In Celebration of Pi Day, I Give You Phi

Today is Pi Day. I’m not sure how Pi relates to photography, but Phi does. Pi the ratio of  a circle’s circumference to its diameter, an irrational number approximately equal to 3.14159. Phi is also an irrational number, approximately equal to 1.61803. Phi is also called the golden ratio. It is the ratio obtained when a line is divided into two unequal parts such that when the longer part is divided by the smaller part the answer is the same as when the whole length is divided by the longer part. (It makes much more sense when you see it as a diagram.) Pi and Phi are somewhat related in that the product of the two numbers (phi times pi) is found in golden geometries.

I am not a mathematician, but I suspect the product of Pi and Phi is related to golden geometries because Phi is an expression of the golden ratio. And the golden ratio is special in photographic composition. Phi, the golden ratio, presents to the human mind a very pleasing relationship. Besides photography, it is found in architecture, painting, and music, as well in nature.

The golden ratio has been used for art since practically forever. The Parthenon is covered with instances of the Phi. It can be found in artworks such as the Mona Lisa and the Last Supper. It is even found in Darth Vader’s mask.

The rule of thirds works, in my opinion, because it is an approximation of Phi. If you take the sweet spot defined by Phi four times in a frame, you get a pattern similar to the rule of thirds, but a little less easy to define on the fly when looking through your viewfinder. Luckily, both Photoshop and Lightroom offer crop overlays that show the golden ratio grid.

The golden ratio can also be expressed in a spiral. A logarithmic spiral with a growth factor of Phi is known a the golden spiral. Again, both Photoshop and Lightroom also have crop overlays based on the golden spiral. The sweet spots of the golden spiral are also close the those of the rule of thirds.

It is easy to access these crop overlays in Lightroom. The various crop overlays in Lightroom are found under the Tools pull-down menu. Or when using the crop tool, use the shortcut of the letter “O” to cycle through the various crop overlays. When using the golden ratio overlay, you can cycle through the various orientations of the spiral (placing it in different quadrants of the image) by using “Shift O”. The same shortcuts are used in Photoshop when using its crop tool.

With a bit of practice, you can imagine the golden ratio proportions in your viewfinder, and you can always perfect the composition with the crop tool in Lightroom and Photoshop. So if you want to move beyond the rule of thirds, remember Phi – the golden ratio – a photographer’s compositional mathematical friend.