Mystery film include "The Gold Bug" (1910), also from France, and "The Murders in the Rue Morgue" (1914). Both are derived from stories by Edgar Allan Poe, which is appropriate as Poe is often credited with creating modern detective fiction as well as the first private detective character, C. Auguste Dupin. Universal Pictures renamed him Pierre Dupin in "Murders in the Rue Morgue" (1932), an atmospheric horror-mystery starring Bela Lugosi. The film was remade twice more in 1953 and 1971. Poe's second Dupin story, "The Mystery of Marie Rogêt", was filmed in 1942. More recently, "The Raven" (2012) presented a fictionalized account
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