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A formation that was supposed to resemble a square, with one couple stationed neatly on each side, wound up looking more like a wavy half-circle.

When he flaps his arms in front of her, the tall majestic bird flaps excitedly in response and dances in a half-circle with her head bobbing.

A kumu hula, or hula teacher, Ms. Holt gathered about 50 listeners into a half-circle, and exhorted them to “lift your voice.”

He reached into his coat pocket and withdrew a folded half-circle of cloth; he unfolded it, kissed it, and smoothed it over his hair.

On a Wednesday evening in early March, eight people sat in a half-circle at Performance Space New York in Manhattan’s East Village, wiping their ears with alcohol pads.