| 单词 | hyperbolic spiral |
| 释义 | > as lemmashyperbolic spiral hyperbolic curvature: the curvature of a surface whose indicatrix is a hyperbola; the same as anticlastic adj. curvature. hyperbolic 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. (abbreviated 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 (opposed 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. 1872-32). 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.extracted from hyperbolicadj.hyperbolic spiral spiral of Archimedes, a curve traced by a point moving uniformly along a line which at the same time revolves uniformly round a fixed point in itself. equiangular spiral, hyperbolic spiral, logarithmic spiral, loxodromic spiral, parabolic spiral: see these words.extracted from spiraln.< as lemmas |
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