Golden Section

The Golden Section, Golden Mean or Golden Ratio all refer to a system of harmonious relationships. The relationships could be between different musical notes, the spaces between objects, or the relative sizes of objects as they are visually or auditorily compared to one another.

This system of ratio is first exemplified by the Fibonacci Number Series:

1, 1, 2, 3, 5, 8, 13 and so on where each number in the sequence is determined by adding the two previous numbers together. (1+1=2, 1+2=3, 2+3=5 and so on).

Artists and designers can use this system to create harmony between objects by assigning placement and size of those objects to locations within a composition that correspond to intervals determined by the ratio. These intervals are also known as dynamic rectangles.

Here the artist applied the Fibonacci Number sequence to a grid to exaggerate specific features by enlarging or diminishing them according to larger or progressively smaller increments of space.

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The Golden Section is a specifically sized rectangle or set of rectangles that all relate to one another because of their original relationship to a square. One of the classic examples of the use of the Golden section is by the ancient Greek architects of the Parthenon.

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This division of space is also related to the number series mentioned above, but it can also be constructed from any size square.

step 1. Draw a square. Make the baseline or bottom side of the square longer

step 2. Find the midpoint of the bottom side of the square

step 3. Place the point of a compass at this midpoint ant the pencil end at either of the top corners and draw an arc from the corner down to the baseline. Everything up to this point is simply to locate the intersection point of the arc and the baseline.

step 4. draw a line perpendicular to the baseline at the intersection point of the arc and baseline. Draw this line as tall as the height of your original square.

step 5. Extend the top of the square over to the perpendicular line. The resulting rectangle is a golden section of the original square.

 

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step 6. Use your compass again from the same midpoint of the original square but now extend the pencil end to the new corner of the golden section and draw a new arc from baseline up till it crosses the height line. The result is another, smaller golden section.

step 7. By continuing to draw arcs from the resulting GS you will create ever smaller sized new golden sections. All of them will be related harmoniously to the size of the original square.

It is important to realize that these are not “compartments” to be filled in, but instead a grid that can be referred to for placement or size of objects as well as spacing intervals between objects or both.

Below the size relationships are expanded in all directions not just left to right.

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The designer Jan Tschichold used the golden section to determine the size of margins and the text area of a book.

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English: Golden ratio Česky: Zlatý řez

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