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Old 12-20-2006, 07:57 PM   #1
Mike McCarty Mike McCarty is offline
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Joined: Dec 2001
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The Golden Section

This topic has been copied from the middle of another thread in order to make it more accessible

I'm going to try and get to the bottom of this "Golden Section."

Phi = 1.618033988749895
phi = .618033988749895

Pronounced Phi as in fish (pheel phree to jump right in).
Small "p" being the reciprocal of the capital "P".

The ratio, or proportion, determined by Phi (1.618 ...) was known to the Greeks as "dividing a line in the extreme and mean ratio" and to Renaissance artists as the "Divine Proportion." It is also called the Golden Section, Golden Ratio and the Golden Mean.

Just as pi is the ratio of the circumference of a circle to its diameter, phi is simply the ratio of the line segments that result when a line is divided in one very special and unique way.

Divide a line (one side of your canvas) such that the ratio of the length of the entire line (A) to the length of the larger line segment (B) is the same as the ratio of the length of the larger line segment (B) to the length of the smaller line segment (C). In other words (C) is to (B) as (B) is to (A). Conphused yet?

The Seurat example below, created by Seurat with full intention of following the golden section principles, is 300w x 195h pixels.

If we consider the whole first we would multiply the top of the canvas 300w by phi .618 and we would get 185. If we then follow over 185 clicks from the left this would be represented by the blue (and continuing down with the white) vertical line on the right. What we now have are two large rectangles which have that special relationship discussed above: A to B to C. Each of the two resulting rectangles would be considered a golden section.

If we then take the 195h and multiply it by phi .618 we get 120. Coming up from the bottom right 120 clicks we see this represented by the horizontal blue line forming the rectangles at the top and bottom right. We now have two more rectangles on the right side of the canvas each being a golden section.

As you can see it goes even phurther, creating more sections from the last.

The idea was to place in these so called golden sections the important aspects of the composition.

And of course any of the multiplications by phi could be done as a division by Phi, it being the recipricol.

And a couple more examples:

1- Tea for the Bishop, Jehan Georges Vibert
2- Superior Court Judge, Tom Edgerton

Long live the phorum.
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Mike McCarty
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