C. Auguste Dupin implies "duping" or deception, a skill Dupin shows off in "The Purloined Letter." Detective fiction, however, had no real precedent and the word "detective" had not yet been coined when Poe first introduced Dupin. The closest example in fiction is Voltaire's "Zadig" (1748), in which the main character performs similar feats of analysis, themselves borrowed from "The Three Princes of Serendip", an Italian rendition of Amir Khusrau's Hasht Bihisht. In writing the series of Dupin tales, Poe capitalized on contemporary popular interest. His use of an orangutan in "The Murders in the Rue Morgue" was inspired by the popular reaction
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