Fibonacci, Golden Rectangle, phi
What is the Golden Ratio?
The Golden Ratio is a unique number, approximately 1.618033989. It is also known as the Divine Ratio, the Golden Mean, the Golden Number, and the Golden Section. Its unique mathematical properties have resulted in a very long and influential history.
What is the Fibonacci Sequence of Numbers?
The Fibonacci numbers are a unique sequence of integers, starting with 1, where each element is the sum of the two previous numbers. For example: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.
Relationship Between the Fibonacci Sequence and the Golden Ratio
The Fibonacci Sequence is an infinite sequence, which means it goes on for ever, and as it develops, the ratio of the consecutive terms converges (becomes closer) to the Golden Ratio, ~1.618. For example, to find the ratio of any two successive numbers, take the latter number and divide by the former. So, we will have: 1/1=1, 2/1=2, 3/2=1.5, 5/3=1.66, 8/5=1.6, 13/8=1.625, 21/13=1.615.
Leonardo Pisano Fibonacci
1170 - 1250
Biography
Golden Mean or
Golden Ratio
The rule of thirds is a widely accepted aesthetic principle that is one of
the long standing rules of photography. It basically says that you will get a
much more aesthetically pleasing image if you place the subject of your photo a
third of the way across the frame instead of in the center of the frame. This is
a simplified form of the principle of the Golden Mean or Golden Ratio. But what
is the Golden Mean or the Golden Ratio? If line A is divided into two sections,
one larger than the other (B and C), the golden ratio is achieved where A/B =
B/C, which is 1.6180339887…Golden Ratio
In photography we talk about a Golden Rectangle, in which the ratio of the longer side to the shorter one turns out to be the golden ratio. In the 12th century, Fibonacci produced a series of numbers by adding together pairs of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 etc (each number is created by adding together the two previous numbers). It turns out that the ratio between each successive pair of numbers gets closer and closer to the Golden Ratio. If you start dividing a Golden Rectangle by the Golden Ratio (represented by the Greek letter PHI)you can keep sub-dividing it down infinitely and joining the corners of the successive rectangles produces a logarithmic Golden Spiral which exactly matches the growth of the Nautilus sea shell . A photograph whose composition follows this idea seems to be visually harmonious.
Ideally, you need to start off with a "canvas" that is a golden rectangle; this is often a little impractical because these rectangles are a little too wide (or tall) for many shots. If you roughly duplicate the path of the Golden Spiral in your photographs though, it will increase your odds of getting appealing results.
Using the Golden ratio forms a fluid line for the eye to trace through the picture, where the Rule of Thirds is more static. Your viewer's gaze will invited along the line of the spiral which creates a more symmetrical visual flow and a compelling experience. You want to place the subject (or focal point) of your photograph in the tightest end of the spiral, and the other elements of the picture should roughly follow the path of the spiral. The Golden Spiral can be rotated in the frame or transposed from top to bottom so you can create more variety when you are composing pictures.
This idea is best suited for landscape photography where the lines are long and dramatic but it can also be effective in close-ups and portraits. Once you understand the basic form of the Golden Spiral, this idea becomes intuitive and thus easy to apply. You don't need difficult mathematical calculations to produce an compelling picture.
Taking pictures using the Golden Spiral is a more fluid and visually compelling way to structure your photos than the more static Rule of Thirds. With practice this method becomes intuitive. It will create a more symmetrical visual flow, especially in landscape photography. Have fun experimenting with it!
The Golden Ratios are approximately (and actually) as follows:
- 6 x 3.75" (6 x 3.70")
- 7 x 4.25" (7 x 4.3")
- 8 x 5.00" (8 x 4.9")
- 9 x 5.50" (9 x 5.56")
- 10 x 6.25" (10 x 6.18")
- 11 x 6.80" (11 x 6.79")
- 16 x 10" (16 x 9.88")
- 18 x 11" (18 x 11.12")
PhiMatrix™ Overview
PhiMatrix is a design and analysis software application for Windows and Mac. The PhiMatrix grid system quickly overlays any image in any software on your screen to identify or apply phi proportions in various grid styles, as well as custom user-defined ratios. It's not a plug-in but a universal overlay, so you can use it with PhotoShop, illustrator, InDesign, Picassa and any other software you use.
Video instructions for
phimatrixSee Also
Goldennumbernet a leading site on Phi
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