## 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.

## Controlling Crowds

On my recent trip to Baltimore, I spent an afternoon at the National Mall in Washington, DC. It seemed to me, with cold weather and snow, as well as being on a Tuesday, there were very many people there. It may have been because the snow closed down the government, so a lot of people had the day off, and that it was sunny and not really that cold. Or it could be there is just always a lot of people there. It is a popular tourist attraction after all. Regardless, with all the people, it made it a challenge to photograph the monuments without a lot of people in my shots.

A great method to remove people from your shots is to use a really long exposure (typically several seconds to minutes). With a long exposure, people moving through the frame are not recorded. To get really long exposures, use a neutral density filter. As I was carrying my tripod and a neutral density filter, I was tempted to use this method to get a shot of the Lincoln Memorial during the afternoon, as it seemed to be the place with the most people gathered. However, even an exposure of several minutes (which I don’t think I could have gotten due to bright light) was probably not good enough in this case because a lot of people were standing in place for minutes at a time. A ten-minute exposure might have work, but I didn’t have the equipment with me for that.

Instead, I came by later, after sunset, when there were many fewer people about. Then using an 8-second exposure, I was able to capture the monument without people (actually, there is the “ghost” of two people in the shot, but I can remove them later with cloning if I want).

Actually, waiting for evening is a great method for controlling crowds. Typically there are many fewer people about and the light is often better than in the middle of the day. In the shot of the Washington Monument from the Vietnam Veterans Memorial, I planned the shot during the afternoon when many people where in front of the war memorial wall, but came back after sunset to make the shot. I shot from this location for about 15 minutes, during which time, only one group of people passed.

Another method is to frame the people out of the picture, as worked for the image here of the Jefferson Memorial. Look for pleasing compositions above the heads of your fellow visitors. A corollary to this method is to shoot details, rather than the big picture, thereby cutting people out of your compositions.

Of course, that doesn’t always work. Sometimes you want the entire building or you want foregrounds that shooting high above people’s heads cannot give. In that case you can try to go with a wide-angle shot. With a wide-angle perspective, you can make the people visible in the shot look much smaller and less of an obstruction, at least if they are not close to the camera. This method worked well for the shot of the Washington Monument with the flags.

Or you can just go to areas that are not as popular. By visiting less popular sites, you don’t only get the advantage of fewer people in the frame, you can capture shots that are more unique (rather than the same shot of the popular attraction that has been shot a million times). Very few people were visiting the Franklin D. Roosevelt Memorial, which is where I took the shot below of the Jefferson Memorial with the snowy tree in the foreground.

Travel photography presents many opportunities, including shooting interesting people and cultures. But sometimes, you views without the people in them. Using some of the methods described above can often allow you to capture shots people-free.