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双语句库分类列表：
数学:
Because a straight line can be thought of as an arc of a circle of infinite radius, its curvature is zero.
直线可视为半径无穷大的圆，曲率为0
属类：自然科学-数学-
In mathematics, an abstract term used to describe the path of a continuously moving point. Such a path is usually generated by an equation. The word can also apply to a straight line or to a series of line segments linked end to end.
数学术语，指按一定路径陆续移动的点的轨迹，通常以方程式表示。这个词也适用于直线或一连串互相连接的线段。
属类：自然科学-数学-
A closed curve is a path that repeats itself, and thus encloses one or more regions. Simple examples include circles, ellipses, and polygons. Open curves such as parabolas, hyperbolas, and spirals have infinite length
封闭曲线的路径是循环的，包围一个或更多区域，简单的例子如圆、椭圆、多边形。拋物线、双曲线、螺线属于开放曲线，其长度无限
属类：自然科学-数学-
Closed curve, one of the conic sections of analytic geometry, consisting of all points whose distances from each of two fixed points (foci)add up to the same value.
解析几何中圆锥截线的一条封闭曲线，包含了与两个定点(焦点)之距离总和相等的所有点。
属类：自然科学-数学-
The midpoint between the foci is the center. One property of an ellipse is that the reflection off its boundary of a line from one focus will pass through the other.
焦点之间的中点为中心。椭圆的一个特性是:连自一个焦点的直线边界反折会通过另一个焦点。
属类：自然科学-数学-
Closed curve, one of the conic sections of analytic geometry, consisting of all points whose distances from each of two fixed points (foci)add up to the same value.
解析几何中圆锥截线的一条封闭曲线，包含了与两个定点(焦点)之距离呈等值增加的所有点。
属类：自然科学-数学-
In an elliptical room, a person whispering at one focus is easily heard by someone at the other. An oval may or may not fit the definition of an ellipse
在椭圆形房间中，人在一个焦点轻声说话时能轻易被在另一焦点的人听到。卵形可能适合或不适合椭圆的定义
属类：自然科学-数学-
In applied mathematics, the difference between a value and an estimate of that value.
应用数学中真值与其估计值或近似值间之差异
属类：自然科学-数学-
In statistics, a common example is the difference between the mean age of a given group of people and that of a sample drawn from the group.
在统计中一个常见的例子即为人口平均值与人口取样之平均值间的差异
属类：自然科学-数学-
In numerical analysis, an example of round-off error is the difference between the true value of pi and commonly substituted expressions like 22/7 and shorter versions like 3.14159.
在数值分析中舍略误差之一例证即为无理值π(pi)与其近似有理化值22/7或3.14159间之差异。
属类：自然科学-数学-
Truncation error results from using only the first few terms of an infinite series. Relative error is the ratio of the size of an error to the size of the quantity measured, and percentage error is relative error expressed as a percent.
舍弃误差则因在无穷级数中仅计算及有限项数而造成。相对误差即为前述数值差除以真值之数。百分率误差即再将之化为百分数
属类：自然科学-数学-
Study of points, lines, angles, surfaces, and solids based on Euclid’s axioms. Its importance lies less in its results than in the systematic method Euclid used to develop and present them.
以欧几里德的公理为基础对点、线、角、面和立体的研究。其重要性不在结果，而在欧几里德用来发展及呈现的系统性方法。
属类：自然科学-数学-
This axiomatic method has been the model for many systems of rational thought, even outside mathematics, for over 2,000 years. From 10 axioms and postulates, Euclid deduced 465 theorems, or propositions, concerning aspects of plane and solid geometric figures.
这种公理方法是2,000多年来许多理性思想体系(甚至体系外之数学)的模范。欧几里德从10个公理和假设中演绎出465个公理或命题，涉及了平面与立体几何图形各方面。
属类：自然科学-数学-
This work was long held to constitute an accurate description of the physical world and to provide a sufficient basis for understanding it. During the 19th century, rejection of some of Euclid’s postulates resulted in two non-Euclidean geometries that proved just as valid and consistent
这项研究工作曾长期进行，以精确地描述实体世界，并为了解几何提供了充足条件的基础。19世纪期间，一些欧几里德假设受到摈弃，因而产生了两个非欧几里德几何，并证实同样有效而连贯。
属类：自然科学-数学-
In mathematics, a function in which a constant base is raised to a variable power.
数学中的一种函数，其中的常数基被提升到变量幂。
属类：自然科学-数学-
Exponential functions are used to model changes in population size, in the spread of diseases, and in the growth of investments. They can also accurately predict types of decline typified by radioactive decay.
指数函数被用来模仿人口的变化、疾病的扩散、投资的成长。它们也能精确地预测辐射衰变特有的衰变类型。
属类：自然科学-数学-
The essence of exponential growth, and a characteristic of all exponential growth functions, is that they double in size over regular intervals. The most important exponential function is ex, the inverse of the natural logarithmic function.
指数成长的基本元素和所有指数成长函数的特征是它们会在一定间隔倍增。最重要的指数函数是ex，即自然对数函数的反数
属类：自然科学-数学-
" For any whole number, the product of all the counting numbers up to and including itself. It is indicated with an exclamation point: 4! (read "four factorial")is 1 × 2 × 3 ×4 = 24. "
数学名词。指所有小于或等于某一给定的正整数的乘积，并用该数和一个惊叹号来表示。如4!(读作4的阶乘)是1×2×3×4=24。
属类：自然科学-数学-
Factorials are particularly useful in calculating the number of ways an event can occur, for example, the number of possible orders of finish in a race
阶乘在计算某项事件中可能发生的方式数目时特别有用，如比赛中决赛的可能序列
属类：自然科学-数学-
In logic, a formal language together with a deductive apparatus by which some well-formed formulas can be derived from others.
在逻辑中，指从一组公理出发，通过推理而产生的词项和内含关系的一种抽象的理论结构。
属类：自然科学-数学-
| 1 | 直线可视为半径无穷大的圆，曲率为0 | Because a straight line can be thought of as an arc of a circle of infinite radius, its curvature is zero. |
|
| 2 | 数学术语，指按一定路径陆续移动的点的轨迹，通常以方程式表示。这个词也适用于直线或一连串互相连接的线段。 | In mathematics, an abstract term used to describe the path of a continuously moving point. Such a path is usually generated by an equation. The word can also apply to a straight line or to a series of line segments linked end to end. |
|
| 3 | 封闭曲线的路径是循环的，包围一个或更多区域，简单的例子如圆、椭圆、多边形。拋物线、双曲线、螺线属于开放曲线，其长度无限 | A closed curve is a path that repeats itself, and thus encloses one or more regions. Simple examples include circles, ellipses, and polygons. Open curves such as parabolas, hyperbolas, and spirals have infinite length |
|
| 4 | 解析几何中圆锥截线的一条封闭曲线，包含了与两个定点(焦点)之距离总和相等的所有点。 | Closed curve, one of the conic sections of analytic geometry, consisting of all points whose distances from each of two fixed points (foci)add up to the same value. |
|
| 5 | 焦点之间的中点为中心。椭圆的一个特性是:连自一个焦点的直线边界反折会通过另一个焦点。 | The midpoint between the foci is the center. One property of an ellipse is that the reflection off its boundary of a line from one focus will pass through the other. |
|
| 6 | 解析几何中圆锥截线的一条封闭曲线，包含了与两个定点(焦点)之距离呈等值增加的所有点。 | Closed curve, one of the conic sections of analytic geometry, consisting of all points whose distances from each of two fixed points (foci)add up to the same value. |
|
| 7 | 在椭圆形房间中，人在一个焦点轻声说话时能轻易被在另一焦点的人听到。卵形可能适合或不适合椭圆的定义 | In an elliptical room, a person whispering at one focus is easily heard by someone at the other. An oval may or may not fit the definition of an ellipse |
|
| 8 | 应用数学中真值与其估计值或近似值间之差异 | In applied mathematics, the difference between a value and an estimate of that value. |
|
| 9 | 在统计中一个常见的例子即为人口平均值与人口取样之平均值间的差异 | In statistics, a common example is the difference between the mean age of a given group of people and that of a sample drawn from the group. |
|
| 10 | 在数值分析中舍略误差之一例证即为无理值π(pi)与其近似有理化值22/7或3.14159间之差异。 | In numerical analysis, an example of round-off error is the difference between the true value of pi and commonly substituted expressions like 22/7 and shorter versions like 3.14159. |
|
| 11 | 舍弃误差则因在无穷级数中仅计算及有限项数而造成。相对误差即为前述数值差除以真值之数。百分率误差即再将之化为百分数 | Truncation error results from using only the first few terms of an infinite series. Relative error is the ratio of the size of an error to the size of the quantity measured, and percentage error is relative error expressed as a percent. |
|
| 12 | 以欧几里德的公理为基础对点、线、角、面和立体的研究。其重要性不在结果，而在欧几里德用来发展及呈现的系统性方法。 | Study of points, lines, angles, surfaces, and solids based on Euclid’s axioms. Its importance lies less in its results than in the systematic method Euclid used to develop and present them. |
|
| 13 | 这种公理方法是2,000多年来许多理性思想体系(甚至体系外之数学)的模范。欧几里德从10个公理和假设中演绎出465个公理或命题，涉及了平面与立体几何图形各方面。 | This axiomatic method has been the model for many systems of rational thought, even outside mathematics, for over 2,000 years. From 10 axioms and postulates, Euclid deduced 465 theorems, or propositions, concerning aspects of plane and solid geometric figures. |
|
| 14 | 这项研究工作曾长期进行，以精确地描述实体世界，并为了解几何提供了充足条件的基础。19世纪期间，一些欧几里德假设受到摈弃，因而产生了两个非欧几里德几何，并证实同样有效而连贯。 | This work was long held to constitute an accurate description of the physical world and to provide a sufficient basis for understanding it. During the 19th century, rejection of some of Euclid’s postulates resulted in two non-Euclidean geometries that proved just as valid and consistent |
|
| 15 | 数学中的一种函数，其中的常数基被提升到变量幂。 | In mathematics, a function in which a constant base is raised to a variable power. |
|
| 16 | 指数函数被用来模仿人口的变化、疾病的扩散、投资的成长。它们也能精确地预测辐射衰变特有的衰变类型。 | Exponential functions are used to model changes in population size, in the spread of diseases, and in the growth of investments. They can also accurately predict types of decline typified by radioactive decay. |
|
| 17 | 指数成长的基本元素和所有指数成长函数的特征是它们会在一定间隔倍增。最重要的指数函数是ex，即自然对数函数的反数 | The essence of exponential growth, and a characteristic of all exponential growth functions, is that they double in size over regular intervals. The most important exponential function is ex, the inverse of the natural logarithmic function. |
|
| 18 | 数学名词。指所有小于或等于某一给定的正整数的乘积，并用该数和一个惊叹号来表示。如4!(读作4的阶乘)是1×2×3×4=24。 | " For any whole number, the product of all the counting numbers up to and including itself. It is indicated with an exclamation point: 4! (read "four factorial")is 1 × 2 × 3 ×4 = 24. " |
|
| 19 | 阶乘在计算某项事件中可能发生的方式数目时特别有用，如比赛中决赛的可能序列 | Factorials are particularly useful in calculating the number of ways an event can occur, for example, the number of possible orders of finish in a race |
|
| 20 | 在逻辑中，指从一组公理出发，通过推理而产生的词项和内含关系的一种抽象的理论结构。 | In logic, a formal language together with a deductive apparatus by which some well-formed formulas can be derived from others. |
|
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