| 释义 |
hyperboloid Geom.|haɪˈpɜːbəlɔɪd|
[f. hyperbola + -oid. Cf. F. hyperboloïde.]
†1. A hyperbola of a higher degree: = hyperbola b. Obs.
1727–41Chambers Cycl., Hyperboloides, are hyperbola's of the higher kind..expressed by this equation: aym + n = bxm (a + x)n. 1740Cheyne Regimen 326 Like the several Orders of the Hyperboloids, some of which meet the Asymptot infinitly sooner and faster than others, but through which all must pass sooner or later. 1796in Hutton Math. Dict.
2. A solid or surface of the second degree, some of whose plane sections are hyperbolas, the others being ellipses or circles. Formerly restricted to those of circular section, generated by the revolution of a hyperbola about one of its axes; now called hyperboloids of revolution.
There are two kinds of hyperboloid: the hyperboloid of one sheet, e.g. that generated by revolution about the conjugate axis (formerly called hyperbolic cylindroid), a figure resembling a cylinder but of continuously varying diameter, like a reel narrower in the middle than at the ends; and the hyperboloid of two sheets, e.g. that generated by revolution about the transverse axis, consisting of two separate parts corresponding to the two branches of the hyperbola. The word is sometimes extended to analogous solids of higher degrees: cf. hyperbola b.
1743Emerson Fluxions 210 The Hyperboloid is always between ½ and 1/3 the circumscribing Cylinder. 1828Hutton Course Math. II. 339 To find the surface of an hyperboloid. 1829Nat. Philos., Hydraulics i. 4 (U.K.S.) Newton..found that the solid figure produced by the streams flowing from all parts to one common centre..was an Hyperboloid of the fourth order. 1840Lardner Geom. 286 If an hyperboloid of revolution be formed by the revolution of an hyperbola on its transverse axis. 1867J. Hogg Microsc. i. ii. 24 If a plano-convex lens has its convex surface part of a hyperboloid. 1895Oracle Encycl. III. 84/1 A point moving round a fixed point at a constant distance from it describes a circle, and a straight line rotating round a fixed line not in the same plane generates a hyperboloid. |