C. Auguste Dupin of life into it?" Many tropes that would later become commonplace in detective fiction first appeared in Poe's stories: the eccentric but brilliant detective, the bumbling constabulary, the first-person narration by a close personal friend. Dupin also initiates the storytelling device where the detective announces his solution and then explains the reasoning leading up to it. Like Sherlock Holmes, Dupin uses his considerable deductive prowess and observation to solve crimes. Poe also portrays the police in an unsympathetic manner as a sort of foil to the detective. The character helped established the genre of detective fiction, distinct from mystery fiction,
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