C. Auguste Dupin prefect "G", who appears in all three stories seeking his counsel. In "The Murders in the Rue Morgue", Dupin investigates the murder of a mother and daughter in Paris. He investigates another murder in "The Mystery of Marie Rogêt". This story was based on the true story of Mary Rogers, a saleswoman at a cigar store in Manhattan whose body was found floating in the Hudson River in 1841. Dupin's final appearance, in "The Purloined Letter", features an investigation of a letter stolen from the French queen. Poe called this story "perhaps, the best of my tales of ratiocination". Throughout
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