C. Auguste Dupin to an orangutan that had been on display at the Masonic Hall in Philadelphia in July 1839. In "The Mystery of Mary Rogêt", he used a true story that had become of national interest. C. Auguste Dupin is generally acknowledged as the first detective in fiction. The character served as the prototype for many that were created later, including Sherlock Holmes by Arthur Conan Doyle and Hercule Poirot by Agatha Christie. Conan Doyle once wrote, "Each [of Poe's detective stories] is a root from which a whole literature has developed... Where was the detective story until Poe breathed the breath
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