The Murders in the Rue Morgue The Murders in the Rue Morgue "The Murders in the Rue Morgue" is a short story by Edgar Allan Poe published in "Graham's Magazine" in 1841. It has been recognized as the first modern detective story; Poe referred to it as one of his "tales of ratiocination". C. Auguste Dupin is a man in Paris who solves the mystery of the brutal murder of two women. Numerous witnesses heard a suspect, though no one agrees on what language was spoken. At the murder scene, Dupin finds a hair that does not appear to be human. As the first fictional detective,
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