# Sheaf of planes

*https://en.wikipedia.org/wiki/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

- 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. doi: 10.1017/S0013091500034763.**^**Vitutor: Sheaf of Planes