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<div>This may be of interest to some for this topic ...</div>
<div>The golden mean and spiral is part of </div>
<div>Sacred geometry - Wikipedia, the free encyclopedia</div>
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<a href="http://en.m.wikipedia.org/wiki/Sacred_geometry">http://en.m.wikipedia.org/wiki/Sacred_geometry</a></div>
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<div style="font-size:9px;color:#575757">Sent from my Verizon Wireless 4G LTE Smartphone</div>
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<div>-------- Original message --------</div>
<div>From: RT <ArchiLogic@yahoo.ca></div>
<div>Date:08/15/2014 10:12 AM (GMT-05:00) </div>
<div>To: Green Building <greenbuilding@lists.bioenergylists.org></div>
<div>Subject: [Greenbuilding] Phi (was Re: Roof slopes ) </div>
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<div class="PlainText">On Thu, 14 Aug 2014 18:35:48 -0400, Michael O'Brien <obrien@hevanet.com>
<br>
wrote:<br>
<br>
> I'm puzzled, of course the golden mean can be generated by arithmetic, <br>
> the formula is (1 + √5) ÷ 2.<br>
> Or did you mean you prefer the geometric option?<br>
<br>
and Vadurro, Rob, EMNRD <rob.vadurro@state.nm.us> wrote:<br>
<br>
> Or algebra: a/b= b/a+b<br>
<br>
<br>
I would venture that if you handed either of the above equations to the <br>
Ancient Greek who was the Project Manager in charge of building the <br>
Parthenon, and asked her to build it thusly, she'd have smacked you <br>
upside the head and handed you over Jake the Rake and his brother Joe the <br>
Hoe and had them bury you up to your ears in the lime pit.<br>
<br>
OTOH, if you handed her a sketch similar to this image (2nd image at <br>
following link)<br>
<br>
<a href="http://rouleauc.blogspot.ca/2009/04/more-you-know-golden-ratio.html">http://rouleauc.blogspot.ca/2009/04/more-you-know-golden-ratio.html</a><br>
<br>
she'd have had no trouble visualising and understanding the design and <br>
could easily replicate the layout drawings using not much more than a <br>
pencil and a piece of string. And I'll bet she'd have been so pleased that <br>
she'd have bought you a coffee.<br>
<br>
**<br>
<br>
Or, let's say I walk up to a person on the street and say to them:<br>
<br>
"Did you know that if you take the square root of 5, add 1 to it and <br>
then divide the sum in half you'd get "phi", the Golden Mean ?<br>
Isn't that beautiful ??!!"<br>
<br>
or "Can you tell me what "a" and "b" are in the equation "a divided by b <br>
equals a plus b divided by b ?"<br>
<br>
I'd venture that their response would likely be something like " Eh ?" (or <br>
"Huh?" in Murrican).<br>
<br>
<br>
OTOH, if I were to generate the logarithmic spiral whose growth factor is <br>
"phi" (aka "Golden Spiral", "Fibonacci spiral" ) using nothing more than <br>
the aforementioned piece of string and pencil and then show them images of<br>
<br>
a nautilus shell section<br>
<br>
<a href="http://biomimicrysandiego.org/hello/">http://biomimicrysandiego.org/hello/</a><br>
<br>
and Botticelli's "Venus"<br>
<br>
<a href="http://tinyurl.com/mmourzr">http://tinyurl.com/mmourzr</a><br>
<br>
<br>
and/or Leo's "Mona"<br>
<br>
<a href="http://tinyurl.com/lryhdvs">http://tinyurl.com/lryhdvs</a><br>
<br>
<br>
and the Milky Way<br>
<br>
<a href="http://tinyurl.com/kngrb45">http://tinyurl.com/kngrb45</a><br>
<br>
etc., chances are pretty good that the reaction would be entirely <br>
different, perhaps even one of awe in some instances.<br>
<br>
That is to say, "Yes" pretty much everything can be described by equations <br>
but I'd venture that sometimes, as in this instance, geometry does a <br>
better job of explaining the beauty and logic of "what, how and why" and <br>
in a more direct way.<br>
<br>
Another example where I think that graphical means does the job more <br>
simply would be in determining the proper horizontal extension to provide <br>
optimal full summer shading/full winter exposure of an equator-facing <br>
opening.<br>
<br>
But don't ask me how this relates to the original subject of "toxic" roof <br>
runoff.<br>
<br>
<br>
<br>
-- <br>
=== * ===<br>
Rob Tom . . . T60BOM<br>
Kanata, Ontario, Canada<br>
<br>
A r c h i L o g i c at Y a h o o dot C A<br>
(manually winnow the chaff from my edress if you hit "reply")<br>
<br>
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