The Murders in the Rue Morgue Poe's Dupin displays many traits which became literary conventions in subsequent fictional detectives, including Sherlock Holmes and Hercule Poirot. Many later characters, for example, follow Poe's model of the brilliant detective, his personal friend who serves as narrator, and the final revelation being presented before the reasoning that leads up to it. Dupin himself reappears in "The Mystery of Marie Rogêt" and "The Purloined Letter". The unnamed narrator of the story opens with a lengthy commentary on the nature and practice of analytical reasoning, then describes the circumstances under which he first met Dupin during an extended visit to Paris.
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