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It's 100 years since Annette Kellerman became the first person to appear nude in a Hollywood film. But this was just one of many remarkable events in her life.

She sat naked on a tree branch, her arms stretched upwards, but her hair largely covered her breasts.

It might not seem very risque today, but this scene, from a film released in 1916, was an important event in the history of film. Annette Kellerman is regarded as the first star - male or female - to appear nude in a mainstream Hollywood production.

The fantasy drama A Daughter of the Gods featured her as a character called Alicia who falls in love with a prince and enlists the help of the inhabitants of Gnomeland to help in his struggles with his enemies. The cast included a sultan, the Witch of Badness, the Fairy of Goodness and several eunuchs. No copies of the film are thought to exist today, but at the time it caused a huge media fuss.

An advert promoting the film among cinema owners proclaimed: "It has made big money wherever shown. Book it now."

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When A Daughter of the Gods came to Kellerman's native Australia in 1917, The Green Room theatrical magazine said anyone not seeing it would miss "one of the greatest events" in the country's history.

"From the far-away sphere of the Unknown we are immediately borne, by this film, to a land of enchantment," it added. "Something of the wonder of the Arabian Nights, of the glory of the East, of our own war, of fairyland, of womanly power and eternal beauty, is manifested to us by this masterpiece of cinematography."

The film was a first for Hollywood but just one of a remarkable series of events in the life of Kellerman - a champion swimmer, vaudeville pioneer, swimwear designer, stuntwoman, businesswoman and health-and-fitness guru.

"She represented the fit, active and spectacular female body, and urged other women to throw away their corsets and become fit and healthy," says Angela Woollacott, professor of history at Australian National University. "She saw herself as something of a guru for women's fitness, but others also saw her as an icon of feminine modernity," she adds.

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Born in Marrickville in Sydney, Australia, on 6 July 1887, the daughter of two musicians, Kellerman was crippled by rickets as a child and took up swimming to overcome the weakness in her legs. By 13 she was healed and by 15 she had learned all the strokes and won her first race.

Kellerman's talent was obvious and, by the early 1900s, she became the holder of all of the women's world records for swimming. Aware of the commercial possibilities her skills provided, she put on shows in which she swam with fish in an aquarium and performed high dives at Melbourne's Theatre Royal.

In 1905, Kellerman moved to the UK, where she swam 27km (17 miles) along the Thames, from Putney to Blackwall. In the same year, she attempted, but failed, to become the first woman to swim the English Channel.

She became a vaudeville star in London and the US, developing a form of underwater ballet combined with high diving. In July 1907, the Chicago Herald Tribune advised its readers: "None should fail to see Miss Kellerman, as she is not only an expert swimmer but a beautiful woman, who is at her best in her bathing suit." In that city she wowed crowds by diving 72ft from the topmast of a steamship. By 1914, she was earning $2,500 a week for her shows, the equivalent of around $60,000 (£41,000) today.

Kellerman pushed sartorial boundaries too. In her native Australia, women taking part in competitions had worn short-legged, non-skirted costumes - the same as men's - since the 1870s.

This wasn't allowed in the UK in 1905, when Kellerman was to give a performance in front of the royal family at London's Bath Club. Kellerman felt a skirt would prevent her swimming effectively, so she improvised, sewing a pair of black tights onto her men's swimsuit to create a full-length, one-piece "figure suit". This is regarded as the beginning of 20th Century women's swimwear.

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In 1907, Kellerman was arrested on Revere Beach, Boston, for wearing one of her suits without a skirt. But the judge accepted it had been designed for exercise and was decent, provided she wore a skirt until entering the water.

The incident received worldwide publicity and Kellerman designed her own range of swimsuits. The style became generically known as a "Kellermann" - the original German spelling of her family name.

The writer Mildred Adams remembered later that, when Kellerman had first come to the US, audiences had "found her free and careless grace exciting, though slightly shocking, and some of them went so far as to adopt her swimming suit". However, most converts had worn skirts over them while on the beach "until a good deal later".

Kellerman began starring in short films. In Neptune's Daughter of 1914, she wore a flesh-coloured body suit for underwater scenes.

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Two years later came A Daughter of the Gods, misleadingly described as Hollywood's first million-dollar-budget film. Variety magazine estimated it had in fact cost $850,000 (£590,000) to make, and had taken $1.39m (£965,000) in total.

In some scenes Kellerman wore a body stocking, but not in others. The film, though, seems to have been more than an attempt at titillation, receiving a largely positive critical reception - although there were unsuccessful attempts to ban it in some US and Australian towns.

Kellerman's fame by now was enormous. In July 1916, the Washington Post commissioned her to write an article on the behaviour of sharks, following a series of attacks on swimmers off New Jersey.

And, from around 1920, she developed a risque cross-dressing routine for her vaudeville act, which was still going strong, appearing as a monocled gent called the English Johnny.

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Her final film, Venus of the South Seas, shot in New Zealand, came out in 1924. It was one of the first to be shot in colour.

Kellerman continued to promote herself, lecturing on health and fitness, offering "physical instruction by mail", as well as producing books and films on the subject and running a health food store in California. But she remains best known for taking her clothes off.

"I don't think she embodied contradictions so much as just how complex Western femininity/womanhood had become in the early 20th Century and how rapidly it was changing," says Woollacott. "She did not label herself a feminist, but in many ways she was one."

She returned to Australia, living by the beach near the Great Barrier Reef. In 1952, MGM released a film of Kellerman's life, Million Dollar Mermaid, starring Esther Williams, herself a former competitive swimmer. Kellerman thought the fictionalisation a little bland.

Kellerman, who was able to do high kicks until well into old age, died in 1975, at the age of 88. In later life she described A Daughter of the Gods as the "best thing" she'd ever done.

Follow Justin Parkinson on Twitter @justparkinson

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