Learn this classical composition technique and you'll find your photographs will be more organized. You can thank Pythagoras and Fibonacci's Rabbits for this.
Editor's note: At the Adorama Learning Center, we often get the question: “What is the Rule of Thirds?” We have explained the Rule of Thirds briefly before, but here PPSOP founder Bryan Peterson gives the most in-depth and enlightening answer we've seen. Surprisingly, as you are about to find out, there is a lot of math involved in this mode of creative expression!
The Golden Section refers to a mathematical calculation whose answer equals 1-2/3, or 1.66. Although there is ample evidence that the Golden Section was in use by the Egyptians, for example in the building of the Pyramids, it wasn't identified until later by ancient Greek mathematicians who, when studying the paintings of their fellow artists, began recognizing a pattern: Objects in a scene were often two-thirds as large as others, landscapes often placed the horizon line with two-thirds of the landscape below and one-third sky above (or vice-versa), and in still lifes, artists seemed to favor compositions in which two-thirds of the frame was filled with the round shapes of fruit and the remaining third with the round shape of the bowl.
These artists and architects had a natural eye—an innate sense about how to create compelling and effective compositions. Thanks to the Greek mathematicians, especially Pythagoras, this compositional arrangement became known as the Golden Section, a rule stating that when any object or shape had two distinct parts, the smaller part should be 2/3 the size of the larger part.
Fibonacci's Rabbits & Engaging Photographs
In the area of composition, it is also important to note the Fibonacci numbers. Fibonacci was an Italian Mathematician who was famous for his calculations on predicting how fast and how many additional rabbits would result from two breeding rabbits in ideal circumstances. I will spare you the details, but a series of numbers arose from these calculations, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610...Do you notice the 'pattern' in this series of numbers? Beginning with 3, each number that follows is a combination of the two numbers before it e.g. 1+2=3, 3+5=8, 5+8=13 and so on.
As if by default, Fibonacci's numbers have a direct correlation to the Golden Section. Look at what happens when you divide each of Fibonacci's numbers by the number before it: 1/1= 1, 2/1=2, 3/2=1.5, 5/3=1.666, 8/5=1.6, 13/8=1.625, 21/13=1.61 and so on and of course you haveundoubtedly noticed the calculations that resulted in a 1.6 result. And it's important to note that this 1.6 will go on forever when one divides each of the Fibonacci numbers by the number before it.
Is this 1.6 result merely a coincidence? Definitely not!
What is perhaps most interesting about the Golden Section is that nature abounds in it. Just about every living and breathing thing in Mother Nature's closet, from flowers and ferns to the smallest microbe, is evidence of the Golden Section. Perhaps I have stumbled upon the reason why so many photographers are drawn to flowers; they are comprised of Fibonacci numbers. Lilies and irises both have three petals, buttercups, columbine and pinks have five petals, delphiniums eight, some daisies and corn marigold have 13, Aster and Black Eyed-Susan's have 21 and check this out, Michaelmas Daisies have 55 petals—again, all of which are Fibonacci numbers.
The pattern continues: Flowers go to seed, and not surprising a poppy seed head has 13 ridges and upon closer inspection, the Purple Coneflower and it's spiraling seed head totals 55 spirals; even the common sunflower has 89 spirals – all Fibonacci numbers again! And back to our friend, the Greek Mathematician Pythagoras; he may have been the first to realize that even the human skeleton was based on the Golden Section! Sure enough, my upper arm bone is roughly 2/3 the length of my lower arm bone, and my upper leg bone is likewise 2/3 the length when compared to my lower leg bone.
Entire books have been written about the Golden Section, and discussing it in detail is beyond the scope of this short "how-to" article, but it is vitally important that I state emphatically that the use of the Golden Section in your compositions will more often than not lead to far more engaging and compelling photographs. The sooner you embrace it, the sooner you will start hearing compliments from complete strangers about your photographs.
To ignore the Golden Section, a.k.a. the Rule of Thirds, is to ignore the natural order of the very universe we live in. The rule of thirds "grid" really can serve you well. It can and should often serve as the foundation of a compelling image, much as a firm and solid foundation should be the basis of every house or skyscraper.
As I drove down one of the many back roads in the Valensole Plain of Provence, my eyes caught sight of a lone tree in the distance. The first image I shot may look familiar to some of you, as it depicts what I often see from students in several of our beginner classes. The horizon line runs through the middle of the frame and the subject, the lone tree, is smack dab in the middle of the frame. But as we can see in the next image, it now "feels" better with the tree in the right third of the frame. And as we see in the next two images, it feels even better still when we place the tree on the right and the horizon line in the upper or lower third of the frame. Why? Because you are now catering to your "inner eye," the eye that instinctively knows about the Golden Section and its desire for "1/3rd-vs-2/3rd's divisions. (All images shot with a Nikon D3X, 70-300mm, @ 200mm, f/32 @ 1/60 second, 200 ISO)
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