### Some articles on *lie, lie transformations, transformations*:

Lie Sphere Geometry in Space and Higher Dimensions - General Theory

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**Lie**sphere geometry in n-dimensions is obtained by replacing R3,2 (corresponding to the**Lie**quadric in n = 2 dimensions) by Rn + 1, 2 ... This is Rn + 3 equipped with the symmetric bilinear form The**Lie**quadric Qn is again defined as the set of ∈ RPn+2 = P(Rn+1,2) with x · x = 0 ... The group of**Lie transformations**is now O(n + 1, 2) and the**Lie transformations**preserve incidence of**Lie**cycles ...Lie Sphere Geometry in The Plane -

... Any element of the group O(3,2) of orthogonal

**Lie Transformations**... Any element of the group O(3,2) of orthogonal

**transformations**of R3,2 maps any null one dimensional subspaces of R3,2 to another such subspace ... Hence the group O(3,2) acts on the**Lie**quadric ... These**transformations**of cycles are called "**Lie transformations**" ...### Famous quotes containing the word lie:

“It is only for a little while, only occasionally, methinks, that we want a garden. Surely a good man need not be at the labor to level a hill for the sake of a prospect, or raise fruits and flowers, and construct floating islands, for the sake of a paradise. He enjoys better prospects than *lie* behind any hill. Where an angel travels it will be paradise all the way, but where Satan travels it will be burning marl and cinders.”

—Henry David Thoreau (1817–1862)

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