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.

Sheaf 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

1. Definition on Mathworld Wolfram
2. Sommerville, D. M. Y. (1909). "Classification of Geometries with Projective Metric". Proceedings of the Edinburgh Mathematical Society. 28: 25–41. doi:10.1017/S0013091500034763.
3. Vitutor: Sheaf of Planes