C. Auguste Dupin prefect "G", who appears in all three stories seeking his counsel. In "The Murders in the Rue Morgue", Dupin investigates the murder of a mother and daughter in Paris. He investigates another murder in "The Mystery of Marie Rogêt". This story was based on the true story of Mary Rogers, a saleswoman at a cigar store in Manhattan whose body was found floating in the Hudson River in 1841. Dupin's final appearance, in "The Purloined Letter", features an investigation of a letter stolen from the French queen. Poe called this story "perhaps, the best of my tales of ratiocination". Throughout
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