[Greenbuilding] Phi (was Re: Roof slopes )
RT
ArchiLogic at yahoo.ca
Fri Aug 15 08:11:34 MDT 2014
On Thu, 14 Aug 2014 18:35:48 -0400, Michael O'Brien <obrien at hevanet.com>
wrote:
> I'm puzzled, of course the golden mean can be generated by arithmetic,
> the formula is (1 + √5) ÷ 2.
> Or did you mean you prefer the geometric option?
and Vadurro, Rob, EMNRD <rob.vadurro at state.nm.us> wrote:
> Or algebra: a/b= b/a+b
I would venture that if you handed either of the above equations to the
Ancient Greek who was the Project Manager in charge of building the
Parthenon, and asked her to build it thusly, she'd have smacked you
upside the head and handed you over Jake the Rake and his brother Joe the
Hoe and had them bury you up to your ears in the lime pit.
OTOH, if you handed her a sketch similar to this image (2nd image at
following link)
http://rouleauc.blogspot.ca/2009/04/more-you-know-golden-ratio.html
she'd have had no trouble visualising and understanding the design and
could easily replicate the layout drawings using not much more than a
pencil and a piece of string. And I'll bet she'd have been so pleased that
she'd have bought you a coffee.
**
Or, let's say I walk up to a person on the street and say to them:
"Did you know that if you take the square root of 5, add 1 to it and
then divide the sum in half you'd get "phi", the Golden Mean ?
Isn't that beautiful ??!!"
or "Can you tell me what "a" and "b" are in the equation "a divided by b
equals a plus b divided by b ?"
I'd venture that their response would likely be something like " Eh ?" (or
"Huh?" in Murrican).
OTOH, if I were to generate the logarithmic spiral whose growth factor is
"phi" (aka "Golden Spiral", "Fibonacci spiral" ) using nothing more than
the aforementioned piece of string and pencil and then show them images of
a nautilus shell section
http://biomimicrysandiego.org/hello/
and Botticelli's "Venus"
http://tinyurl.com/mmourzr
and/or Leo's "Mona"
http://tinyurl.com/lryhdvs
and the Milky Way
http://tinyurl.com/kngrb45
etc., chances are pretty good that the reaction would be entirely
different, perhaps even one of awe in some instances.
That is to say, "Yes" pretty much everything can be described by equations
but I'd venture that sometimes, as in this instance, geometry does a
better job of explaining the beauty and logic of "what, how and why" and
in a more direct way.
Another example where I think that graphical means does the job more
simply would be in determining the proper horizontal extension to provide
optimal full summer shading/full winter exposure of an equator-facing
opening.
But don't ask me how this relates to the original subject of "toxic" roof
runoff.
--
=== * ===
Rob Tom . . . T60BOM
Kanata, Ontario, Canada
A r c h i L o g i c at Y a h o o dot C A
(manually winnow the chaff from my edress if you hit "reply")
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