solutions based on discontinuous functions may also be defined. in particular, for some placements of the two points the optimal solution is generated by a discontinuous function that is nonzero at the two points and zero everywhere else. this function leads to a surface of revolution consisting of two circular disks, one for each point, connected by a degenerate line segment along the axis of revolution. this is known as a goldschmidt solution after german mathematician carl wolfgang benjamin goldschmidt, who announced his discovery of it in his 1831 paper "determinatio superficiei minimae rotatione curvae data duo puncta jungentis circa datum axem ortae" ("determination of the surface-minimal rotation curve given two joined points about a given axis of origin").