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Bundle of Planes

A bundle of planes is a set of planes sharing a point in common. For planes specified in Hessian normal form, a bundle of planes can therefore be specified as

(n_1^^x+p_1)+lambda_1(n_2^^x+p_2)+lambda_3(n_3^^x+p_3)=0,

where lambda_1,lambda_2 are free real parameters. This can be made more symmetrical by introducing homogeneous parameters lambda_1=mu_2/mu_1 and lambda_2=mu_3/mu_1 to obtain

mu_1(n_1^^x+p_1)+mu_2(n_2^^x+p_2)+mu_3(n_3^^x+p_3)=0

(Gellert et al. 1989, p. 543).

See also

Plane, Plane-Plane Intersection, Sheaf of Planes

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References

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.

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Bundle of Planes

Cite this as:

Weisstein, Eric W. "Bundle of Planes." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BundleofPlanes.html

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