Thursday, October 13, 2011

The Golden Ratio and Proportion in Design

The “golden ratio” has been a subject of fascination for artists and mathematicians for millenia.  The golden ratio occurs in nature, and is a mathematical formula used by artists, designers, architects, and even musicians in creating beauty.

What is this magic ratio?  Technically it’s 1.1688.  But for artistic  uses it’s often simplified to this:  1:1.5, or a 2:3 ratio.

The Swiss architect Le Corbusier, who applied the golden ratio (as well as the related Fibonacci sequence) in his work, believed the golden ratio naturally appeals to the human eye, and that people throughout time and space are drawn to it whether they know it as mathematical formula or not.

Corbusier’s idea is an intriguing one, and there’s ample evidence to support it.  Art and science both recognize that faces and figures considered “beautiful” throughout history have features that relate to each other in the golden ratio.  Leonardo da Vinci was intrigued by the golden ratio and depicted it in his famous Vitruvius Man (above).

Architecture, art, and design of all media also use a 2:3 ratio in many applications for good aesthetics.  These two diagrams show “good” and “bad” proportion in art compositions—the “good” rectangle approximating the golden ratio.

In addition, well-proportioned clothing has historically been based on the golden ratio.  Here’s a picture from a 1926 high school home economics textbook, in a chapter about proportion in clothing construction.  The figure on the right captures it; the one on the left is off.  The two sections of the dress at right are generally in golden-ratio proportion, and the sleeve divides the girl’s arm into golden ratio sections.

Isn’t this fascinating?

For more about the golden ratio, here’s a site you might like, and here’s one more.

Please come check out my collection of well-proportioned vintage dresses, vintage shoes, and other vintage clothes at Chronologie Fine Vintage!    Love,

sallymandy

Protege said...

Ah, I love the idea of ratios and proportions.

It exists all around us.
The Nautilus Shell is used often as an example of the golden ratio.;)

And I LOVE "The Vitruvian Man"; as you have noticed, I have the drawing in my header.
As a scientist, I am fascinated by it and by Leonardo's genius. As an artist, I am in constant awe of everything he created.;))

Lovely post as always.;))

drollgirl said...

it is so funny to reduce creativity and design elements to a formula, BUT IT WORKS! it is so cool.

Imogen Lamport said...

The golden mean is a difficult concept to grasp, so I just tell my clients that they need to wear two rectangles, and one should be longer than the other!

sallymandy said...

Protege: It's kind of intimidating posting this for a world that's probably way better at math than I am, BUT I checked out most of my ideas with my engineer hubby. He acted all cool like Fibonacci's sequence is easy as pie, but mostly he was nice and supported me. :)

Drollgirl: Yes, it's both funny and cool. I've always felt that if I can learn the "rules" to something then I'm much freer to break them. So...that's why I went to the trouble to learn what this golden ratio is in a little more depth than I knew before.

Imogen: I think that's wise. Said hubby above was trying to show me an "easy" way to apply the actual 1.61 golden ratio to a floral design and I said, whoa there, I don't need that much detail. Mostly this is a fun mental exercise, and I love knowing that these principles of aesthetics that apply to clothes have this tremendous history and crossover to other arts and even science.

Stephanie N. said...

The home econmics illustration is adorable.

I thoroughly appreciate your thoughful and comprehendable explanations of design principles via mathematics, engineering, art, and more. Keep 'em coming!

Duchesse said...

When working with two elements, 1/3x and 2/3 y works; hope that makes your flower arranging easier.

Relyn said...

I've long been fascinated by the Golden Ratio. In fact, I taught my second grade students a little about it when we recently painted our self-portraits.

Lorna said...

Yes, this is fascinating, and I have seen tv programs (Discovery Channel) that go into everything that you mentioned in your post.

WHAT AN INTERESTING BLOG YOU HAVE!!!!!!!!!

~Lorna