Sheaf of planes

From Wikipedia
https://en.wikipedia.org/wiki/Sheaf_of_planes
Sheaf of Planes

In mathematics, a sheaf of planes is the set of all planes that have the same common line. [1] [2] It may also be known as a pencil or fan of planes.

When extending the concept of line to the line at infinity, a set of parallel planes can be seen as a sheaf of planes intersecting in a line at infinity. To distinguish it from the more common definition the adjective parallel can be added to it, resulting in the expression: parallel sheaf of planes. [3]

See also

Notes

  1. ^ Definition on Mathworld Wolfram
  2. ^ Sommerville, D. M. Y. (1909). "Classification of Geometries with Projective Metric". Proceedings of the Edinburgh Mathematical Society. 28: 25. doi: 10.1017/S0013091500034763.
  3. ^ Vitutor: Sheaf of Planes