| 单词 | paraboloid of revolution |
| 释义 | > as lemmasparaboloid of revolution 2. A solid or surface whose cross sections in two mutually perpendicular directions are parabolas and those in the third are either ellipses (including circles as a special case) or hyperbolas; spec. (more fully paraboloid of revolution) one with circular cross sections, generated by the rotation of a parabola about its axis of symmetry.elliptic paraboloid: see elliptic adj. Compounds 1. hyperbolic paraboloid n. a paraboloid having hyperbolic cross sections, being concave in one direction and convex in another (like a saddle). ΘΚΠ the world > space > shape > curvature > curved three-dimensional shape or body > [noun] > solid of revolution having conic section conoida1664 paraboloid1677 the world > relative properties > number > geometry > shape or figure > [noun] > three-dimensional > solid of revolution > formed from curve conoida1664 paraboloid1677 parabolic conoid1702 spindle1706 hyperboloid1743 1677 R. Boyle in Philos. Trans. 1676 (Royal Soc.) 11 800 It may suffice for me to refer the Fluids..to such of the more known Figures as they seemed to be the least remote from, without troubling you or my self with..Spheroids, Conoids, Paraboloids, and other hard words. 1702 J. Raphson Math. Dict. Paraboloid, is a Solid formed by the Circumvolution of a Parabola about its Ax. 1807 C. Hutton Course Math. (ed. 5) II. 127 The Solid Content of a Paraboloid..is equal to Half its Circumscribing Cylinder. a1831 Encycl. Metrop. (1845) I. 730/2 A parabola is x2 = 2pz. Then the equation of a paraboloid of revolution is x2 + y2 = 2pz. 1842 Penny Cycl. XXIII. 304/2 For the elliptic paraboloid, let a parabola revolve about its principal axis, and let the circular sections become ellipses. 1842 Penny Cycl. XXIII. 304/2 Let two parabolas have a common vertex, and let their planes be at right angles to one another, being turned contrary ways. Let the one parabola then move over the other, always continuing parallel to its first position, and having its vertex constantly on the other: its arc will then trace out an hyperbolic paraboloid. 1883 Analyst 10 47 The volume of a paraboloid is one-half the volume of its circumscribing cylinder. 1935 A. H. G. Palmer & K. S. Snell Mechanics xiii. 266 A homogeneous solid, in the form of a paraboloid of revolution cut off by a plane perpendicular to its axis, is balanced vertex downwards on the top of a fixed rough sphere. 1972 M. Kline Math. Thought xxiii. 547 The hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces, that is, each can be generated in two different ways by the motion of a line or each surface is formed by two systems of lines. 1993 Discover Feb. 18/1 To convert a hunk of glass into a perfect paraboloid—the right shape for collecting and focusing light into a point—requires painstaking grinding and polishing. 1993 College Math. Jrnl. 24 244 The graph..of this function is an elliptic paraboloid opening upward. < as lemmas |
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