Armchair detective an arm-chair, my brother would be the greatest criminal agent that ever lived." "The first example of armchair detecting can be found in the work of Edgar Allan Poe. In "The Mystery of Marie Rogêt" (1842), C. Auguste Dupin, working wholly from newspaper accounts, arrives at the correct explanation for a young woman's mysterious disappearance." Baroness Orczy's Old Man in the Corner sits in a restaurant and talks to an acquaintance about cases, almost always finishing by revealing that he has solved the crime. A more literal use of this term can be found in Rex Stout's Nero Wolfe novels
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