hyperplane

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hyperplane

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Etymology tree

Proto-Indo-European *úp

Proto-Indo-European *-er

Proto-Indo-European *upér

Proto-Hellenic *hupér

Ancient Greek ῠ̔πέρ (hŭpér)

Ancient Greek ῠ̔περ- (hŭper-)der.

English hyper-

English plane

English hyperplane

From hyper- + plane.

hyperplane (plural hyperplanes)

(geometry) An n-dimensional generalization of a plane; an affine subspace of dimension n − 1 that splits an n-dimensional space. (In a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane.)
- 2020 April 7, Peter Conrad, “Abolish Silicon Valley by Wendy Liu review – rebooting our reality”, in The Guardian‎^[1], archived from the original on 14 June 2025:
  We now have good reason to question the pursuits of the vaunted innovators with whom Liu consorted in California – the blissed-out cultists at Google, whose only worry is over “the wrong kind of sparkling water in the microkitchens”, or the manic experts who specialise in “envisioning hyperplanes in n-dimensional space”.

an n-dimensional generalization of a plane