Which rectangle is more appealing

A real thing can be "more or less" large as the golden ratio. But let's take the number 1. The beauty of the golden ratio lies in its definition: it's conceptual, not visual. By the way: in nature, one can find a lot of "numbers", both rational and irrational.

In a simple cubic lattice, the diagonal of each face is the square root of 2, and the diagonal of each cube is the square root of 3 both irrational. Measuring the distance between different points, you can find many "magical numbers".

And, of course, I agree that every piece of art has its "right" proportions and measures, depending on its content. Mario, thanks for those important points. Even the most fine-tuned artist's eye probably can't judge ratios of height to width closer than 1 or 2 percent. And for those who aren't familiar with math terminology, when a number is "irrational" it doesn't mean crazy, it just describes a certain kind of number that can't be written as a simple fraction.

Another one is "pi," the ratio of the circumference to the diameter of a circle. That one has always fascinated me more than "phi" because I've always played around with wheels, anemometers, and other circular things. I was thinking that if the GR appears in nature so much it is likely more related to structural integrity than aesthetic appeal. Perhaps engineers, and physicists have already explored this thought.

There are often very practical reasons for things to exist in the natural world. There is hardly a given method, process or rule by which beauty can or ought to be created. The more we develop vision and insight, the better; that's what I gather from these posts. A great series of posts that I will share on my own blog.

And I love the conclusion you come to in this last paragraph. Beautifully written! Well, what a relief! I read your posts on this subject the past few days with much interest. I'm very glad to be able to choose my compositions and painting dimensions according to what pleases me rather than a mathematical formula. Sometimes painting can be a tedious enough. I think I would lose interest altogether if I had to first go through the mental gymnastics required for the golden mean in the planning stages.

It wears me out just thinking about it. Not to say that planning shouldn't be done, of course. I have really appreciated your posts on this topic. My art education is quite limited and I find your writing easy to read. I am learning lots. I was wondering though if the concepts explored in the Golden Mean are present in visual art and architecture from other cultures.

Has it been found in Japanese work, for instance? Or Aztec? Or Sudanese? I occasionally write for a photo blog, and some time back, did an essay on the "proper" size for photographs. Of course, there really is no such thing, but the question I was exploring involved the fact that photographic print sizes had always been constrained by mechanical aspects of the craft, such as grain size which affects practical enlargement size and the size of practical enlargers and so on.

This changed with the rise of digital photography and digital printers. My question was, if you take an art that is viewed in very much the same way as wall-hung photographs, that do not have these mechanical constraints -- I was thinking of painting -- what size is most often chosen by artists?

We feel pleasure and we call it beauty. Bejan, an award-winning engineer who developed a new law of physics governing the design of matter as it moves through air and water in , believes this "constructal law" governs systems that evolve in time, from cars in traffic to blood in the circulation, to how vision develops.

Vision and cognition evolved together, he said. Getting smarter is the constructal law in action. Earlier this year, in a paper published in the Journal of Experimental Biology, Bejan demonstrated how this law was behind his theory of how elite athletes had got taller, bigger and thus faster in the past years. This article is more than 11 years old. Refractive Lens Exchange. Stye and Chalazion. Chemical Peel. Cleft lips and cleft palates. Drooping Eyelid Ptosis.

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In the world of art, architecture, and design, the golden ratio has earned a tremendous reputation. Those who believe the golden ratio is the hidden math behind beauty are falling for a year-old scam. The value this works out to is usually written as 1. The most famous application of the golden ratio is the so-called golden rectangle, which can be split into a perfect square, and a smaller rectangle that has the same aspect ratio as the rectangle it was cut away from.

You can apply this theory to a larger number of objects by similarly splitting them down. In plain English: if you have two objects or a single object that can be split into two objects, like the golden rectangle , and if, after you do the math above, you get the number 1. It comes out to 1. You can get close with more standard aspect ratios.