![]() These can be vertical, horizontal, diagonal or spiral. I use a handy piece of software called PhiMatrix ( ) that enables you to lay lines over an image to see where Golden Ratios may be present. It is often necessary to crop the image, so that phi can be applied. If I am using a reference photograph, I first look to see if there are any elements of it where Golden Ratios can be used. Most of my paintings are riddled with dimensions based on phi. I am a strong advocate of using golden sections when planning my paintings. You can see the extract here: "Donald in Mathmagic Land". Walt Disney produced a fascinating short movie in 1959 called "Donald in Mathmagic Land" in which he explains to Donald Duck the numerous ways the Golden Section appeasrs in mathematics, art and nature. Toyota), automobiles, consumer goods and buildings (e.g., the Taj Mahal and the Acropolis in Athens). It is also used deliberately in industry for the design of logos (e.g. Nevertheless, it appears to have been used by Leonardo Da Vinci (notably in “The Last Supper), Salvador Dali (in his painting “The Sacrament of the Last Supper”, which is painted on a golden section canvas) and several others. However, some think that these claims tend to be exaggerated. There are numerous claims of how the Golden Ratio appears prominently in art, architecture, sculpture, anatomy, etc. However, Phi is simply the ratio of line segments that result when a line is divided as shown below. If you want more information, there is plenty on the Internet. I do not want to bore you with the mathematics associated with phi and the Golden Section but in simple terms, they can be shown in the diagrams below. Its mathematical cousin is the Fibonacci Sequence (0, 1, 1, 2, 3, 5, 8, 13, 21 …). Phi with an upper case “P” is 1.618…, while phi with a lower case “p” is 0.618…, the reciprocal of Phi and also Phi minus 1. It is normally denoted by “Phi” ø (most often pronounced fi like "fly") and the number 1.618. The Golden Ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon. I believe that this gives my paintings a better balance than using the more traditional "rule of thirds". You may note that the position of the sun or some other key feature or length often fits this ratio. (In fact, the ratio is a number that begins 1.32472… and carries on forever).I am a strong advocate for using the Golden Ratio (Phi - 1:1.618) in my paintings. It turned out that the ratio 1.325, which gives you the rectangle that creates the Harriss spiral has been written about – it is known as the “ plastic number” – but Harriss could find no previous drawings of the spiral. His first concern was that maybe someone else had had, in fact, drawn the spiral “One thing about mathematical discoveries and mathematical art is that even if the process is completely new there is no guarantee that someone else has not already explored it.” “It’s more difficult to make something mathematically satisfying that people haven’t seen before.” “It’s not hard to make something that no one has seen before,” he said. But he was particularly delighted because he arrived at the spiral using a very simple mathematical process. ![]() Harriss was overjoyed when he first saw the spiral because it was aesthetically appealing – one of his primary aims was to draw branching spirals like you might find in Islamic art or the work of Gustav Klimt.
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