[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>  

> 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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