Using the Golden Section
 

To locate the center of interest with the Golden Section: Divide the height of your canvas by 2.62 and determine a horizontal line through this point.

Then divide the width of your canvas by 2.62 and draw a vertical line through this point.

The intersection of these two lines is a magical spot for your center of interest. (i.e., 8.5 divided by 2.62 = 3.2

There was a series on one of the educational channels regarding the subject of beauty and the Golden Section entered into it. The research of Dr. Stephen Marquandt was part of the basis behind the series.

He has a very interesting web site at http://www.beautyanalysis.com. In there, he also discusses the Golden Section in relation to faces and which Karin talks about above in relation to a painting.

Especially fascinating is the section on Marquandt's site that shows how the less symmetrical a face, the less aesthetic we consider it to be and he gives examples with his "map" placed over the faces.

Example
 

The intersection of the two lines described above is the exact point of the kiss in my painting below.

I tried different compositions with this, but I think it worked best with the Golden Mean.

Thanks for the simplified explanation of how to apply the golden mean.

I was always surprised this topic never really took off since I find it fascinating.

Here's an interesting page about Leonardo da Vinci and his use of the Golden Rectangle. Be sure to mouse-over the images and you'll see the golden rectangles.
http://library.thinkquest.org/27890/applications6.html

That page is within a larger dicussion on the Fibonacci Series. Here is an introduction: http://library.thinkquest.org/27890/theSeries1.html

And, here is about the Fibonacci series in nature: http://library.thinkquest.org/27890/theSeries1.html

Perhaps this explains why four people in a painting are difficult in terms of creating an aesthetic composition. The number 4 is not a number in the Fibonacci series.

Aaahhh, the Fibonacci series. I couldn't stand math class in high school and had to pick a topic for a presentation. As you might guess, my favorite subject in high school was art. So.... I did a presentation on the Fibonacci series. I remember it to this day!

What I can't believe, Michele, is that I got to this age in my life and only heard of the Fibonacci series last week. It was never mentioned in school, but absolutely fascinating!

Thank You!
 

Thank you so much for posting this thread. I will be using the Fibonacci Spiral in my next oil painting, "Ralph!"

This whole concept is awesome, especially when you look at all things pleasing applying these rules. Cynthia the site link http://library.thinkquest.org/27890/...=1&tqtime=1010
Is a wonderful tool for so many things, you are truly a wealth of knowledge.

The Science Channel is the first place I go on the TV and I heard about the Fibonacci series last week on TV. I was so fascinated by this show, I had to go find out about it. So, of course, I looked on the internet and managed to find it even though I didn't know how to spell Fibonacci at the time.

I think it's fascinating beyond belief! Food for my mind!

I tried to apply this today. I did it two ways in my "value" sketch phase.

Karin's way, was easier, but the interest point was very low - funny it ended up being just about the perfect spot though.

By way of the site, I searched the house to find a compass but someone made off with my circle templates; after laboring, the size wasn't going to work. But wow, it is a different way of looking at things. I am surprised in my photography classes this wasn't taught since we spent so much time on Gestalt Psych.

Compass substitute
 

Hi Elizabeth,

You don't need a compass. Tie a string around your pencil, hold the other end steady, and you can scribe a circle. You're looking for the intersecting lines of the circles drawn, and this method will be quite accurate.

Mari,

Not to sound too lame, but do you do it to size or a smaller scale on your sketches? It seems that in the Golden Rectangle, the movement would start at the top left and sway down and up. Do you find this translates into your work? Any samples you could share with me? Thanks.

Math/science connection to art
 

Movement can originate from any of the four corners of the canvas; in Western art, paintings generally read from left to right, just as we read a book.

There are two very interesting ways to look at the

Mari, I found this statement particularly interesting. It rings a bell of something I read long ago and perhaps you, or someone else, can fill in details because my memory has faded. It was along the lines that in the past (I'm not sure how distant), learning was not as segregated as it is now and therefore the student gained a more holistic view of the world and education, and was aware of such things that math and art are different ways of expressing the same thing.

I'd be interested in more information on this subject, how it was in those earlier times and how, why, when it changed.

I suppose this could start to majorly veer off the main subject of this thread, or perhaps it will only be a slight meandering. But, I had to ask.

I imagine this wholistic way of learning began (and maybe ended?) in the Renaissance -- hence the term Renaissance Man, used to describe someone who is learned in a wide range of fields.

This is why Leondardo da Vinci became who he was, I guess. He was as learned in the arts as he was in the sciences.

Too bad organized education doesn't still teach that way. I had a difficult time as a high school senior choosing whether to pursue a science major or an art major in college. It would have been nice to study both. (I chose art but for fun I have been known to read books on nuclear physics -- no kidding!)

Michele,

What you say makes sense. I consider myself to be artistic even though I'm not a painter. I could have easily been an interior designer, for example. I love working with color and form. However, I have books on quantum physics and it's one of my favorite subjects. :)

Cynthia, I'll be in Florida in February. We really should meet and talk about portraits and protons over coffee sometime!

Art and Science
 

The art in science and the science in art is very interesting to me.

After a fine arts "major" in high school, I put my brushes on a shelf and obtained undergraduate degrees in Philosophy and General Science. It was during that time I developed a poetic love for science. "Differential Equations" was one of my electives, as I learned about the the universal language of mathematics and the sheer wonder of nature.

I went on to study medicine at the University of Florence, Italy. I did a number of years there leading toward Pediatric Cardiac Surgery. As my career progressed, I became progressivey more isolated and unhappy. I dropped out prior to taking the Hippocratic oath.

Feeling rather guilty about leaving med school after all those years of study, I attended a special exhibit of DaVinci notebooks (on loan from the National Gallery of London) at the Palazzo Vecchio in 1984. I really went to make my apologies to my idol, Leonardo.

A tour guide was telling a small group about Leonardo and his passion for both science and art. I listened in as she explained that he would frequently flip from one job to another - from engineering to scuplture, mathematics to painting - often to the dismay of his patrons who would be stuck with incomplete work!

I felt deeply and profoundly understood.

My teacher now, George Passantino, warns against over-analyzing. He likes to quote Sorolla who said something like "If I can't paint fast, I don't paint!"

Still, the underpinnings of beauty can be analyzed. I like to call my methodology "Alla prima dopo" which translates into "At first after" or, for me, "Spontaneous brushwork after careful design."

Thanks to you - the designers and members of this forum - I feel understood once again!

"Spontaneous brushwork after careful design." That's the best description of what I'd like to aim for in my work, too. Well put!

I suppose that's also what Sargent was doing when he would hold his brush motionless in the air for a very long time -- and then paint with great energy.

I think I'm going to try and find a reasonable place to break this thread away into the Cafe and call it Art and Science. We are getting philosophical here, so it's where part of it should go. But, the evolution of the topic will make it difficult.

Ok, I've moved the whole thing over and called it "Golden Section discussion becomes Art & Science discussion". Let's post any more philosophical things there. http://forum.portraitartist.com/show...s=&threadid=91

Anything technical should continue here.