The Murders in the Rue Morgue Poe's Dupin displays many traits which became literary conventions in subsequent fictional detectives, including Sherlock Holmes and Hercule Poirot. Many later characters, for example, follow Poe's model of the brilliant detective, his personal friend who serves as narrator, and the final revelation being presented before the reasoning that leads up to it. Dupin himself reappears in "The Mystery of Marie Rogêt" and "The Purloined Letter". The unnamed narrator of the story opens with a lengthy commentary on the nature and practice of analytical reasoning, then describes the circumstances under which he first met Dupin during an extended visit to Paris.
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