![]() ![]() Let’s consider a simple case of a two column layout with a fixed width of 960px. The first use of the golden section is when creating a grid for your design. Now how do you actually apply these principles in your design and when might you use them? Hopefully some of the above has convinced you of the aesthetic qualities of golden section proportions. Click the image above to see how some golden shapes can be constructed. Think outside the box or in this case outside the golden rectangle. You can create golden rectangles, triangles, ellipses, pentagrams, and spirals. However, a variety of mathematics can be applied to different layouts and a variety of shapes can be constructed from golden section proportions. When people think of shapes with golden section ratios they typically think of a golden rectangle where one side divided by the other is 1.618. Many biological growth patterns approach the golden section instead of being exact in the same way the Fibonacci Sequence approaches the golden section ratio. The ratio of the numbers 13/8 are found in pine cone spirals and the ratio of numbers 34/21 are found in the spiral of a sunflower. Vitruvious, da Vinci, and Durer used it to create divine proportions of man. It’s found in the musical compositions of Mozart. Some have argued that Virgil used the sequence in the poetry of the Aenid. With early numbers in the sequence this may not appear to be true, but as we continue along the sequence the division approaches 1.618 rather quickly.Īs you might expect the Fibonacci sequence is also found in art and nature. ![]() If you take any number in the sequence and divide it by the previous number the result approximates Phi or the golden ratio. I’ll spare you the deep mathematics talk (we’ll just do a bit of division), since what we’re mainly interested in is how the sequence relates to the golden section. ![]() If you’re unfamiliar with the fibonacci sequence, it begins by definition with the numbers 0, 1 and then each successive number in the sequence is the sum of the previous two numbers. The mathematics behind the golden ratio is heavily connected to the Fibonacci Sequence. The golden ratio or divine proportion is a visual representation of the golden number Phi (Φ) which is approximately 1.618. This is more easily seen in a simple diagram. The golden ratio is one where the ratio of the smaller segment to the larger segment is the same as the larger segment to the sum of both segments. We have a preference toward objects that use golden proportions. Whether we’ve been genetically programmed to like them or we find them pleasing due to all the examples around us, the golden section has clearly been a part of nature and human creation throughout history. Golden section proportions are also present in Greek art, writing, and architecture, and in the spiral shape of shells. They exist in the proportions of human beings, the growth patterns of plants, animals, and insects, and structures like Stonehenge and the Parthenon. Golden section proportions can be found in both nature and man-made structures. “The power of the golden section to create harmony arises from its unique capacity to unite different parts of a whole so that each preserves its own identity and yet blends into the greater pattern of a single whole.” ![]()
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