Bundle of Planes
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 PlanesExplore with Wolfram|Alpha
WolframAlpha
More things to try:
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.Referenced on Wolfram|Alpha
Bundle of PlanesCite this as:
Weisstein, Eric W. "Bundle of Planes." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BundleofPlanes.html