brachistochrone vs curved shape

brachistochrone and curved shape both are nouns.

Word	Noun	Adjective	Verb	Adverb
brachistochrone	Yes	No	No	No
curved shape	Yes	No	No	No

As nouns, curved shape is a hypernym of brachistochrone; that is, curved shape is a word with a broader meaning than brachistochrone:

brachistochrone: a curve between two points along which a body can move under gravity in a shorter time than for any other curve.
curved shape: the trace of a point whose direction of motion changes

Other hypernyms of brachistochrone include curve.

brachistochrone (noun)	curved shape (noun)
a curve between two points along which a body can move under gravity in a shorter time than for any other curve.	the trace of a point whose direction of motion changes