英语词汇“hypersphere”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

(b) In substantives in which hyper- has the sense ‘the analogue in a space of four or more dimensions of (what is denoted by the second element) in ordinary three-dimensional space’; as hypercube, hypercylinder, hyperplane, hypersphere, hypersurface.

1895 Proc. Royal Soc. 58 p. xxxi The manifoldness in this space..is the quadri-quadric two-dimensional amplitude common to thirteen quadric hyper-cylinders.

1903 C. M. Jessop Treat. Line Complex xiii. 244 Any linear equation of the form Σ51a_iX_i = 0 singles out ∞³ points from S₄, which will then form a space of three dimensions; the locus of these ∞³ points will be called a hyperplane.

1903 C. M. Jessop Treat. Line Complex xiii. 251 In four-dimensional space, the three-dimensional quadric spaces through the intersection of S²₃ and X₅ = 0..may be termed ‘hyperspheres’.

1909 Sci. Amer. 3 July 6/2 Just as portions of our space are bounded by surfaces,.. so portions of hyperspace are bounded by hyper~surfaces (three-dimensional), i.e., flat or curved 3-spaces.

1909 Sci. Amer. 6/3 Of these [regular hyper-solids], C₈ (or the hyper~cube) is the simplest, because, though with more bounding solids than C₅, it is right-angled throughout.

1955 O. Klein in W. Pauli Niels Bohr & Devel. Physics 100 Let..x¹, x², x³, x⁴ be the four space-time coordinates regarded as c-numbers, x¹, x², x³ forming a space-like hypersurface for any given value of the general time coordinate x⁴.

1966 A. Battersby Math. in Managem. v. 122 When the number of variables exceeds three..we could represent the process of solution by a series of three-dimensional solid bodies showing successive cross-sections of the solution space when cut by the ‘hyper-plane’ of P.

1968 H. Rosenberg & D. A. Johnson Geom. xiii. 520/2 If the solid cube moves in a direction ‘perpendicular’ to its original space, it may trace a solid hypercube.

1969 R. J. Bumcrot Mod. Projective Geom. ii. 30 Subspaces of dimensions 1, 2, n–1 are called, respectively, lines, planes, and hyperplanes.

1970 E. E. Kramer Nature & Growth Mod. Math. vii. 160 To say that a relation like x² + y² + z² + w² = 9 is a hyper~sphere with radius 3 is so much easier than to state that the relation is the set of all ordered quadruples of real numbers such that the sum of the squares of these four numbers is always 9.

1972 Computer Jrnl. 15 214/1 The problem of optimising a function globally over the vertices of a hypercube is encountered, for example, in hierarchical classification.

单词	hypersphere
释义	> as lemmas hypersphere (b) In substantives in which hyper- has the sense ‘the analogue in a space of four or more dimensions of (what is denoted by the second element) in ordinary three-dimensional space’; as hypercube, hypercylinder, hyperplane, hypersphere, hypersurface. Π 1895 Proc. Royal Soc. 58 p. xxxi The manifoldness in this space..is the quadri-quadric two-dimensional amplitude common to thirteen quadric hyper-cylinders. 1903 C. M. Jessop Treat. Line Complex xiii. 244 Any linear equation of the form Σ51a_iX_i = 0 singles out ∞³ points from S₄, which will then form a space of three dimensions; the locus of these ∞³ points will be called a hyperplane. 1903 C. M. Jessop Treat. Line Complex xiii. 251 In four-dimensional space, the three-dimensional quadric spaces through the intersection of S²₃ and X₅ = 0..may be termed ‘hyperspheres’. 1909 Sci. Amer. 3 July 6/2 Just as portions of our space are bounded by surfaces,.. so portions of hyperspace are bounded by hyper~surfaces (three-dimensional), i.e., flat or curved 3-spaces. 1909 Sci. Amer. 6/3 Of these [regular hyper-solids], C₈ (or the hyper~cube) is the simplest, because, though with more bounding solids than C₅, it is right-angled throughout. 1955 O. Klein in W. Pauli Niels Bohr & Devel. Physics 100 Let..x¹, x², x³, x⁴ be the four space-time coordinates regarded as c-numbers, x¹, x², x³ forming a space-like hypersurface for any given value of the general time coordinate x⁴. 1966 A. Battersby Math. in Managem. v. 122 When the number of variables exceeds three..we could represent the process of solution by a series of three-dimensional solid bodies showing successive cross-sections of the solution space when cut by the ‘hyper-plane’ of P. 1968 H. Rosenberg & D. A. Johnson Geom. xiii. 520/2 If the solid cube moves in a direction ‘perpendicular’ to its original space, it may trace a solid hypercube. 1969 R. J. Bumcrot Mod. Projective Geom. ii. 30 Subspaces of dimensions 1, 2, n–1 are called, respectively, lines, planes, and hyperplanes. 1970 E. E. Kramer Nature & Growth Mod. Math. vii. 160 To say that a relation like x² + y² + z² + w² = 9 is a hyper~sphere with radius 3 is so much easier than to state that the relation is the set of all ordered quadruples of real numbers such that the sum of the squares of these four numbers is always 9. 1972 Computer Jrnl. 15 214/1 The problem of optimising a function globally over the vertices of a hypercube is encountered, for example, in hierarchical classification. extracted from hyper-prefix < as lemmas
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