Notwithstanding the 20th Century development of "theater in the round"--which often is in the square or oval--Western culture abandoned the circle as a primary theatrical shape some 2200 years ago, when the rising Roman civilization co-opted the waning Greeks. The most obvious feature of a Greek theater was the perfectly circular space at the very center of things, a space the Greeks called the orchestra, or "dancing place." It had nothing to do with a group of musicians playing instruments (although they were there, too), but with the chorus who sang, chanted and danced.
The Romans eliminated the chorus, and cut the orchestra in half, making it into a semi-circle of largely-decorative function. With the re-discovery of Roman architecture during the Renaissance, and the development of the first indoor theaters, Western Europe took the semi-circle--still called the orchestra--and elongated it into the horseshoe shape of classic theaters of the 17th, 18th and 19th centuries. Today, we use the word orchestra to mean a group of instrumentalists, not dancers. In theater, they sit in the orchestra pit between the stage and most expensive seats on the main floor of the theater, the orchestra seats.
But the circle remains a seminal performing space in virtually all of the world beyond Broadway, London's West End, the boulevard theaters of Paris and opera houses everywhere.
Think of a three-ring circus. Think of a circle dance, which might be found anywhere from a hoedown to a tribal warrior dance or fertility rite, to a folk dance such as the hora or tarantella.
I've been reminded recently of the fundamental importance and power of the circle in connection with performance, as I've hiked and horsebacked through Anasazi ruins in the desert southwest, climbing into kivas and witnessing Native American dancers. The primary shape is the circle. In creating the first purpose-built theater buildings (open air though they were), the Greeks adapted the circle from earlier, more primitive rites going back to the most primordial storytelling and spiritual practices conducted around a fire.
The dance around the fire, the story told around the fire, the prayer ritual around the fire: religion, music, dance and theater all began together as one thing, as a way to explain that which could not be explained. It's been the same in every culture on earth, living or dead. Only later--much later--did the performing arts become something separate from religious ritual, and far too often a source of suspicion for those calling themselves pious.
Why a circle around a fire? Think of a primitive, pre-historic community. Fire is good, and probably sacred, because it's an essential of life and of security. Your family, tribe or clan sits around the fire at night not only because it provides light and warmth, but because you can see the faces of people you know and trust. Even more, the circle allows the people opposite you to see anything that might be coming out of the dark at your back, and you serve the same security function for those across from you. The circle--quite literally the ring of fire--becomes the most important symbol of community cohesion and ceremonial activity.
From the circle around the fire to the orchestra ancient and the orchestra contemporary, may the circle be unbroken. From primitive stories and rites to the stories of the modern stage and rituals associated with it (tearing a ticket, reading a program, the lights going down, the curtain calls), may the circle be unbroken. From Dionysus, the Greek god of wine, music and fertility, to Kokopelli, the flute-playing god common to all southwestern Native American tribes, may the circle be unbroken.