Detective fiction underworld and undercover surveillance, rather than brilliance of imagination or intellect. Detective fiction in the English-speaking world is considered to have begun in 1841 with the publication of Poe's "The Murders in the Rue Morgue", featuring "the first fictional detective, the eccentric and brilliant C. Auguste Dupin". When the character first appeared, the word detective did not even exist. However, the character's name, "Dupin", originated from the English word dupe or deception. Poe devised a "plot formula that's been successful ever since, give or take a few shifting variables." Poe followed with further Auguste Dupin tales: "The Mystery of Marie
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