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 fan of planes or a pencil 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 general definition, the adjective parallel can be added to it, resulting in the expression parallel sheaf of planes. [3]
See also
- Book embedding, a notion of graph embedding onto sheafs of half-planes
Notes
- ^ Definition on Mathworld Wolfram
- ^ Sommerville, D. M. Y. (1909). "Classification of Geometries with Projective Metric". Proceedings of the Edinburgh Mathematical Society. 28: 25–41. doi: 10.1017/S0013091500034763.
- ^ Vitutor: 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 fan of planes or a pencil 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 general definition, the adjective parallel can be added to it, resulting in the expression parallel sheaf of planes. [3]
See also
- Book embedding, a notion of graph embedding onto sheafs of half-planes
Notes
- ^ Definition on Mathworld Wolfram
- ^ Sommerville, D. M. Y. (1909). "Classification of Geometries with Projective Metric". Proceedings of the Edinburgh Mathematical Society. 28: 25–41. doi: 10.1017/S0013091500034763.
- ^ Vitutor: Sheaf of Planes