-----Original Message-----
From: Randolph Fritz [SMTP:randolph@xxxxxxxxxxxxxxxxxxxx]
Sent: Monday, 16 March, 1998 8:55
To: DESIGN-L@xxxxxxxxxxxxx
Subject: Re: ARCHITECTURE & MUSIC
On Sun, 15 Mar 1998, kurt jensen wrote:
> In response to:
> FERNANDO IMPERATORI
> fernandi@xxxxxxxxxxxxxxxxxxxxx
> I saw a paper the other day that explored the connection of music and
> architecture... in the paper the author related the golden section to
> music as well as the fibonacci series 1,1,2,3,5,8,13,21,34,55 that Bela
> Bartok used in a composition. Can any one tell me more about the
> fibonacci series? I never heard of this before. The only thing i know
> is that it's based on modular man. Any clues?
>
Aaagh! This isn't a troll for people with math degrees, right?
[Surendra] fibonacci is elementary - you cannot escape from it in real life. as i said it is elementary - one does not require a maths degree to understand it. it's really simple.
[Surendra]
The Fibonacci series was discovered by the 13th-century mathematician
Leonardo Pisano (= of Pisa), originally Leonardo Fibonacci. He introduced
"Arabic" (really Hindu-Arabic) numeration to western Europe. The
Fibonacci series is defined by:
f[0] = 1
f[1] = 1
f[n] = f[n-1] + f[n-2] (for n>1, of course)
So 1, 1, 2 (= 1 + 1), 3 (= 2 + 1), 5 (= 3 + 2), etc.
It is interesting because it pops up in all kinds of problems where
"growth" is the subject. Thus in biomorphology and computer science.
The ratio of successive Fib. numbers gets closer & closer to
the golden ratio the larger the numbers are; in fractured mathematical
symbology:
lim f[n]/f[n-1] = the golden ratio
n->infinity
For more on this, take a look in the Britannica, which has good
introductory articles on the Fibonacci series and the golden ratio. Also
see *The Algorthmic Beauty of Plants* and follow the references for
applications in plant form.
The architectural application of the golden ratio goes back to the ancient
Greeks at least.
Randolph
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