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Narrator: Listen to part of a lecture in an art class.
Professor:
    Symmetry is a concept that, yes, is expressed in the graphic arts, but to understand its fundamental  Q6
nature, we must g0 beyond art. We find symmetry in nature, it reverberates in music, translates" into
choreography for dance, and, . . underlies basic mathematical formulas. But m getting ahead of  Q7  
myself. Let’s begin with a dictionary definition of symmetry. And I’m reading here from the American
Heritage Dictionary of the English Language: Symmetry is "exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis." And it’s also identified in the same source as "beauty as a result of balance or harmonious arrangement." So we experience beauty and harmony when symmetry of form is expressed, and the form may be interpreted by any of the senses as, uh, harmonious. But in this class we’re going to focus on symmetry in the visual arts, and that’s symmetry in a visual plane.
    Let’s just look at some examples. In general, there are four types of symmetry in a plane, and a pattern is symmetrical if there’s at least one type of symmetry. So, let me show you the four types since it’s much easier to understand when you see them.
    This is rotation symmetry. For this example, I used the letter R, but any object could have been used. And in the rotation, the object, in this example, the letter R, is turned around a center. In this case, there’s a right angle, but any angle could have been selected.
    Reflection is...wait a minute, Okay, here’s the slide  Q8
    Reflection is what we see in a mirror, so every reflection has a mirror line. A reflection of the letter R is a mirror image or a backwards letter R. So, unlike the rotation around a circle, this type of symmetry flips the object over.
    Here’s a translation. To translate an object means that we move it, but we do it without rotation or
reflection. It’s simply placed somewhere else on the plane. And for our purposes, we’re talking about a
flat plane. So, in this example, uh, we just moved it over a little bit.
    Okay, this is my last example of symmetry and it’s referred to as glide reflection. This is the most
complex type of symmetry because it involves two steps instead of one. A glide reflection is a combination of a reflection and a translation along the direction of the mirror line. So, uh, you can see the two
steps here. First, we flip it over and then we move it somewhere else on the plane.
    Of course these concepts can be generalized to include spatial symmetry as well. But, symmetry on
a flat plane involves positioning all points around the plane so their positions in relationship to each
remain constant.., although their absolute positions may be subject to change. To put it in simple
terms, if an object looks the same to you after you spin it around, flip it over, or look at it in a mirror, then that object probably has symmetry.
    Symmetry is such a fundamental organizing principle that an object with symmetry can be identified  Q9
... without our being able to see the, uh,... the entire object. Our brains somehow piece together the missing pieces to form a symmetrical whole. Which is really rather extraordinary, when you think about it. At some very basic level, symmetry may be part of the way that we... that we organize our thinking. And of course, that would explain why it’s so pleasing.
    So now let’s return to symmetry in art. Symmetry stands out and attracts attention. It’s the system of organization for patterns. But what is a pattern? A pattern has three characteristics-a system for organization,  Q10
and like we said before, this is often symmetry, but a pattern also has a basic unit, that is, uh,
it’s an object that’s the smallest discrete part of the image. As you’ll recall from the types of symmetry that we discussed, the letter R was the basic unit, Okay, finally, a pattern has repetition, which can be the repetition Of a unit or a group of units. And, uh, this repetition, in much of art, this repetition is arranged symmetrically. Just look around the classroom. Look at the tiles on the floor. Here you see a symmetrical design with four repeating tiles. The tiles were not placed at random. There’s a pattern here with all three characteristics of a pattern-first, there’s a unit, a basic unit, of four tiles; second, there’s repetition of the tiles with solid tiles surrounding them; and, uh, third, there’s symmetry.., within the four tiles, which to be specific, looks like rotation symmetry to me.
    Now, for your studio assignment, I want you to draw a pattern that has as its organizing principle; a  Q11
symmetrical design, It can be either in color or in black and white, but it must fit on a piece of standard
by 11-inch paper. On a second sheet of paper, I want you to identify the type of symmetry that you used. Perhaps some of you will want to experiment with several types of symmetry, but if you do, please be sure to identify each of them clearly in your narrative. For this first effort, I recommend that you stick to something relatively simple, like the tile floor. So, when you come to class next week, be ready to share your design with three other people in a group. Then I’ll collect them at the end of the hour.