Just as a liberal arts education prepares its students to seek the good and true, it also teaches them to appreciate the beautiful. "Beauty" may be even more evasive than the "True" or the "Good," as it has become commonly accepted that "Beauty is in the eye of the beholder."
There are also different contexts in which we employ the word "beauty." We might call a kind soul, a sublime view, a strong horse, a fit person, a well-designed blouse, a geometrical pattern, a chair, and a spider web all beautiful.
For sake of definition, let's look at "Beauty" comparisons between Athens and Sparta. Athens was a city that prospered in trade and arts, whereas Sparta flourished in the art of war. An Athenian might see beauty in a pot, sculpture, or building, whereas a Spartan might see beauty in personal fitness and simple dwellings. In each case, their definitions of beauty, or attractiveness, revolve around their particular pursuit of the Good.
As I mentioned before, the Good and True exist independent of perception, as must Beauty. However, should Beauty be a reflection of the Good? Should it make us want to pursue the Good, even if it depicts evil? What role does Truth have in Beauty? Can beauty serve any other purpose—say, as a dwelling or a chair—or should it be beautiful by itself? Can a technique be beautiful, or does the actual product need to be?
The best education can answer only some of these questions. What becomes most obvious to a student is that you can figure out what someone perceives as Good and True based on what they see as Beautiful. And, thus, if beauty is in the eye of the beholder, what you perceive as beautiful reflects who you are.