Now that you're familiar with the Golden Mean and one of its many permutations-the Golden Spiral-let's explore a very different way to use the ratio of the Golden Mean in your photographs: the timeless Golden Triangle.
Let's start by learning how to divide up your camera's frame effectively. For practical purposes, imagine your camera view forms a true Golden Rectangle. Choose your subject, look through the lens, and get ready to see in a whole new way
Use your eye to trace an imaginary diagonal line within the frame from corner to corner (whether you start from the top right or the top left will depend on the photo you're about to shoot). The interior of your frame will now be divided into two congruent, corresponding triangles.
The ratio of the long side to the short side of each triangle is roughly 1. 618, or the Golden Ratio. This pretty much guarantees you're on our way to a beautifully composed pic-by ancient Greek standards, anyway!
Next, trace a perpendicular line from the far vertex to the diagonal line. The rectangle is now divided into several triangles of different sizes whose corresponding sides are proportional and angles congruent. All of the triangles in this case are (roughly) "Golden", and will therefore lend a sense of symmetry and order to your results.
More of these aesthetically pleasing triangles materialize if you trace another perpendicular line. Each point of intersection represents a spot where placing the focus of your image will be most captivating. Place the secondary elements of the photograph along the diagonal lines between points to give the image more depth.
When you use Golden Triangles to break up your frame, you're creating an effect dubbed by professional photographic experts as "dynamic symmetry". Try to keep your focal subject on one of the intersecting points (called "saddle points"), and place other visual information into the triangles you've already divided out. The result will be a very attractive composition you may not have otherwise attained.
The Golden Triangle technique is also very effective when your photograph has no single, obvious focal point, e. g. , in vast landscapes. In the photo below, subscriber John Craver has stunningly captured the Mendenhall Glacier in Juneau Alaska with the Golden Triangle technique.
Using imaginary diagonal and perpendicular lines give this photo awesome depth, and draw the viewer directly to the "saddle point", where the ivory glacier is quietly napping in the crevasse of the mountain valley.
The contours of the mountains trace the lines of the triangles seamlessly, giving the photograph strong dynamic symmetry and aesthetic appeal. A total success! Remember: The more complicated or busy your photograph, the more triangles you can add to the frame.
Click photos for larger examples.
Photos by subscriber John Craver.