Sherlock Holmes primarily relies on abduction: inferring an explanation for observed details. "From a drop of water", he writes, "a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other". In "A Scandal in Bohemia", Holmes infers that Watson had got wet lately and had "a most clumsy and careless servant girl". When Watson asks how Holmes knows this, the detective answers: In the first Holmes story, "A Study in Scarlet", Dr. Watson compares Holmes to C. Auguste Dupin, Edgar Allan Poe's fictional detective, who employed a similar methodology. Alluding to
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