typography 2
math and graphic design
Fibonacci SeriesIn the 12th century, Leonardo Fibonacci discovered a simple numerical series that is the foundation for an incredible mathematical relationship behind phi. Starting with 0 and 1, each new number in the series is simply the sum of the two before it.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
or think of it this way:
0+1=1
1+1=2
1+2=3
2+3=5
3+5=8
5+8=13 ... The ratio of each successive pair of numbers in the series approximates phi (1.618…) , as 5 divided by 3 is 1.666..., and 8 divided by 5 is 1.60.
Fibonacci's rule: Each term is the sum of the two terms preceding.
The Golden Ratio
A ratio with the elements of a form, such as height to width, approximating 0.618.
It is also known as golden mean, golden number, golden section, golden proportion, divine proportion, and sectio aurea.
The golden ratio is irrational (never-ending decimal) and can be computed with the equation (
5-1)/2. Adding 1 to the golden ratio yields 1.618... referred to as Phi The values are used interchangeably to define the golden ratio, as they represent the same basic geometric relationship. Geometric shapes derived from the golden ration include golden ellipses, golden rectangles and golden triangles. 
The golden ratio is the ratio between two segments such that the smaller (bc) segment is to the larger segment (ab) is to the sum of the two segments (ac), or bc/ab=ab/ac =0.618.
The golden ratio is found throughout nature, art, design, and architecture. Pine cones, seashells, and the human body all exhibit the golden ratio. Piet Mondrian and Leonardo da Vinci commonly incorporated the golden ratio into their painting. Stradivari utilized the golden ratio in the construction of his violins. The Parthenon, the Great Pyramid of Giza, Stonehenge, and the Chartres Cathedral all exhibit the golden ratio.
While many manifestations of the golden ratio in early art and architecture were likely caused by processes not involving knowledge of the golden ratio, it may be that these manifestations result from a more fundamental, subconscious preference for the aesthetic resulting from the ratio. A substantial body of research comparing individual preferences for rectangles of various proportions supports a preference based on the golden ratio. However, these findings have been challenged on the theory that preferences for the ratio in past experiments resulted from experimenter bias, methodological flaws, or other external factors.
Whether the golden ratio taps into some inherent aesthetic preference or is simply an early design technique turned tradition, there is no question as to its past and continued influence on design. Consider the golden ratio when it is not at the expense of other design objectives. Geometries of a design should not be contrived to create golden ratios, but golden ratios should be explored when other aspects of the design are not compromised.
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Some of the above information taken from:
University Principles of Design, William Lidwell, Kritina Holden, Jill Butler. ISBN 1-59253-007-9
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HOW TO: Finding the Golden Ratio
A quick and easy way to get a rough estmate on finding the golden ratio is to divide or multiply by 1.618.
Example: 5 / 1.618 = 3.0902349 (using the correct formula it would be 3.0901699)
This simple equation works well for designers because we don't need to worry about what is after the decimal point. Feel free to round to the nearest point to become more accurate.
Also download the James Mellers Phicalculator (free) The Phicalculator will give you an accurate answer. Works on both PC and Mac.
Note: If you are shooting a rocket to the Moon or Mars you may want to use the correct formula. :-)
The Ratio and Typography
Some typefaces are designed to the golden ratio. Adrian Frutiger was fascinated with the golden ration. After developing Univers, he was so upset that it wasn't more accurate he spent years developing the typeface after his name known as Frutiger. The typeface Meta, created by Erik Spiekermann is also a good example of using the golden ratio in type design.
You can also use the golden ratio to change different sizes in type.
If type sizes are chosen according to the golden section, the results is a Fibonacci series:
(a) 5•8•13•21•34•55•89 …
These sizes alone are adequate for many typographic tasks but to create a more versatile scale of sizes, as second or third interlocking series can be added.
(b) 6•10•16•26•42•68•110…
(c) 4•7•11•18•29•47•76…
All three of these series a,b and c obey the Fibonacci rule (Each term is the sum of the two terms preceding). Series b is also related to series a by simple doubling. The combination of a and b is therefore a two-stranded Fibonacci series with incremental symmetry, forming a very versatile scale of type sizes:
(d) 6•8•10•13•16•21•26•34•42•55•68…
Depending on how you want to design, if you use one of these scales, a,b,c, or d in your development process you can find how to arrange your hierarchy in your design. Here it is for us visual designers...
Example:
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Some of the above information taken from:
The Elements of typographic Style, Robert Bringhurst. ISBN 0-88179-206-3
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The Ratio and the Grid
Just like type you can use the golden ratio in your grid! Mark Boulton has constructed a fantastic website on the grid.
1. Subdividing ratios
2. Ratios and complex grid systems
3. Grid systems for web design: Part 1
4. Grid systems for web design: Part 2 Fixed
5. Grid systems for web design: Part 3 Fluid
The Ratio and Photography
Looking at photography you can see the golden section within the images.
Should I be looking for the Ratio?
This is a good question. I think it is important to try to look for it, because of its natural properties as well as historical usage in graphic design, art, music, and architecture. If you don't look for the golden ratio, it will happen in your work naturally even without trying to find it…
That being said, being aware of the ratio may make you a better designer.
More on the Golden Ratio:
James Mellers Phicalculator
Donna Stanton and Phi
The Golden Rule
What the hell is the Fibonacci Series
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