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


  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
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