If every New Yorker regularly did Gyrotonics — a type of exercise that builds on yoga, ballet, tai chi, and swimming — ours would be a far more beautiful, happy, and relaxed city. Created in the 1980s by a classically trained dancer whose career had been put on hold due to an injury, Juliu Horvath, Gyrotonics uses movements that are both circular (thus gyro, a Greek word meaning “spiral”) and rhythmic. The exercises encourage the body to lengthen, strengthen, and relax. Mr. Horvath invented a number of machines that use pulleys, straps, and weights to help guide and extend the body’s range of movement and increase balance and coordination.