The name of this sequence of numbers is derived from Italian mathematician
Leonardo Fibonacci, who lived from approximately 1170 to 1240. He is said to have first
arrived at the sequence of numbers in the year 1202, when calculating how fast rabbits
could breed under ideal circumstances. The sequence of numbers that revealed itself
in terms of the number of pairs of rabbits in the field at the start of each month
became known as the Fibonacci numbers.
But the reason that Fibonacci numbers and their derivatives (such as so-called Fibonacci
rectangles and Fibonacci spirals) are so interesting is that Fibonacci and others
later realized the existence of these numbers in a wide variety of natural contexts:
petals on flowers, dimensions of snail shells, seed heads, pine cones, leaf arrangements
and more.
In the words of mathemetician H.S.M. Coxeter, the Fibonacci numbers represent
"not a universal law but [rather] a fascinatingly prevalent tendency"
(Introduction to Geometry, Wiley, 1961, page 172). In other words,
though it is not an "iron law" that all aspects of all phenomena follow the Fibonacci
number sequence, the extent to which this is nonetheless true is quite remarkable.
You can learn more about Fibonacci numbers at
Ron Knott's Surrey University Website, which treats the subject in great depth
(some 200 pages!) but contains an excellent and relatively concise
introductory section, featuring superb use of graphics, to illustrate the main points.
If more material like this was utilized in math instruction, motivation among children
in the U.S. to learn math would be substantially higher (and, for a variety of reasons,
the world would be a better place).
What we have yet to read about anywhere else is the application of certain Fibonacci numbers
(lower numbers in the sequence) to music and writing. As an example from music, consider
the structure of
Beethoven's fabled Fifth Symphony. Hum the opening to yourself (or click on the link
provided immediately above, to listen to it on the Web) and notice
how prominently the number three figures into the structure of the melody.
Much more could be said about Beethoven's Fifth and music overall as it
relates to Fibonacci numbers (additional case in point: the famous
"Circle of Fifths")
but our focus here is writing, so let us now move to the
application of Fibonacci numbers to verbal expression and the craft of writing,
where the most powerful Fibonacci numbers are three and five.
"Liberty, fraternity, equality" (the battle cry of the French Revolution).
"Life, liberty and the pursuit of happiness" (from the U.S. Declaration of Independence).
"Three People's Principles" (the ideology on which Sun Yat-sen based his revolution,
overthrowing China's last imperial dynasty in 1912, and helping to demonstrate
the trans-cultural nature of the Fibonacci phenomenon).
Hook, line and sinker. Lock, stock and barrel. "The Good, the Bad and the Ugly."
The list could go on and on (and on!).
The point here is that in the art of verbal expression, including the craft of writing,
three, especially, is a magic number (and a Fibonacci number). Imagine trying to
articulate any of the above as sets of four rather than three. Would they work well? No.
Would they sound right? Hardly. Would they deliver their message with the same force?
Certainly not.
And did you notice, by the way, how many rhetorical questions we just asked? (Three.)
And how many examples were given in the paragraphs of examples that
precede this one? Three, again. How many items are on the tips menu
here? Twenty-one (yet another Fibonacci number).
Pondering the metaphysical implications of Fibonacci numbers could be a lifetime endeavor
or something akin to falling into a bottomless pit. For the time being, let's keep the
discussion practical, in a nuts-and-bolts sort of way: If you want to write effectively,
with clarity, power and authority (there's that Fibonacci number again), think in terms of
the numbers three, especially, and five — for summations, slogans, lists, bullet points
and so on. And when you read something that's masterfully written, observe the application
of this principle therein (probably done intuitively, by the writer).
Leonardo was definitely on to something, more than 800 years ago, in probably more ways
than he ever imagined at the time. For an array of fascinating books on the topic,
click through to Amazon.com from the featured titles in the Amazon.com box below.
We are indebted to Jim Armstrong, multi-talented freelance animator and
award-winning new media artist extraordinaire,
of 2112 F/X, for first introducing us
to the fascinating world of Fibonacci numbers. For this and everything else:
Thank you, Jim! We fondly dedicate this page to you.
All original material at this Website is copyrighted © 1996-2005 by ACI/Daniel K. Berman, Ph.D. Such material may not be produced, stored in a retrieval system or transmitted in any form or by any means — electronic, mechanical, photocopying, recording or otherwise — without written permission. Any queries concerning the rights to or use of original materials at this site may be addressed to DBnearSF @ yahoo.com.