Edgar Allan Poe 19th century to become more popular in Europe than in the United States. Poe is particularly respected in France, in part due to early translations by Charles Baudelaire. Baudelaire's translations became definitive renditions of Poe's work throughout Europe. Poe's early detective fiction tales featuring C. Auguste Dupin laid the groundwork for future detectives in literature. Sir Arthur Conan Doyle said, "Each [of Poe's detective stories] is a root from which a whole literature has developed... Where was the detective story until Poe breathed the breath of life into it?" The Mystery Writers of America have named their awards for excellence
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