英语词汇“circular or spherical inversion”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

23. Geometry. Any of several methods for transforming a geometric figure in a manner regarded as analogous to turning (a section of) it inside out; spec. (in later use) that in which each point within a circle, sphere, or hypersphere of a given radius is substituted for a point lying a certain distance along a line passing through both the centre and the original point (more fully circular or spherical inversion).The centre of the circle, sphere, or hypersphere determining the inversion is called the origin or centre of inversion.Early methods of inversion include quadric inversion, in which a conic section is employed in the role more usually occupied by a circle, sphere, or hypersphere, and tangential inversion, in which the form of the inversion is determined by the translation of the figure's tangents, rather than its points.

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the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > replacing quantities

conversion1570

composition1660

substitution1694

inversion1843

reciprocation1852

1843 London, Edinb., & Dublin Philos. Mag. 23 339 From the theorem of the three perpendiculars from the angles of a triangle on the opposite sides meeting in a point, we get by inversion the three polar circles perpendicular to the opposite sides of the polar triangle.

1858 London, Edinb., & Dublin Philos. Mag. 4th Ser. 16 166 They are at the same time anti-parallel sections of a cone whose vertex is the centre of inversion.

1865 Proc. Royal Soc. 14 91 (heading) On the quadric inversion of plane curves.

1881 Q. Jrnl. Pure & Appl. Math. 17 313 Familiar theorems are now applied to generate by tangential inversion the quadricuspid hypocycloid.

1925 H. F. Baker Princ. Geom. (2010) IV. i. 14 These are the formulae of inversion in the plane ω, in which (ξ, η, ζ) are the coordinates of a point, and (ξ', η', ζ') those of the inverse point.

1949 Q. Appl. Math. 6 387 Another method of handling homogeneous harmonic functions of integral degree n is by differentiation of functions of degree zero, and spherical inversion.

1992 H. Eves Fund. Mod. Elem. Geom. ii. 104 When working with inversion in space, we add to the set S of all points of space a single ideal point at infinity.

2012 D. A. Brannan et al. Geometry (ed. 2) v. 336 Inversion in a circle is a one-one transformation of the plane minus the centre of inversion onto itself.

单词	circular or spherical inversion
释义	> as lemmas circular or spherical inversion 23. Geometry. Any of several methods for transforming a geometric figure in a manner regarded as analogous to turning (a section of) it inside out; spec. (in later use) that in which each point within a circle, sphere, or hypersphere of a given radius is substituted for a point lying a certain distance along a line passing through both the centre and the original point (more fully circular or spherical inversion).The centre of the circle, sphere, or hypersphere determining the inversion is called the origin or centre of inversion.Early methods of inversion include quadric inversion, in which a conic section is employed in the role more usually occupied by a circle, sphere, or hypersphere, and tangential inversion, in which the form of the inversion is determined by the translation of the figure's tangents, rather than its points. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > replacing quantities conversion1570 composition1660 substitution1694 inversion1843 reciprocation1852 1843 London, Edinb., & Dublin Philos. Mag. 23 339 From the theorem of the three perpendiculars from the angles of a triangle on the opposite sides meeting in a point, we get by inversion the three polar circles perpendicular to the opposite sides of the polar triangle. 1858 London, Edinb., & Dublin Philos. Mag. 4th Ser. 16 166 They are at the same time anti-parallel sections of a cone whose vertex is the centre of inversion. 1865 Proc. Royal Soc. 14 91 (heading) On the quadric inversion of plane curves. 1881 Q. Jrnl. Pure & Appl. Math. 17 313 Familiar theorems are now applied to generate by tangential inversion the quadricuspid hypocycloid. 1925 H. F. Baker Princ. Geom. (2010) IV. i. 14 These are the formulae of inversion in the plane ω, in which (ξ, η, ζ) are the coordinates of a point, and (ξ', η', ζ') those of the inverse point. 1949 Q. Appl. Math. 6 387 Another method of handling homogeneous harmonic functions of integral degree n is by differentiation of functions of degree zero, and spherical inversion. 1992 H. Eves Fund. Mod. Elem. Geom. ii. 104 When working with inversion in space, we add to the set S of all points of space a single ideal point at infinity. 2012 D. A. Brannan et al. Geometry (ed. 2) v. 336 Inversion in a circle is a one-one transformation of the plane minus the centre of inversion onto itself. extracted from inversionn. < as lemmas
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