C. Auguste Dupin implies "duping" or deception, a skill Dupin shows off in "The Purloined Letter." Detective fiction, however, had no real precedent and the word "detective" had not yet been coined when Poe first introduced Dupin. The closest example in fiction is Voltaire's "Zadig" (1748), in which the main character performs similar feats of analysis, themselves borrowed from "The Three Princes of Serendip", an Italian rendition of Amir Khusrau's Hasht Bihisht. In writing the series of Dupin tales, Poe capitalized on contemporary popular interest. His use of an orangutan in "The Murders in the Rue Morgue" was inspired by the popular reaction
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