C. Auguste Dupin of life into it?" Many tropes that would later become commonplace in detective fiction first appeared in Poe's stories: the eccentric but brilliant detective, the bumbling constabulary, the first-person narration by a close personal friend. Dupin also initiates the storytelling device where the detective announces his solution and then explains the reasoning leading up to it. Like Sherlock Holmes, Dupin uses his considerable deductive prowess and observation to solve crimes. Poe also portrays the police in an unsympathetic manner as a sort of foil to the detective. The character helped established the genre of detective fiction, distinct from mystery fiction,
Dupin cyclide also used to refer to a more general class of quartic surfaces which are important in the theory of separation of variables for the Laplace equation in three dimensions. Dupin cyclides were investigated not only by Dupin, but also by A. Cayley und J.C. Maxwell. Today, Dupin cylides are used in computer-aided design (CAD), because cyclide patches have rational representations and are suitable for blending canal surfaces (cylinder, cones, tori, and others). There are several equivalent definitions of Dupin cyclides. In formula_1, they can be defined as the images under any inversion of tori, cylinders and double cones. This shows