I say 're-invented' because, in addition to his graceful (!) flowing lines, Botticelli's Graces present characteristics differing from the classical model, which are together quite uncommon. They truly dance. They link hands, as indeed in renaissance dances of Botticelli's time. They look toward each other. And they -- or two of them -- raise their joined hands joyfully above. (And they are gauzily clad rather than nude, albeit no less sexy for that -- probably more so.)
The Tate's online description could hardly recall Botticelli less: 'The jagged forms of Three Dancers convey an explosion of energy. The image is laden with Picasso's personal recollections of a triangular affair, which resulted in the heart-broken suicide of his friend Carlos Casagemas. Love, sex and death are linked in an ecstatic dance. The left-hand dancer in particular seems possessed by uncontrolled, Dionysian frenzy. Her face relates to a mask from Torres Strait, New Guinea, owned by the artist, and points to Picasso's association of 'primitive' forms with expressiveness and sexuality.'
John Richardson's acute analysis argues a 'Jazz Age interpretation' of La Danse. The vital 'antithesis' of the 'central crucificial dancer' is the 'Dionysiac dancer' on the left, 'a maenad...dancing a demonic Charleston'. ' The notion of a Charleston tallies with a fantasy Picasso had described to Diaghilev: "a chorus of music-hall girls [coming] on stage to the music intended for a proccession of bacchantes" -- and then performing "a French can-can number".'
[Richardson, A Life of Picasso: The Triumphant Years, 1917-1932 (Knopf, 2007), p. 282]
However, Richardson tells us that 'La Danse had started life as a balletic Three Graces '. Richardson does not mention Botticelli; but Picasso visited Florence in 1917, including the Uffizi holding Botticelli's Primavera with his Three Graces.
Characteristically, Picasso has drawn on the deepest heritages of European art and literature (and, here, of New Guinea art too), and married it to modernity by his genius.
I suggest Botticelli did something similar in his own day. And that Picasso must have known and incorporated Botticelli's Three Graces.
These comparisons point up both Botticelli's innovativve interpretation, especially for his own time, ...
Finally, back to Botticelli and Picasso!
Botticelli's Three Graces are performing an up-to-the-minute Florentine renaissance dance; Picasso employs the same idea for his own Jazz Age.
... and the surprising , remarkable similarities between Botticelli's Three Graces (in the Primavera) and Picasso's (in La Danse), as each artist re-invented the classical model --
Photos are from Wikimedia Commons, in the public domain, except the Tate Picasso 'Three Dancers', and the medals which are from mcsearch.info The medieval & modern coin search engine.
-- and as Picasso re-interpreted Botticelli's model, however wildly different Picasso's Jazz Age 20th century dancing Graces may seem at first glance from Botticelli's 15th century dancing Tuscan Graces.