This is not just the nice direct, uncomplicated translation that these entries imply.
1) The OED has it with a small t at the start, as does Merriam-Webster. The capital T is obviously also OK, but both need to be given.
2) M-W does not add "formal" or "humerous", but Oxford does, and considering how rarely the word is used, it wouldn't surprise me if it was at least formal in AE too.
I'd also possibly add "rare" or "dated" as I'd never come across it before today and the frequency chart agrees with me.
3) However it's translated into German, it would be "the terpsichorean art" in English, otherwise it would describe art (=drawing, painting) rather than an art (a branch of creative activity, here the terpsichorean one).
- DANCES AND DOUBTS; Is There Any Progress in the Terpsichorean Art? NY Times, 1912
- The Terpsichorean art is very difficult and the dancing girls must begin practice very young. Manawatu Times, NZ, 1937
- H. G. Wells is taking laborious pains in teaching himself the delights of the modern terpsichorean art. TIME, 1923