Investigation Four: Exploring Symmetry

In Investigations One, Two, and Three, students investigated various aspects of perspective, a concept central to art. Finally, in Investigation Four, students expand their exploration of science and art by focusing on symmetry.

In the scientific and mathematical fields, symmetry represents one type of pattern. As you can imagine, because there is a myriad of scientific as well as mathematical disciplines, there is not just one way in which symmetry is described or studied within these fields. As students progress in their education, they will likely encounter symmetry discussions at various times and levels. Investigation Four allows students to focus on two types of symmetry within those fields: bilateral symmetry and radial symmetry. Bilateral and radial symmetry can be associated with biology and organisms as well as mathematical constructs.

Bilateral Symmetry

To better understand bilateral symmetry, think of the human body. Observe the body, and you observe two arms, two legs, two hands, and two feet. Observe more closely as you can see that each part of the pair is almost exactly like the other except for slight differences in orientation. Each hand’s thumbs do not point toward the same side of the body. Instead, each points inward towards the chest. The same relationship exists between the two legs, feet, and arms.

A pattern emerges if an imaginary line is drawn down the middle of the body from the head to the feet. What is on one side of the line is the mirror image of what is on the other side of the line. This “line” is referred to as a “plane of symmetry” and “bilateral symmetry” is the specialized term that describes the exterior of the body. Bilateral symmetry refers to the ability to draw a median axis or line through a structure with the result being that two essentially two equal halves are created. Objects that have bilateral symmetry contain only ONE plane of symmetry. A spider and bird are two other examples of organisms that have bilateral symmetry – there are many others.

Look outside or in a zoo, and symmetry becomes readily apparent. Many organisms within our world exhibit external bilateral symmetry. And yet, that symmetry may fail to maintain its consistency internally. For example, our veins, arteries, nerves, and skeletal muscles tend to be bilaterally symmetrical within our bodies. However, our heart, liver, appendix, and other organs are not.

Radial Symmetry

In addition to the multitude of organisms that posses bilateral symmetry, there are a number of organisms that exhibit radial symmetry. Organisms or objects that are radially symmetrical have similar parts arranged around a central axis. A starfish is an example of an organism with radial symmetry. Each of the five arms of a starfish extends out from a central axis. Another way to think of radial symmetry is to imagine that the object or organism can be divided into equal halves by a plane passing through the central point or axis at ANY angle. In other words, an object with radial symmetry has MORE THAN ONE plane of symmetry. A pine tree, when viewed from above, a snowflake and a starfish are examples of organisms that have radial symmetry.

Symmetry in Art

Symmetry also exists in art, whether it be in painting, sculpture, architecture, theater, or music. Part of this may be because of a focus on the human form. However, part of it may simply come from an almost intrinsic human desire and preference for symmetry. Recent research into human perception has shown that within 0.05 seconds of viewing an object, humans scan the object for symmetrical properties.

Regardless of the reasons, for many artists and patrons of art, symmetry in all aspects of illustration creates harmony and consistency. Marcus Vitruvius Pollio, a prominent architectural engineer during the Renaissance, displayed what he considered the beauty of anatomical symmetry when he created the drawing below. Vitruvius believed this beauty and balance carried through all forms of nature, including his architectural drawings. The artist and scientist Leonardo da Vinci also noticed and ascribed great importance to the symmetry of human anatomy. His perhaps more famous drawing is shown here.

Over the course of history, artists have also manipulated the human desire for symmetry by creating asymmetrical pieces of work. In doing so, they often hoped to elicit drama and heightened emotions as a result of this asymmetry.

In some cases it is easy to see where art and science overlap with regards to symmetry. Just take Vitruvius’s or da Vinci’s drawings as an example. Both illustrate the bilateral symmetry of the human form. In other cases, however, the definition of symmetry as one moves between the fields may become more blurred or inconsistent. Bilateral and radial symmetry as defined by science require the formation of mirror images, something that is not often the focus of art.

Discussion of symmetry in art, therefore, often becomes a more lenient comparison of elements within the work of art. In addition, the word balance is often used as a substitute for symmetry. In Investigation Four, students will have the opportunity to explore symmetrical and asymmetrical balance in artwork and compare these descriptions to those of bilateral and radial symmetry.

Through their work in Investigation Four, students will find that symmetrical balance suggests the ability to find a central focus of a painting and divide the painting into left and right halves with equivalent number and sizes of objects on either side. Art with asymmetrical balance, however, often lacks a central focus around which it can be divided into left and right halves.