There is considerable debate about the placement of cycloids within the Arthropoda. The two points tracing the cycloids are therefore at equal heights. A point on the circle thereby traces out two cycloids. In an unpublished dissertation, Neil D. L. Clark proposed in 1989 that cycloids were copepods. The brachistochrone curve is the same shape as the tautochrone curve; both are cycloids. Cycloids were later considered to be members of the Xiphosura, true crabs, and branchiurans.