History of modern literature born. Mikhail Lermontov published "A Hero of Our Time" In 1841 Phillipe-Ignace François Aubert de Gaspé died. Edgar Allan Poe published two short stories: "A Descent into the Maelström" and "The Murders in the Rue Morgue". The latter introduced the fictional detective C. Auguste Dupin. Mikhail Lermontov was killed in a duel. In 1842, Nikolai Gogol published "Dead Souls". In 1843 the transatlantic author Henry James was born. Edgar Allan Poe published a poem: "Lenore" and four short stories: "The Gold-Bug", "The Black Cat", "The Tell-Tale Heart" and a C. Auguste Dupin short story called "The Mystery of Marie Roget".
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