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

3. Geometry. Designating a line on the surface of a sphere or other surface which traces the shortest possible distance on the surface between two given points; (more generally) a line on a surface that locally minimizes the distance between its end-points. Also: of or relating to such lines. Frequently in geodesic curve, geodesic line. Cf. geodetic adj. 2.Originally with reference to the surface of the earth. A geodesic line on a sphere is a great circle. In relativity theory a geodesic is the path in space-time that a particle follows when it is not acted on by an external force.

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1809 Philos. Mag. 34 255 The geodesic line is a curve whose first side is a tangent in any given direction to the surface of the earth.

1837 Math. Probl. Senate-House Exam. Papers xvi. 227 State the theorem by which the computation of a triangle on the terrestrial sphere is reduced to that of a plane triangle having sides of the same length, and apply it to solve a geodesic triangle where two sides and the included angle are given.

1862 London Univ. Cal. p. cxciv A geodesic curve is drawn on a surface of revolution, and this curve is projected on a plane perpendicular to the axis and cutting the axis in the point O.

1898 Proc. London Math. Soc. 29 275 (title) The geodesic geometry of surfaces in non-Euclidean space.

1907 M. Merriman Elem. Precise Surv. & Geodesy (ed. 2) vii. 175 On a sphere the two normal sections and the alignment and geodesic curves between A and B coincide in an arc of a great circle.

1935 Geogr. Jrnl. 85 466 The equation of the orthodrome (geodesic line).

1972 M. Kline Math. Thought xxxvii. 886 Two points on the same generator of a circular cylinder are connected by a geodesic along the generator but also by an infinite number of geodesic helices.

2001 G. Cole in P. Moore 2002 Yearbk. Astron. ii. 194 The path of a test mass in the presence of a gravitational field is represented by a special path (a geodesic path) in the chosen geometry.

2002 K. Heusch tr. H. Fritzsch Curvature of Spacetime x. 133 The straight world-lines of objects moving freely in two-dimensional spacetime are, as we see, the geodesic lines in spacetime.

2. Geometry. = geodesic adj. 3. Chiefly in geodesic curve, geodetic line.

ΚΠ

1811 C. Hutton Course Math. III. v. 115 A line traced in the manner we have now been describing..is called a geodetic or geodesic line: it has the property of being the shortest which can be drawn between its two extremities on the surface of the earth.

1853 Proc. Royal Irish Acad. 1850–3 5 340 If the proposed boundary B be a closed geodetic curve returning into itself, the total curvature of the included portion of the surface will be equal to a hemisphere.

1870 Nature 13 Jan. 297/2 To obtain the length of the arc of any orthogonal trajectory to the two geodetic lines in question.

1917 Science 23 Nov. 513/2 Linear growth of the former [spicules] under restraint leading to forms which have for their mathematical basis geodetic curves.

1966 Proc. National Acad. Sci. U.S. 55 1401 Nets that form manifolds with boundaries that are disjoint, simply connected closed geodetic polygons.

2002 J. Chay Unequal Partners Peace & War ii. 33 The 38th parallel, a geodetic line, which cuts Korea indiscriminately, created a critical situation on the peninsula.

单词	geodesic curve
释义	> as lemmas geodesic curve 3. Geometry. Designating a line on the surface of a sphere or other surface which traces the shortest possible distance on the surface between two given points; (more generally) a line on a surface that locally minimizes the distance between its end-points. Also: of or relating to such lines. Frequently in geodesic curve, geodesic line. Cf. geodetic adj. 2.Originally with reference to the surface of the earth. A geodesic line on a sphere is a great circle. In relativity theory a geodesic is the path in space-time that a particle follows when it is not acted on by an external force. ΚΠ 1809 Philos. Mag. 34 255 The geodesic line is a curve whose first side is a tangent in any given direction to the surface of the earth. 1837 Math. Probl. Senate-House Exam. Papers xvi. 227 State the theorem by which the computation of a triangle on the terrestrial sphere is reduced to that of a plane triangle having sides of the same length, and apply it to solve a geodesic triangle where two sides and the included angle are given. 1862 London Univ. Cal. p. cxciv A geodesic curve is drawn on a surface of revolution, and this curve is projected on a plane perpendicular to the axis and cutting the axis in the point O. 1898 Proc. London Math. Soc. 29 275 (title) The geodesic geometry of surfaces in non-Euclidean space. 1907 M. Merriman Elem. Precise Surv. & Geodesy (ed. 2) vii. 175 On a sphere the two normal sections and the alignment and geodesic curves between A and B coincide in an arc of a great circle. 1935 Geogr. Jrnl. 85 466 The equation of the orthodrome (geodesic line). 1972 M. Kline Math. Thought xxxvii. 886 Two points on the same generator of a circular cylinder are connected by a geodesic along the generator but also by an infinite number of geodesic helices. 2001 G. Cole in P. Moore 2002 Yearbk. Astron. ii. 194 The path of a test mass in the presence of a gravitational field is represented by a special path (a geodesic path) in the chosen geometry. 2002 K. Heusch tr. H. Fritzsch Curvature of Spacetime x. 133 The straight world-lines of objects moving freely in two-dimensional spacetime are, as we see, the geodesic lines in spacetime. extracted from geodesicadj.n. geodesic curve 2. Geometry. = geodesic adj. 3. Chiefly in geodesic curve, geodetic line. ΚΠ 1811 C. Hutton Course Math. III. v. 115 A line traced in the manner we have now been describing..is called a geodetic or geodesic line: it has the property of being the shortest which can be drawn between its two extremities on the surface of the earth. 1853 Proc. Royal Irish Acad. 1850–3 5 340 If the proposed boundary B be a closed geodetic curve returning into itself, the total curvature of the included portion of the surface will be equal to a hemisphere. 1870 Nature 13 Jan. 297/2 To obtain the length of the arc of any orthogonal trajectory to the two geodetic lines in question. 1917 Science 23 Nov. 513/2 Linear growth of the former [spicules] under restraint leading to forms which have for their mathematical basis geodetic curves. 1966 Proc. National Acad. Sci. U.S. 55 1401 Nets that form manifolds with boundaries that are disjoint, simply connected closed geodetic polygons. 2002 J. Chay Unequal Partners Peace & War ii. 33 The 38th parallel, a geodetic line, which cuts Korea indiscriminately, created a critical situation on the peninsula. extracted from geodeticn.adj. < as lemmas
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