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 of Dupin cyclides is invariant under the larger group of all Lie sphere transformations; any two Dupin cyclides are Lie-equivalent. They form (in some sense) the simplest class of Lie-invariant surfaces after the spheres, and are therefore particularly significant in Lie sphere geometry. The definition also means that a Dupin cyclide is the envelope of the one-parameter family of spheres tangent to three given mutually tangent spheres. It follows that it is tangent to infinitely many Soddy's hexlet configurations of spheres. A further special property of a cyclide is: An elliptic cyclide can be represented parametrically by the following formulas