Eine kinematische Kennzeichnung der gleichseitigen Paraboloide (Q1252637)

For a given quadric exist (in general) \(\infty\) generating methods by means of cones. In the case of the equilateral hyperbolic paraboloid we know, due to H. Brauner, an explicit generation by an equilateral hyperbola. More general we show: The only quadrics which can be generated with cones by a cylindrical vibration are the equilateral paraboloids. The generating cones are equilateral hyperbolas or parabolas, resp. Some special properties are demonstrated.