Bundle of layers
The plane bundle is in the perspective representation of three-dimensional objects, the amount that contain a common point of all levels, the carrier of the plane bundle.
If the beam is a far point , that is, an "intersection" of a set of parallel straight lines, then all the intersection lines of the bundle planes are parallel. The spatial bundle of planes is a basic structure of the second level, comparable to the bundle of straight lines in the plane.
definition
In synthetic geometry , based on axioms and theorems, the phrase "contains the common point" is replaced by "incised with a point" and the definition is:
In synthetic projective geometry, the plane bundle is the set of all planes that intersect with a point .
See also
- Intersection , common point of two curves in a plane or in space.
- Intersection line , the intersection of two non-parallel planes in three-dimensional space.
literature
- Hanfried Lenz : Lectures on projective geometry , Leipzig 1965
- Small Encyclopedia of Mathematics ; Leipzig 1970, pp. 216-217.