C. Auguste Dupin with an emphasis on the analysis and not trial-and-error. Brander Matthews wrote: "The true detective story as Poe conceived it is not in the mystery itself, but rather in the successive steps whereby the analytic observer is enabled to solve the problem that might be dismissed as beyond human elucidation." In fact, in the three stories which star Dupin, Poe created three types of detective fiction which established a model for all future stories: the physical type ("The Murders in the Rue Morgue"), the mental ("The Mystery of Marie Rogêt"), and a balanced version of both ("The Purloined Letter"). Fyodor
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