C. Auguste Dupin able to read the mind of his companion, the unnamed narrator of all three stories. Poe created the Dupin character before the word "detective" had been coined. The character laid the groundwork for fictional detectives to come, including Sherlock Holmes, and established most of the common elements of the detective fiction genre. Dupin is from what was once a wealthy family, but "by a variety of untoward events" has been reduced to more humble circumstances, and contents himself only with the basic necessities of life. He now lives in Paris with his close friend, the anonymous narrator of the stories.
Dupin cyclide "R" are a 3-dimensional vectors, and "A" and "B" are constants. Families of cyclides give rise to various cyclidic coordinate geometries. In Maxime Bôcher's 1891 dissertation, "Ueber die Reihenentwickelungen der Potentialtheorie", it was shown that the Laplace equation in three variables can be solved using separation of variables in 17 conformally distinct quadric and cyclidic coordinate geometries. Many other cyclidic geometries can be obtained by studying R-separation of variables for the Laplace equation. Dupin cyclide In mathematics, a Dupin cyclide or cyclide of Dupin is any geometric inversion of a standard torus, cylinder or double cone. In particular, these latter