The Gold-Bug given. Nevertheless, the Legrand character is often compared to Poe's fictional detective C. Auguste Dupin due to his use of "ratiocination". "Ratiocination", a term Poe used to describe Dupin's method, is the process by which Dupin detects what others have not seen or what others have deemed unimportant. Poe originally sold "The Gold-Bug" to George Rex Graham for "Graham's Magazine" for $52 but asked for it back when he heard about a writing contest sponsored by Philadelphia's "Dollar Newspaper". Incidentally, Poe did not return the money to Graham and instead offered to make it up to him with reviews he
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