Fictional detectives Fictional detectives Fictional detectives are characters in detective fiction. These characters have long been a staple of detective mystery crime fiction, particularly in detective novels and short stories. Much of early detective fiction was written during the "Golden Age of Detective Fiction" (1920s-1930s). These detectives include amateurs, private investigators and professional policemen. They are often popularized as individual characters rather than parts of the fictional work in which they appear. Stories involving individual detectives are well-suited to dramatic presentation, resulting in many popular theatre, television, and movie characters. The first famous detective in fiction was Edgar Allan Poe's C. Auguste
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