C. Auguste Dupin with an emphasis on the analysis and not trial-and-error. Brander Matthews wrote: "The true detective story as Poe conceived it is not in the mystery itself, but rather in the successive steps whereby the analytic observer is enabled to solve the problem that might be dismissed as beyond human elucidation." In fact, in the three stories which star Dupin, Poe created three types of detective fiction which established a model for all future stories: the physical type ("The Murders in the Rue Morgue"), the mental ("The Mystery of Marie Rogêt"), and a balanced version of both ("The Purloined Letter"). Fyodor
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