More on the remarkable properties of the special cyclide
Abstract
As is well known, the French mathematician Dupin used the name "cyclides" to refer to certain curious surfaces which can be defined as surfaces enveloped by the totality of all spheres tangent to three given spheres. These surfaces are extraordinarily are distinguished by many simple properties inherent to them, studied both by the author himself and by several other mathematicians. They possess two special axes, and if a plane is rotated about these axes, it will intersect the surface in a continuous series of circles, consequently, this surface can be conceived as the trace of a circle moving according to a specific law, being at every point perpendicular to all circles of another such system. All the properties of cyclides are set forth in my manual “New Geometry as the Basis for Drawing” . Therein, however, a special cyclide possessing extremely interesting properties was also derived.
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