Do Your Math
Finally, I have an answer to the age-old question, “Why should you study geometry?” Because geometry is a useful tool to strengthen your photography compositions. Okay, that is a stretch argument for studying geometry, but artists have been using geometry since the 4th century BC when the Greek sculptor, Polykleitos, wrote a canon on the ideal proportions for a male nude. Geometric shapes and even the suggestion of geometric shapes are compositional tools that can add a layer of meaning to a picture.
Horizontal lines can suggest tranquility, calmness, and lack of change. They are the least dynamic line. Perhaps that is why it is so important for the horizon line in a picture to be truly horizontal. If it is not, it becomes an implied diagonal and it messages something quite different from what we associate with horizons. I believe that this can create some dissonance for the viewer.
Vertical lines are more dynamic than horizontal lines. If you think about the vertical lines that we experience in our environment, like trees or tall buildings, it is clear why they suggest stability, growth, and dominance.
Diagonal lines give the sense of movement, energy and depth. When you take pictures of people walking, there is more energy in the picture if you get them in stride. Perhaps this is because of the implied diagonal lines formed by their legs. Our eyes tend to follow diagonal lines, so they can provide a path to move us through a picture. An especially effective use of this phenomena is the inclusion of leading lines in a photo.
Rectangles, including squares, give a sense of conformity and stability.
Triangles can add tension. When they are sitting on a long side they are stable, but if they are flipped over they are balancing on a point, which is the most possible unstable state. In this street picture of a mom and her son at an art museum, the vertical and horizontal lines and the rectangles give the sense of the art museum experience: a quiet, calm experience that is shared by most of the people in attendance. Tension is created by the child who is a part of an implied triangle created by the stroller.
Circles and ovals suggest completeness. They can also suggest movement because there are no corners to stop movement.