The Gold-Bug given. Nevertheless, the Legrand character is often compared to Poe's fictional detective C. Auguste Dupin due to his use of "ratiocination". "Ratiocination", a term Poe used to describe Dupin's method, is the process by which Dupin detects what others have not seen or what others have deemed unimportant. Poe originally sold "The Gold-Bug" to George Rex Graham for "Graham's Magazine" for $52 but asked for it back when he heard about a writing contest sponsored by Philadelphia's "Dollar Newspaper". Incidentally, Poe did not return the money to Graham and instead offered to make it up to him with reviews he
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