Sheaf of Planes


The set of all planes through a line. The line is sometimes called the axis of the sheaf, and the sheaf itself is sometimes called a pencil (Altshiller-Court 1979, p. 12; Gellert et al. 1989, p. 542).

The equation of a sheaf of planes specified in Hessian normal form is


See also

Bundle of Planes, Line, Parallel Planes, Pencil, Plane, Plane-Plane Intersection, Star

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Altshiller-Court, N. Modern Pure Solid Geometry. New York: Chelsea, 1979.Gellert, W.; Gottwald, S.; Hellwich, M.; Kästner, H.; and Künstner, H. (Eds.). VNR Concise Encyclopedia of Mathematics, 2nd ed. New York: Van Nostrand Reinhold, 1989.Kern, W. F. and Bland, J. R. Solid Mensuration with Proofs, 2nd ed. New York: Wiley, p. 13, 1948.Woods, F. S. Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry. New York: Dover, p. 12, 1961.

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Sheaf of Planes

Cite this as:

Weisstein, Eric W. "Sheaf of Planes." From MathWorld--A Wolfram Web Resource.

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