数学专业英语答案之2.2 几何与三角

2.2 几何与三角

词组翻译

1.学会institution，建筑师 architect, 机械师 machinist, 制图员draftsman, 测量者surveyor, 木匠carpenter

2.点point, 端点endpoint, 线line, 直线straight line, 线段 line segment, 曲线curved line, 折线 broken line, 射线ray , 平面 plane,曲面 curved surface

3.立体solid, 柱体cylinder, 立方体cube,球 sphere, 棱锥pyramid,圆锥 cone ,

4.圆circle,圆心 center, 直径diameter, 半径radius, 半圆semicircle, 弦chord, 弧arc, 优弧major arc, 劣弧minor arc

5.角angle, 边side, 三角形triangle, 直角三角形right triangle,斜边 hypotenuse, 直角边right-angle side

6.长度length,宽度 breadth/width,厚度 thickness, 位置position

7.几何的geometrical,立体的 three-dimensional , 弯曲的curved,等距离的equidistant ,无限的 infinite

8.培养创造力train originality,必须的毅力 necessary perseverance , 提高鉴赏力raise/improve the appreciation ability

9.消失了的边界vanishing boundaries/landmarks,有序性和优美感 orderliness and sense of beauty, 几何图形大量存在geometric forms abound in , 定理成立的先决条件a prerequisite to a theorem 汉译英

1.许多专家都认为数学是学习其他科学技术的必备基础和先决条件。

Many experts say that mathematics is a base and prerequisite to learning other science and technology.

2.西方国家的专家认为几何起源于巴比伦和埃及人的土地测量技术，其实中国古

代的数学家对几何做了许多出色的研究。

Experts of western countries think that geometry had its origin long ago in the measurements by the Babylonians and Egyptians of their lands. In fact, China’s ancient mathematicians made lots of excellent studies to geometry.

3.几何的学习使学生在思考问题时更周密和审慎，他们将不会盲目接受任何结

论。

In studying geometry, students are taught to think clearly and critically, and are led away from the practice of blind acceptance of any conclusions.

4.数学培养学生的分析问题的能力，使他们能应用毅力、创造性和逻辑推理类解决问题。

Mathematics can cultivate students’ ability to analyze problems, and to utilize perseverance, originality and logical reasoning in solving the problems.

5.几何主要不是研究数，而是形，例如三角形，平行四边形和圆，虽然它也与数有关。

Although geometry is related with number, geometry mainly studies form, not number, such as triangle, parallelogram and circle.

6.一个立体（图形）有长、宽和高；面（曲面或平面）有长和宽，但没有厚度；线（直线或曲线）有长度，但既没有宽度，也没有厚度；点只有位置，却没有大小。

A solid （figure） has length, breadth and thickness. A surface (curved surface or plane surface) has length and breadth, but has no thickness. A line (straight line or curved line) has length, but has neither breadth nor thickness. A point only marks a position, but has no length, no width and no thickness.

7.射线从某个点出发无限延伸；两条从同一点出发的射线构成了角。这两条射线称为这个角的两边，当这两边位于同一直线上且方向相反时，所得的角是平角。

A ray extends infinitely far from a point， and two rays extending from the same point form an angle. These two rays are called two sides of this angle. When these two sides locate in the same straight line and have opposite directions, they form a straight angle.

8.平面上的闭曲线当其中每一点到一个固定点的距离均相等时叫做圆。这个固定点称为圆心，经过圆心且其两个端点在圆周上的线段称为这个圆的直径，直径的一半叫做半径，这条直线的长度叫做周长。

A circle is a closed curve lying in one plane, all points of which are equidistant from a fixed point called the center. A diameter of a circle is a line segment through the center of the circle with endpoints on the circle.A half of a diameter is called a radius. The length of a circle is called the circumference. 英译汉 1.In geometry an angle is defined as the set of points determined by two rays

l 1and l

2

having the same endpoint O. 在几何学里从同一点O出发引出的两条射线l

1

和l

2

所组成的点的集合叫做角。

2.In trigonometry we often interpret angles as rotations of rays.To obtain an angle we

may start with a fixed ray l

1

having endpoint O,and rotate it about O,in a plane,to a

position specified by ray l

2.We call l

1

the initial side, l

2

the terminal side,and O the

vertex of angle. 在三角学里，我们经常解释角就是射线的旋转。在平面上，我们许

会从端点是O的射线l

1开始让它绕着端点O旋转，转到一个位置，由射线l

2

标