The shy bookseller played by Audrey Hepburn in 1957’s Funny Face wears couture versions of ballet pumps. The actor had been a dancer, and the movie’s couture costumes, designed by Hubert de Givenchy, climax in a wedding dress (for Hepburn’s marriage to a fashion photographer played by an elderly Fred Astaire) with a full ballerina skirt. So beautiful were the designs that they sprang out of the film and inspired style on the street. Everybody could afford a pair of pumps, even if they didn’t look like Hepburn while wearing them.

Sarah Jessica Parker as Carrie Bradshaw during the filming of Sex in the City. Photograph: Rex

The opening sequence from Sex and the City also drew inspiration from ballet. Sarah Jessica Parker’s swirl of tulle was both a homage to dance and a copiable fashion statement. That simple tutu conjured a world of romance located in the historic iconography of ballet – and was speedily undercut when a New York City bus steered into a puddle, splashing our heroine.

Dior’s creative director, Maria Grazia Chiuri, brought dance and fashion together in her 2019 spring/summer ready-to-wear collection. The show was trailed by a video of a performance created by the Israeli hotshot choreographer Sharon Eyal with the caption “the story comes from inside the body”. The unveiling of the collection was accompanied by famous quotations about dance, including Isadora Duncan’s contention that “Dance is the movement of the universe concentrated in an individual.”

But it is hip-hop and street dance and its high and low brand aesthetic that has arguably influenced general culture more than any other dance trend since the thrilling arrival of Diaghilev’s Ballets Russes in Paris in 1910 sparked a sensation. Stars such as Nijinsky and Tamara Karsavina transformed ballet into a thrilling vehicle for transmitting avant-garde ideas, and the lavish, exotic designs of Alexander Benois, Leon Bakst and Natalia Goncharova offered an entry into a more exciting world.

‘The story comes from inside the body’ … from Christian Dior’s spring/summer 2019 show. Photograph: Jasper Abels

“They brought colours and fabrics from Russia that people didn’t know,” says Madelief Hohé, curator of Let’s Dance, an exhibition on fashion in dance “from tutus to sneakers” at the Kunstmuseum in The Hague. “Everybody was wearing grey and beige and pink, and then Goncharova arrives with costumes in golds and dark blues and turquoises in striking combinations that just hadn’t been used before.”

Cutting edge … one of Natalia Goncharova’s costumes Ballets Russes. Photograph: Allard Pierson/University of Amsterdam

Goncharova’s involvement in Ballets Russes was part of Diaghilev’s cultivation of innovation in all aspects of the company’s work, from the music to the choreography to the design. Dance’s ability to position itself on the cutting edge of culture is one reason it has such a close relationship to the clothes we wear. The dance crazes of the tango and charleston expressed a new sense of freedom after the first world war. “With their beads and their fringes women’s clothes were designed to be at their most beautiful when women were dancing,” says Hohé. “In the same way, when the rock’n’roll dance craze began in the 1950s, skirts grew bigger and stockings were replaced with pantyhose because women were moving and showing their legs more.”

The liberated grace of Duncan and her loose, classical clothes inspired Mariano Fortuny’s 1920s experiments with pleats; the elegance of Astaire and Ginger Rogers encouraged designers to market the same kind of sophisticated dresses to their customers; the energetic kids from Fame in the 1980s put an entire generation in legwarmers, while hip-hop music did the same for trainers.

Woolly jumpers … the kids from 1980’s film Fame take legwarmers out into the streets. Photograph: MGM/Kobal/Rex/Shutterstock

But Hohé argues that the relationship between dance and fashion run deeper, suggesting that the elaborate dances of the 17th-century French court – which were the origins of ballet – are the equivalent of today’s couture catwalk shows. “If you wanted to design something spectacular and new, you designed it for the ballet, to be performed in front of the king.”

Designers have always wanted to show off their wares on the dance stage. In 1928, Coco Chanel designed for Diaghilev, creating costumes for Bronislava Nijinska’s Le Train Bleu that evoked the life of the young and fashionable on the French Riviera in all their sporty glory. Her costumes for Apollo, George Balanchine’s first collaboration with Stravinsky, were daring in the short, pleated cut of the tunics, unlike anything seen on stage before.

The ballet costume worn by Louis XIV as Apollo, the Sun God in Ballet Royal de la Nuit in the exhibition at the Kunstmuseum in The Hague. Photograph: Hollandse Hoogte/Lebrecht Music & Arts

How designers have created designs for ballet is scrutinised in a forthcoming exhibition. Couturiers de la Danse at the National Centre of Stage Costume in Moulins, France, examines the contribution designers have made to the look of ballet and its relationship to the modern world. “[Ballet] is a kind of laboratory for the designer and choreographer alike,” says curator Philippe Noisette. “They exchange ideas through this medium. For the designer, it’s like having a blank sheet of paper. Every idea is possible. The only thing is that in the end, the costume is alive.” Choreographers, in turn, have been inspired by the designs offered them.

Clothes for dancing in have to be practical, however. Designers know this but can get carried away. Both exhibitions feature the tutus designed by Viktor & Rolf for Dutch National Ballet in 2014 – square, sheared on one side, they challenged the eye of the viewer, accustomed to seeing the graceful circle of the traditional outfit, as well as the male dancers who risked cutting themselves on the costumes’ sharp edges as they partnered the ballerinas. “A solution had to be found,” says Hohé – in this case by the choreographer Jorma Elo, who created steps that could work around the problem.

When Jean Paul Gaultier, who forged a close, fruitful creative relationship with the French choreographer Régine Chopinot, wanted to make a design like a second skin, with the entire body covered head to toe by one single piece of clothing, he was forced to rethink his concept. “The eye and nose holes were really small and there was not enough space for the dancer to breathe,” Noisette explains. “He had to redesign it and make it more wearable.”

Some collaborations, Noisette acknowledges, are superficial. But the results of those that really work can be electric and revelatory. Issey Miyake created 200 costumes of staggering, beautiful intensity for the choreographer William Forsythe’s 1991 work The Loss of Small Detail. Forsythe told Noisette: “Issey and I exchanged all kinds of images, literature, photography and poems. Then he came to Frankfurt with several assistants and garbage bags full of the most extraordinary designs imaginable. Actually, they were unimaginable. No one had ever produced forms of that kind with fabric.” This was a time when Miyake was experimenting with what became his signature pleats. Noisette says: “I think he used the dance world to make those designs really practical and alive. It became a trend throughout his life.”

Mythical touch … Natalia Osipova in Medusa by Sidi Larbi Cherkaoui at the Royal Opera House, London, with costumes by Olivia Pomp. Photograph: Tristram Kenton/The Guardian

Stylist and fashion editor Olivia Pomp, who designed the costumes for the Royal Ballet’s recent piece Medusa, choreographed by Sidi Larbi Cherkaoui, points out, however, that the aims of the two forms are not synonymous. “Ultimately fashion is a business about creating sales for the next new thing. Dance is a completely different story. The best dance costumes are made for longevity by people who understand the body, space and movement.”

That’s why, Pomp says, the designs produced by the Bauhaus thinker Oskar Schlemmer have stood the test of time when other, more transient and initially fashionable creations now look old hat. “He was way ahead of his time. One hundred years later, his designs still work because they were never narrowly fashionable. That’s the danger when you get designers working in dance: you need someone who has a real sense of style, rather than someone who is just trying to be fashionable.”

• Let’s Dance! Fashion in Dance, from Tutus to Sneakers is at the Kunstmuseum, The Hague, until 12 January; Couturiers de la Danse is at the National Centre for Stage Costume, Moulins, France, from 30 November to 3 May