History of crime fiction (1839) and Maurits Christopher Hansen's ""Mordet paa Maskinbygger Roolfsen" - The Murder of Engineer Roolfsen" (1839). An example of an early crime/revenge story is the American poet and short story writer Edgar Allan Poe's (1809–1849) tale "The Cask of Amontillado", published in 1846. Poe created the first fictional detective (a word unknown at the time) in the character of C. Auguste Dupin, as the central character of some of his short stories (which he called "tales of ratiocination"). In the words of William L. De Andrea ("Encyclopedia Mysteriosa", 1994), he One of the early developments started by Poe was the
Dupin cyclide of Dupin cyclides is invariant under the larger group of all Lie sphere transformations; any two Dupin cyclides are Lie-equivalent. They form (in some sense) the simplest class of Lie-invariant surfaces after the spheres, and are therefore particularly significant in Lie sphere geometry. The definition also means that a Dupin cyclide is the envelope of the one-parameter family of spheres tangent to three given mutually tangent spheres. It follows that it is tangent to infinitely many Soddy's hexlet configurations of spheres. A further special property of a cyclide is: An elliptic cyclide can be represented parametrically by the following formulas