On a trip to Sydney in 1956, Joan Anderson was amazed to discover a new trend sweeping Australia’s beaches and streets. People were “doing the hoop” — twirling a sturdy, circular ring of bamboo around their hips for exercise or just for fun.

Ms. Anderson, an Australian native who lived in Los Angeles and was back visiting family, had trouble at first when she tried to join in. “It looked like fun,” she later said, “but it was really hard.” Still, she found herself enthralled by the toy. After returning to the United States, she had her mother ship her a hoop.

Its arrival confounded the local mailman. “He said, ‘Why would anyone send something like this all the way from Australia?’ ” Ms. Anderson recalled in a 2018 documentary, “Hula Girl.” “I often wonder if he put it together that what

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