Eureka: A Prose Poem Poe's fiction work, including attempts at breaking beyond the obstacle of death and specifically characters who return from death in stories like "The Fall of the House of Usher" and "Ligeia". Similar to his theories on a good short story, Poe believes the universe is a self-contained, closed system. In coming to his conclusions, Poe uses ratiocination as a literary device, through his character C. Auguste Dupin, as if Poe himself were a detective solving the mystery of the universe. "Eureka", then, is the culmination of Poe's interest in capturing truth through language, an extension of his interest in cryptography.
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