# The Golden Rectangle and other eye pleasing formulas.

• posted on December 18, 2004, 6:33 pm
I would love to see a discussion of this. When designing things like garden gates and arbors, even fence panels and window placement I often create stuff that doesn't look quite right, other times it looks great.
I understand to concept sorta, of the golden rectangle but what about other shapes like rounded top gates, ovals, etc.
Examples. I make one gate it looks great another looks a little off, but I really can't see why. I make a lattice frame arbor and it looks terrific, change the size and shape of the 'holes' or the boards and it looks awkward, clunky.
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• posted on December 18, 2004, 9:27 pm
The Golden Ratio (1 plus root 5 / 2 = PI) is, for the sake of argument, 1.618. It is the relationship of: 1. the side of a rectangle to the width 2. the height of the Great Pyramid of Giza to 1/2 its base 3. the first 5 planets in the Solar System to one another (almost) 4. the height of the columns in the Parthenon to the width of the edifice 5. the height of the Parthenon roof to the width of the edifice 6. the height of a Pompadour Highboy to the height of the base 7. our eyes divide our head ant the Golden Ratio 8. our navel divides our body at the Golden Ratio
There are a lot of others, but these should suffice for a start.
Think of your gate as a rectangle. The walkway is the width and the passageway the height. If these are not in agreement the overall look will be, somehow, amiss. We are genetically (?) predisposed to observe things in this manner.
The same is true for your lattice
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PDQ --
| | I would love to see a discussion of this. | When designing things like garden gates and arbors, even fence panels and window | placement I often create stuff that doesn't look quite right, other times it | looks great. | | I understand to concept sorta, of the golden rectangle but what about other | shapes like rounded top gates, ovals, etc. | | Examples. | I make one gate it looks great another looks a little off, but I really can't | see why. | I make a lattice frame arbor and it looks terrific, change the size and shape of | the 'holes' or the boards and it looks awkward, clunky. | |
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• posted on December 18, 2004, 10:03 pm

One small correction:
It's PHI, pronounced "fi", rhyming with "fly", PI is something else.
In Dan Brown's "DaVinci Code" they stated that it's pronounced "fee", but dictionaries disagree.
Barry
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• posted on December 18, 2004, 10:19 pm
Ba r r y wrote:

One more (even smaller?) correction/amplification... :)
phi = (1 + sqrt(5))/2
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• posted on December 19, 2004, 4:18 am
I stand corrected. I wonder where the H the "H" went?
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PDQ --
| | >The Golden Ratio (1 plus root 5 / 2 = PI) is, for the sake of argument, 1.618. | >It is the relationship of: | | One small correction: | | It's PHI, pronounced "fi", rhyming with "fly", PI is something else. | | In Dan Brown's "DaVinci Code" they stated that it's pronounced "fee", | but dictionaries disagree. | | Barry
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• posted on December 19, 2004, 6:49 am
wrote:

It's a Greek letter, and the Greeks pronounce it "fee". Who would know better?
B.
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• posted on December 18, 2004, 11:33 pm
The Golden Ratio (1 plus root 5 / 2 = PI) is, for the sake of argument, 1.618. It is the relationship of: 1. the side of a rectangle to the width 2. the height of the Great Pyramid of Giza to 1/2 its base 3. the first 5 planets in the Solar System to one another (almost) 4. the height of the columns in the Parthenon to the width of the edifice 5. the height of the Parthenon roof to the width of the edifice 6. the height of a Pompadour Highboy to the height of the base 7. our eyes divide our head ant the Golden Ratio 8. our navel divides our body at the Golden Ratio
There are a lot of others, but these should suffice for a start.
Think of your gate as a rectangle. The walkway is the width and the passageway the height. If these are not in agreement the overall look will be, somehow, amiss. We are genetically (?) predisposed to observe things in this manner.
The same is true for your lattice
I learned it was expressed X+1=X ^2 (x squared) which can be expressed as x^2-x-1=0. Solve it with the quadratic formula and you get 1.618 or -0.618 -
just like another poster stated. :-)
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PDQ
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• posted on January 2, 2005, 6:20 pm

FWIW: How could those both be correct? Wouldn't that require that the height of the roof and the height of the columns be equal, and as best as I can tell that is not the case -- though maybe it is a parallax issue.
http://classics.lss.wisc.edu/~khallen/courses/cla517/Parthenon%20acropolis.jpg
http://www.unice.fr/LEML/coursJDV/images/morpho/parthenon-1.jpg
- Igor
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• posted on December 18, 2004, 10:27 pm

Look for this book: The Geometry of Design. It's available on amazon.com. Everything you want to know and more. It gets mixed reviews, but I like it.
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• posted on December 18, 2004, 11:20 pm
I read a book this summer by a mathematician that blew the Golden Ratio off it's pedestal. It's not clear that the GR is all that "Golden". People point to various buildings, flowers, the shell of the nautilas, etc, but when you try to really figure this out, it doesn't hold true for many things. However there ratio of 1.6 to 1 has been proven to be pleasing to the eye and since the GR is close enough, then you can't go wrong in using it.
I just wouldn't try to design something that is to a specific ratio, but perhaps to a scale of the things around it. A garden gate that is out of scale of the fence will feel uncomfortable, etc.
I love Frank Lloyd Wright's work and what I take from him is to design based on function and the surroundings. Look to nature for your models. Good luck!
MJ Wallace
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• posted on December 19, 2004, 4:56 pm
You might borrow some ideas from photography as well. See 'rule of thirds'.
Dave

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• posted on December 20, 2004, 1:40 am
"The Golden Mean" is the name we were taught by professors from Pratt and Cooper Union back in the 60's and while he didn't invent the ratio, the master matmetician Leonardo Pisano (aka. Fibonacci) calculated and recorded the formula. In the 70's I worked with an artist named Richard Botto on a corporate design team... Dick's true love was oil painting and the integration of the Golden Mean in his work. He has since become well known in the art field as perhaps one of the best equine artists in the country, and many refer to him as the painter of champions. Not all, but many of his works follow the golden mean, and he used to actually analyze many elements within his paintings to utilize the formula. Dick re-introduced the Golden Mean to me and I can't tell you how many times I've used it in designing graphics projects. The ratio makes for a very "comfortable" shape and this has been proven over and over by various institutions and organizations.
It may be inadvertent or intentional, but have you noticed that today's new HDTVs are _almost_ dead-on with the Golden Mean? Old TVs are 4:3 ratio and the HDTVs are 16:9... change that to 1618:1 and you'd have the "perfect" picture.
Mike