[Greenbuilding] Phi (was Re: Roof slopes )

futureship0000 futureship0000 at hotmail.com
Fri Aug 15 08:56:39 MDT 2014

This may be of interest to some  for this topic ...
The golden mean and spiral is part of
Sacred geometry - Wikipedia, the free encyclopedia


Sent from my Verizon Wireless 4G LTE Smartphone

<div>-------- Original message --------</div><div>From: RT <ArchiLogic at yahoo.ca> </div><div>Date:08/15/2014  10:12 AM  (GMT-05:00) </div><div>To: Green Building <greenbuilding at lists.bioenergylists.org> </div><div>Subject: [Greenbuilding] Phi (was Re: Roof slopes ) </div><div>
On Thu, 14 Aug 2014 18:35:48 -0400, Michael O'Brien <obrien at hevanet.com>

> 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)


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


and  Botticelli's "Venus"


and/or Leo's "Mona"


and the Milky Way


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

But don't ask me how this relates to the original subject of "toxic" roof

=== * ===
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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