Rotary quadric
In mathematics, a square of rotation is a surface in three-dimensional Euclidean space , which is characterized by special symmetry properties. It can be characterized as a second-order rotating surface .
Rotary squares belong to the quadrics . These are the swept areas of rotating conic sections in three-dimensional space, i.e. those areas that are swept over when a conic section rotates around one of its axes of symmetry in three-dimensional space . Like all quadrics, they can be understood in Cartesian coordinates as sets of zeros in a quadratic equation .
classification
A distinction is made between the following types of quadrants of rotation:
Single-shell rotational hyperboloid
Double-shell rotational hyperboloid
The last two types have singularities .
literature
- Rudolf Bereis: Descriptive Geometry . tape I. . Akademie-Verlag, Berlin 1964, XI second-order rotating surfaces .
- Rudolf Bereis: About the slope lines on turning squares . In: Monthly books for mathematics . tape 56 , no. 4 , 1952, pp. 344-351 , doi : 10.1007 / BF01302720 .
- VRML files of rotating squares. Geometry Forum, accessed April 4, 2013 .
- Helgrid Müller: Turning squares in Solid Edge. (PDF; 543 kB) Data sheet 18 from the spatial geometry textbook. Retrieved April 4, 2013 .