Hercule Poirot and Frank Howel Evans' Monsieur Poiret, a retired Belgian police officer living in London. A more obvious influence on the early Poirot stories is that of Arthur Conan Doyle. In "An Autobiography", Christie states, "I was still writing in the Sherlock Holmes tradition – eccentric detective, stooge assistant, with a Lestrade-type Scotland Yard detective, Inspector Japp". For his part, Conan Doyle acknowledged basing his detective stories on the model of Edgar Allan Poe's C. Auguste Dupin and his anonymous narrator, and basing his character Sherlock Holmes on Joseph Bell, who in his use of "ratiocination" prefigured Poirot's reliance on his
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