The House of Silk the possibilities of an Atlantic or a Niagara? Can he astonish us? Can he thrill us? Are there "the rapid deductions, as swift as intuitions, and yet always founded on a logical basis" that we yearn for? Emphatically, yes. In chapter one there is some mention of C. Auguste Dupin, a character developed by author Edgar Allan Poe, and his ability to make astounding deductions based on visible emotions reflected through the physical medium. Holmes demonstrates this by uncovering Watson's anxiety and the source thereof. This mention of Dupin is in itself a reference to a reference made by Conan
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