[Artemisia] 16th century mathematicians and philsophy

[Aghren]

I am wondering if anyone could shed more light on the Golden Number and
Fibonacci's number. I am also active in a yahoo group on Brick (Bread)
Ovens. A construction question was recently asked regarding the height of
the door in relationship to the height of the dome. The answer came back at
62%. But, this is what followed and I am very interested in following this
thread.

Take a look (it is a bit long) and comment.

YIS,
Aghren (aka the bread guy.)

 

>>OK, now I'm testing the limits of what's "off topic" here, but Fibonacci
is related to bread (and I can't help myself): As a non-mathematical artist,
I've gained a greater love of math thanks to a dead Italian mathematician.
The famous "number" named after him isn't really a number, but a series of
numbers, where each one is the sum of the preceding two: 0, 1, 1, 2, 3, 5,
8, 13, 21, 34, 55, etc. If you divide each number by the following number,
you get this series: 1, .5, 0.66..., 0.6, 0.625, 0.6153, 0.6190, 0.6176,
0.6181, 0.6179, 0.6180, etc. 

The sequence always takes the same form, no matter where you start. The
"number" (tho it really isn't one) that you approach is commonly called the
Golden Mean. In 1502, Luca Pacioli wrote a book about it called "The Divine
Proportion;" the illustrator was Leonardo DaVinci (recall the famous drawing
of the man w/four arms and legs, enclosed in both a circle and a square).
Pacioli wrote that "just like God cannot be properly defined, nor can be
understood through words, likewise our proportion cannot be ever designated
by intelligible numbers, nor can it be expressed by any rational quantity,
but always remains concealed and secret, and is called irrational by the
mathematicians." (Quoted by Mario Livio, in The Golden Ratio, page 132.)

The label "irrational" came about because mathematicians of the day were
mystified to discover that certain numbers, when divided one into the other,
never "resolved" themselves into a finite quantity. We're not taught much
philosophy now, when we learn long division, but such things quickly become
very significant if you're using numbers to understand the visible world.
For example, try counting flower leaves, or petals, or the number of
opposing seed whorls in the head of a sunflower, or try to figure out
exactly how many diameters fit into the circumference of a circle. 

Einstein said that "the fairest thing we can experience is the mysterious.
It is the fundamental emotion which stands at the cradle of true art and
science." Anyway, there's a lot to learn about Fibonacci, and I certainly
don't know it all, but I just wanted to suggest that there's as much
fundamental mystery in the "irrational" whole number relation 2/3
(0.66666....) as there is in the "golden mean." And that the ratio of door
height to dome height is probably just as basic (and, within the natural
limits of combustion and containment, as variable) as the ratio of finger
length to hand length in humans (again, see DaVinci's drawing).

Anyway, if you're interested, there are not only a lot of good books on the
topic, there's one specifically about bread! The Diet Code, Revolutionary
Weight Loss Secrets from Da Vinci and the Golden Ratio, by a Portland (ME)
baker named Stephen Lanzalotta. Also good are Mario Livio's book, and one
called The Self-Made Tapestry: Pattern Formation in Nature, by Philip Ball,
and A Beginner's Guide to Constructing the Universe, by Michael S. Schneider
(about numbers and philosophy). 

Read them with a good piece of bread...

-- Kiko Denzer<<

 

PS- we are working on the bread oven at the site of the URFFF. Help is still
welcomed. We will be out there all day Saturday and Sunday. If you couldn't
make it to Crown Tourney your help would be welcomed.

Thanks,
 Aggie
801-732-0390