Geometry plays an integral role in the composition and interpretation of photographs. With mobile devices becoming more and more ubiquitous, photography is perhaps one of the most accessible disciplines in which students can explore and apply the concepts that they learn in the classroom. Ask a student to define parallel lines and they may say something like “lines that never touch,” and in their head they are visualizing this:
I wonder if students would have a different perception and appreciation for mathematics if they saw it as a tool to create a story. What if students, equipped with a camera or their mobile device, were asked to go find and analyze a scene with parallel lines? Perhaps, they would take a picture like the train tracks above, where even though we know the tracks never touch, they appear to intersect as they disappear into the depth of the landscape. What properties of parallel lines help generate perspective? Why do converging lines seem to create optical distortion?
Although you probably will not see any discussion about photography in your math textbooks, lines are used by photographers to create mood and elicit emotion in their work. What kinds of lines are apparent in the photograph below? How do parallel lines and intersecting lines help the photographer tell their story?
Horizontal lines typically tend to portray a sense of stability and consistency. Using horizontal lines, for example, photographers can convey a feeling of rest or the message that there is a lack of change in a scene. Objects that appear horizontally in a photograph can serve as a dividing line in the composition or provide an anchor to the picture’s subject. Vertical lines, on the other hand, help to give interpretation to the mood. These lines elicit powerful emotions and convey strength, often providing a sense of length or height. The photos below use both horizontal and vertical lines, creating a contrast between stability and strength.
Diagonal lines draw the viewer’s attention to the subject of the picture. Photographers use diagonal lines to create a point of interest. Depending on the direction of a diagonal line, it can even portray movement.
Tell your Geometry teacher that a line is curved and he might pull his hair out, but curved lines in photography can have an even greater impact on composition. Consider the railing that moves from the lower right across the center of the scene below. Although the line is not straight, it is parallel to the far bank and helps to frame the movement of the river towards the point where it vanishes.
Finally, angles formed by intersecting lines can also make a scene more complex depending on the viewpoint of the camera. The relationships between these lines and the angles they form can help students give meaning to the mundane problems of parallel lines cut by a transversal.
Photographers and artists enjoy what they do because they use their work to tell a story. I wonder how we can create opportunities for students to use mathematics to tell their story.