C. Auguste Dupin features Dupin befriending a young boy named Edmund. The two solve mysteries together in Providence, Rhode Island. Dupin is revealed to be Edgar Allan Poe himself. Novelist George Egon Hatvary uses Dupin in his novel "The Murder of Edgar Allan Poe" (1997) as detective and narrator. Dupin travels to America to investigate the circumstances of Poe's mysterious death in 1849. In the novel, Dupin and Poe became friends when Poe stayed in Paris in 1829, and it was Poe who assisted Dupin in the three cases about which Poe wrote. Hatvary writes that Dupin resembles Poe, so much so that
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