Mathematics and Art
Although not immediately obvious to the untrained eye, both ancient and contemporary art depend on a great quantity of mathematical concepts. Artists vary scale, perspective, proportion and other ideas from mathematics in order to evoke a particular feeling, convey a particular idea, or represent a particular scene. Some artists, such as Jean Baptiste Camille Corot, use scale and proportion common to human experience in order to create "life-like" works, while other artists, such as Salvador Dali, use purposefully misleading elements of scale and perspective in order to craft surrealist images. Indeed entire schools of thought in art have centered on basic principles of mathematics--Corot is generally classified as part of the Realist movement and Dali generally classified as part of the Surrealist movement. Even colors, or hues, used by artists are related to mathematics--in order to create a desired color, for example, many mediums require artists to combine base, or primary, colors into a new hue. To achieve the same color later, the same proportion of the base colors must be used.
Artists work in both two-dimensional (such as paintings) and three-dimensional (such as sculptures) media. Works created in two-dimensional space are contained within a confined area of a plane. Works created in three-dimensional space have a finite mass that encompasses a finite volume.
The idea of the line is significant in both science and art; it represents the path of a object moving in space. In art, a line may be straight or serpentine (S-shaped); it may form the distinct outline of an object or simply be inferred as a border between two objects of an piece of art. In either case, the line draws a viewer's eyes through a painting, sculpture, or other type of artwork; it leads the viewer from one object to the next within the composition. Lines have a recognized effect on the human psyche--a thin, delicate line may invoke a sense of fragility, while a diagonal line is generally suggestive of movement, vigor, or instability. When a number of objects in a composition are placed along a particular line, the line is called an axis. A piece of art may have more than one axis contained within it, but if so, generally one axis will dominate. City plans provide excellent examples of the use of lines as axes.
Some art of ancient Egypt portrayed three-dimensional objects—such as animals, boats, and humans--on two-dimensional surfaces, such as temple walls and pottery. Although beautiful for their detail, the objects generally appear "flat"--the three-dimensional qualities of the objects are not captured in the artists' images. In other works, however, artists incorporate perspective--an organization of objects in space in terms of a single point--to evoke a sense of continuity in the composition. As the point toward which the lines converge is approached, objects diminish in size and appear to recede into the distance. Leonardo da Vinci's The Last Supper provides an excellent example of perspective. In the painting, the lines of perspective converge on Christ's head, projecting the image "into" the wall on which the painting appears. Although da Vinci's painting uses a point in space centrally located on the frame, other artists have used points in space offset from the center, or even beyond the borders of the canvas.
In art, proportion is the mathematical relationship between two or more objects in a composition; it provides an aesthetic means to relate the size of objects relative to each other. Generally speaking, proportion is both intuitive and common to the human experience--as our cognition develops in childhood and beyond, we generally associate an expected size to objects, especially relative to each other. We expect trains to be larger than cars, cars to be larger than bicycles, and bicycles to be larger than roller skates. We also expect objects further away to appear smaller than objects closer to us. When an object appears out of proportion--a woman walking on stilts, for example, whose long legs appear "out of proportion" with her torso--the object attracts our attention.
Artists manipulate the proportion of objects to draw attention to a particular object (or even the relationship between objects) or perhaps evoke a particular sentiment. Figures of authority--kings, deities, emperors--may be portrayed as larger than their subjects in order to evoke a sense of power or perhaps awe; at other times, they may be portrayed as the same relative size of their subjects of evoke a sense of commonality or accessibility. Some artists use skewed proportion to disturb viewers of their works and perhaps focus them on a particular idea. On the other hand, one of the many reasons that Michelangelo's Davidis considered so magnificent is that despite its super-human size (13' 5"), David's entire figure is well-proportioned relative to itself.
Mathematical principles—especially scale, proportion, and perspective—underlie all forms of art, regardless of medium. Although artists may work with these concepts intuitively instead of making specific measurements, the net effect is the same--using the common human experience with basic mathematics to convey a specific idea.
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