More about the remarkable properties of a special cyclide

Abstract

As is known, the French mathematician Dupin used the name cyclides to refer to curious surfaces that can be defined as being encircled by the set of all balls tangent to three data. These surfaces are extremely diverse and stand out for their many simple properties. studied both by the author himself and by some other mathematicians. They have two special axes, and if you rotate a plane around these axes, it will cut the surface in a continuous series of circles, which is why this surface can also be imagined as the trace of a circle moving according to a well-known law, at all points perpendicular to all circles of another similar system . All properties of cyclides are set out in my manual “New Geometry as the Basis of Drawing” (101). But here, in addition, a special cyclide with extremely interesting properties was derived.