Sheaf of planes explained

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

1. http://mathworld.wolfram.com/SheafofPlanes.html Definition on Mathworld Wolfram
2. Sommerville. D. M. Y.. Classification of Geometries with Projective Metric. Proceedings of the Edinburgh Mathematical Society. 1909. 28. 25–41. 10.1017/S0013091500034763. free.
3. http://www.vitutor.com/geometry/space/sheaf_planes.html Vitutor: Sheaf of Planes