| 释义 |
hyperbolic, a.|haɪpəˈbɒlɪk|
[ad. Gr. ὑπερβολικ-ός extravagant, f. ὑπερβολή hyperbole; in sense 2 used as the adj. of hyperbola. So F. hyperbolique in both senses.]
1. Rhet. = hyperbolical 1.
1646Chas. I. Let. to Henderson (1649) 56 There are alwaies some flattering Fooles that can commend nothing but with hyperbolick expressions. 1748Richardson Clarissa (1811) II. xxx. 191 Eternal gratitude, is his word, among others still more hyperbolic. 1835I. Taylor Spir. Despot. ii. 55 The claims of God's ministers will be asserted in a hyperbolic yet insidious style.
2. Geom. Of, belonging to, or of the form or nature of a hyperbola.
hyperbolic branch (of a curve): an infinite branch which, like the hyperbola, continually approaches an asymptote (opp. to parabolic). h. conoid: a conoid of hyperbolic section, a hyperboloid of revolution. † h. cylindroid: name given by Wren to the hyperboloid of revolution of one sheet. h. paraboloid: see paraboloid.
1676Halley in Rigaud Corr. Sci. Men (1841) I. 240 Foci and diameter describe that hyperbolic line, whose vertex is nearest to A. 1797Encycl. Brit. VII. 687/2 When the vessel is a portion of a cone or hyperbolic conoid, the content by this method is found less than the truth. 1827G. Higgins Celtic Druids 104 Their doctrine that comets were planets, which moved in hyperbolic curves. 1852Salmon Higher Plane Curves v. (1879) 172 Cubics having three hyperbolic branches are called by Newton redundant hyperbolas.
b. Applied to functions, operations, etc., having some relation to the hyperbola.
hyperbolic curvature: the curvature of a surface whose indicatrix is a hyperbola; the same as anticlastic curvature. hyperbolic hyberbolic function: a function having a relation to a rectangular hyperbola similar to that of the ordinary trigonometrical functions to a circle; as the hyperbolic sine, hyperbolic cosine, hyperbolic tangent, etc. (abbrev. sinh, cosh, tanh, etc.). hyperbolic geometry: the geometry of hyperbolic space. hyperbolic involution: an involution of points (or lines) whose double points (or lines) are real (opp. to elliptic involution, where they are imaginary). hyperbolic logarithm: a logarithm to the base e (2·71828..), a natural or Napierian logarithm; so called because proportional to a segment of the area between a hyperbola and its asymptote. hyperbolic navigation: navigation that utilizes the difference in the times of arrival or the phases of signals transmitted in synchronism by two radio stations to determine a hyperbola on which the receiver must lie, two intersecting hyperbolas from two pairs of stations determining its position; so hyperbolic system, etc. hyperbolic space: (a) the space between a hyperbola and its asymptote or an ordinate; (b) name given by Klein to a space, of any number of dimensions, whose curvature is uniform and negative (see quot. 1872–3). hyperbolic spiral: a spiral in which the radius vector varies inversely as the angle turned through by it; so called from the analogy of its polar equation (rθ = constant) to the Cartesian equation of the hyperbola (xy = constant). hyperbolic substitution: term for a class of substitutions in the theory of homographic transformation.
1704J. Harris Lex. Techn., Hyperbolick-Space, is the Area or Space contained between the Curve of an Hyperbola, and the whole Ordinate. 1743Emerson Fluxions 97 The Fluxion of any Quantity divided by that Quantity is the Fluxion of the Hyperbolic Logarithm of that Quantity. Ibid., The hyperbolic Space between the Assymptotes. 1816tr. Lacroix's Diff. & Int. Calculus 129 An equation which belongs to the hyperbolic spiral. 1872–3Clifford Math. Papers (1882) 189 That geometry of three-dimensional space which assumes the Euclidian postulates has been called by Dr. Klein the parabolic geometry of space, to distinguish it from two other varieties which assume uniform positive and negative curvature respectively, and which he calls the elliptic and hyperbolic geometry of space. Ibid. 236 note, According to Dr. Klein's nomenclature, a space, every point of which can be uniquely represented by a set of values of n variables, is called elliptic, parabolic, or hyperbolic, when its curvature is uniform and positive, zero, or negative. 1880Chrystal Non-Euclidean Geom. 19 In hyperbolic space a straight line has two distinct real points at infinity. 1893Forsyth The. Functions 517 If the multiplier be a real positive quantity, the substitution is called hyperbolic. 1894Charlotte Scott Mod. Anal. Geom. 162 A hyperbolic involution is non-overlapping. 1945Electronics Nov. 94/1 Loran..is one of a family of systems known as ‘hyperbolic navigation systems’, which measure the relative time of arrival of two or more radio signals sent synchronously from known points. 1959[see Decca]. 1972Jrnl. Inst. Navigation XXV. 308 The navigator has three main aids—d.f. using the world-wide chain of shore-based transmitter beacons, the short-range hyperbolic systems, mainly Decca, and his own radar. |