C. Auguste Dupin able to read the mind of his companion, the unnamed narrator of all three stories. Poe created the Dupin character before the word "detective" had been coined. The character laid the groundwork for fictional detectives to come, including Sherlock Holmes, and established most of the common elements of the detective fiction genre. Dupin is from what was once a wealthy family, but "by a variety of untoward events" has been reduced to more humble circumstances, and contents himself only with the basic necessities of life. He now lives in Paris with his close friend, the anonymous narrator of the stories.
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