In 1956, Joan Anderson, a Los Angeles housewife and onetime model, flew to Australia, her home country, to visit her parents. When she arrived, she realized that a curious fitness craze had taken hold.

“Everywhere I would go, everybody was giggling,” Ms. Anderson said in “Hula Girl,” a 2018 documentary. “I asked what was going on and they said, ‘Oh, everyone’s doing the hoop.’”

The “hoop,” she discovered, was an exercise ring, made of wood, that was swiveled around the waist and hips.

“Everyone was having such fun,” she added, “I thought, ‘I’d like to do that, too.’”

Back in Los Angeles, Ms. Anderson asked her mother to mail her one of the rings from Australia, and it soon brought joy to the Anderson household.

Her children played with it. Ms. Anderson swerved it around her hips for friends at dinner parties. When someone told her that it looked as if she was “doing the hula,” the traditional Hawaiian dance, Ms. Anderson was struck with inspiration.

She named the object the hula hoop.

What transpired next would place Ms. Anderson at the center of what she described as an American tale of shattered dreams and promises, a business deal made on a handshake, and, eventually, a lawsuit.