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[原创]求锥体的定义 锥体！力求准确
[这个贴子最后由luyuanhong在 2010/07/23 00:55pm 第 6 次编辑]
WorldLingo 中的解释及其中文翻译
http://www.worldlingo.com/ma/enwiki/en/Cone_%28geometry%29/1
Cone (geometry) 锥体（几何中的）
A cone is a three-dimensional geometric shape that tapers smoothly from a flat, round base
to a point called the apex or vertex. More precisely, it is the solid figure bounded by a
plane base and the surface (called the lateral surface) formed by the locus of all straight
line segments joining the apex to the perimeter of the base. The term "cone" sometimes
refers just to the surface of this solid figure, or just to the lateral surface.
The axis of a cone is the straight line (if any), passing through the apex, about which the
lateral surface has a rotational symmetry.
锥体是一个三维几何体，它从一个平的底面开始，光滑地逐渐缩小，直到成为一点，这个点称为它的顶点。
更严格的定义如下：设有一个平面图形，这平面图形称为锥形的底面，另外还有一个点，这点称为锥形的
顶点。作连接顶点与底面边界上各点的线段，这些线段全体的轨迹，形成了一个锥形的侧面。锥体，就是
由底面和上述锥形侧面围成的立体图形。
名词“锥体”，有时也被认为就是上述立体图形的表面，或认为仅仅就是上述立体图形的锥形侧面。
如果有一条通过锥体顶点的直线，锥体的侧面关于它成旋转对称，那么，这条直线就称为锥体的中心轴。
In general, the base may be any shape, and the apex may lie anywhere (though it is often
assumed that the base is bounded and has nonzero area, and that the apex lies outside the
plane of the base). For example, a pyramid is technically a cone with a polygonal base.
In common usage in elementary geometry, however, cones are assumed to be right circular,
where right means that the axis passes through the centre of the base (suitably defined)
at right angles to its plane, and circular means that the base is a circle. Contrasted
with right cones are oblique cones, in which the axis does not pass perpendicularly through
the centre of the base.
锥体的底面，可以是任何形状，锥体的顶点，也可以处在任何位置（虽然通常总是假设：底面是有界的，
底面的面积不等于零，顶点位于底面所在的平面之外）。例如，棱锥就是以多边形为底面的锥体。然而，
在初等几何中，常把锥体定义为就是正圆锥，它的底面，是一个正圆形，它有一个通过底面中心的、与
底面垂直的中心轴。与正圆锥成对比的是斜圆锥，斜圆锥的中心轴不通过底面中心，也不垂直于底面。
Other mathematical meanings 其他的数学意义
In mathematical usage, the word "cone" is used also for an infinite cone, the union of any
set of half-lines that start at a common apex point. This kind of cone does not have a
bounding base, and extends to infinity. A doubly infinite cone, or double cone, is the union
of any set of straight lines that pass through a common apex point, and therefore extends
symmetrically on both sides of the apex.
在数学中，名词“锥体”也用来指一个无限锥体，即从一个公共顶点出发的一些射线组成的集合。这种
锥体，没有一个有界的底面，它一直延伸到无穷远处。无限双锥体，或双锥体，是通过一个公共顶点的
一些直线组成的集合，双锥体的两侧锥体，关于它的顶点成中心对称。
The boundary of an infinite or doubly infinite cone is a conical surface, and the
intersection of a plane with this surface is a conic section. For infinite cones, the word
axis again usually refers to the axis of rotational symmetry (if any). One half of a double
cone is called a nappe.
无限锥体或双无限锥体的边界，是一个锥形面，当锥体是正圆锥时，平面与锥形面的交线，称为圆锥曲线。
如果有一条直线，无限锥体的锥形面，关于它成旋转对称，则称这条直线为无限锥体的中心轴。双锥体的
一半，称为它的一叶。
Depending on the context, "cone" may also mean specifically a convex cone or a projective cone.
有时，根据上下文，“锥体”也会专指凸锥体或射影锥体。
Further terminology 更进一步的名词解释
The perimeter of the base of a cone is called the directrix, and each of the line segments
between the directrix and apex is a generatrix of the lateral surface. (For the connection
between this sense of the term "directrix" and the directrix of a conic section, see
dandelin spheres.)
锥体的底面的边界，称为这个锥体的准线，连接锥体顶点与准线的线段，称为这个锥体的母线。（关于
在这个意义上的“准线”与圆锥曲线的准线之间的关系，参看丹德林球面。）
The base radius of a circular cone is the radius of its base; often this is simply called
the radius of the cone. The aperture of a right circular cone is the maximum angle between
two generatrix lines; if the generatrix makes an angle θ to the axis, the aperture is 2θ.
圆锥的底半径，就是它的底面的圆的半径，通常就简称为这个圆锥的半径。一个正圆锥的两条母线之间
的最大的夹角，称为这个圆锥的顶角，如果母线与中心轴的夹角为 θ ，那么这个圆锥的顶角就是 2θ 。
A cone with its apex cut off by a plane parallel to its base is called a truncated cone or
frustum. An elliptical cone is a cone with an elliptical base.
一个锥体，被一个平行于底面的平面截去带顶点的那一部分后剩下的部分，称为截锥体，或平截头锥台。
底面是椭圆的锥体，称为椭圆锥。 |
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