Gentleman detective shares some features with the later gentleman detective. He was "…the first fictional detective of importance and the model for virtually every cerebral crime solver who followed." More specifically, Dorothy L. Sayers noted that "Sherlock Holmes modelled himself to a large extent upon (Poe's) Dupin, substituting cocaine for candlelight, with accompaniments of shag and fiddle-playing." Dupin is French, not English, but is probably a "gentleman". He comes from a once wealthy family but has been reduced "by a variety of untoward events" to more humble circumstances. He is entirely amateur and contents himself only with the basic necessities of life.
Dupin cyclide that the class of Dupin cyclides is invariant under Möbius (or conformal) transformations. In complex space formula_2 these three latter varieties can be mapped to one another by inversion, so Dupin cyclides can be defined as inversions of the torus (or the cylinder, or the double cone). Since a standard torus is the orbit of a point under a two dimensional abelian subgroup of the Möbius group, it follows that the cyclides also are, and this provides a second way to define them. A third property which characterizes Dupin cyclides is that their curvature lines are all circles (possibly through