non-orientableadj.
/ˌnɒnɔːrɪˈɛntəbl/, /ˌnɒnɒrɪˈɛntəbl/, U.S. /ˈˌnɑnɔriˈɛn(t)əb(ə)l/ Mathematics.
Of a manifold (manifold n.1 5): not having a well-defined global coordinate system; not orientable; spec. (of a surface) such that a figure in the surface can be continuously transformed into its mirror image by taking it round a closed path in the surface.
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the world > relative properties > number > geometry > surface > [adjective]
monoid1863
anallagmatic1869
scrolar1869
torsal1869
closed1882
vicinal1895
orientable1920
non-orientable1925
1925 Trans. Amer. Math. Soc. 27 335 If the generating circle returns with sense preserved the surface is orientable; if with sense reversed it is non-orientable.
1949 S. Lefschetz Introd. Topol. ii. 76 The combination of the first type is called nonorientable.
1952 P. Nemenyi tr. D. Hilbert & S. Cohn-Vossen Geom. & Imagination vi. 306 The classification of surfaces into two-sided and one-sided surfaces is identical with the classification into orientable and non-orientable.
1984 R. M. Wald Gen. Relativity App. B. 430 On the other hand, the Möbius strip..provides a simple example of a nonorientable manifold.
1997 Proc. Royal Soc. A. 453 1779 The phase is of a different kind: global, and associated with non-contractible circuits in the doubly connected (and non-orientable) configuration space.
This entry has been updated (OED Third Edition, December 2003; most recently modified version published online March 2022).
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adj.1925