**radian 弧度**

A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle, approximately 57°17′44.6″.

**radical 根**

- A root of a number or quantity.
- The set of elements of a ring, some power of which is contained in a given ideal.

**radicand 被开方数**

A number or quantity from which a root is to be extracted, under a radical sign: 3 is the radicand of √3.

**radius 半径**

A straight line extending from the center of a circle or sphere, or regular polygon to the circumference or surface.

**radix 根；基数**

- The base of a system of numbers, such as 2 in the binary system and 10 in the decimal system.
- The base of a system of logarithms.

**random 随机**

Statistics. of or characterizing a process of selection in which each item of a set has an equal probability of being chosen.

**random Sample 随机抽样**

A sample in which every element in the population has an equal chance of being selected.

**range 区间；范围；排列**

- The set of all values attained by a given function throughout its domain.
- The maximum extent or distance limiting operation, action, or effectiveness, as of a sound, radio signal, instrument, firearm, or aircraft.
- To place or arrange systematically; set in order.

**range of a function 函数的值域**

The set of values of the dependent variable for which a function is defined. For example: the image of f(x) = x^{2} is the set of all non-negative real numbers if the domain of the function is the set of all real numbers.

**ratio 比率**

A relationship between two quantities, normally expressed as the quotient of one divided by the other; for example, the ratio of 7 to 4 can be written 7:4 or 7/4. A ratio can often also be expressed as a decimal or percentage.

**rational expression 有理式**

An algebraic expression involving no literal symbol in a radical. Examples are a^{2} + b and x/(y – z^{3}). If the literal symbols in a rational expression are regarded as variables, the expression defines a rational function of these variables.

**rational function 有理方程**

A function that can be written as the quotient of two polynomials with integral coefficients.

**rational number 有理数**

A number that can be expressed exactly by a ratio of two integers. Like the form a/b, where a and b are integers and b is not zero, as 2 or 8/33.

**ray 射线**

A straight line extending from a point.

**real number 实数**

A number that is rational or irrational and not imaginary. The numbers 2, 3/7, √5, and π are all real numbers.

**reciprocal 倒数**

A number related to another in such a way that when multiplied together their product is 1. For example, the reciprocal of 7 is 1/7 ; the reciprocal of 2/3 is 3/2 .

**rectangle 矩形**

A four-sided plane figure with four right angles.

**rectangular coordinate system 平面直角坐标系**

Also named Cartesian coordinate system. A system in which the location of a point is given by coordinates that represent its distances from perpendicular lines that intersect at a point called the origin. A Cartesian coordinate system in a plane has two perpendicular lines: the x-axis and y-axis.

**rectangular prism 长方柱体**

A geometric solid whose six faces are rectangles; rectangular parallelepiped.

**recurring decimal / repeating decimal 循环小数**

A rational number that contains a pattern of digits repeated indefinitely after the decimal point. Also called: circulating decimal or repeating decimal.

**recursive 递归**

A method of defining a sequence of objects, such as an expression, function, or set, where some number of initial objects are given and each successive object is defined in terms of the preceding objects. The Fibonacci sequence is defined by recursion: 1, 1, 2, 3, 5, 8, 13, 21, 34 … … Or given the base clause f(0) = 0, f(n + 1) = f(n) + 3 specifies the successive terms of the sequence f(n) = 3n.

**reduce 缩减; 简化**

- To become smaller in size, number, extent, degree, or intensity, or make something smaller in this way.
- To simplify the form of (an expression, such as a fraction) without changing the value.

**reflection 映像; 反射; 反转**

- An image in a mirror, on a shiny surface, on water, etc.
- The action or process of sending back light, heat, sound, etc. from a surface
- A transformation in which the direction of one axis is reversed or which changes the sign of one of the variables.

**reflection symmetry 轴对称, 反射对称**

Also named line symmetry, mirror symmetry, mirror-image symmetry, is symmetry with respect to reflection.

**reflex angle 优角**

An angle greater than 180° and less than 360°.

**regular polygon 正多边形**

A polygon with all sides and all angles equal.

**regular polyhedron 正多面体**

Whose faces are congruent regular polygons and whose polyhedral angles are all congruent.

**relatively prime 互素，互质**

Two numbers are said to be relativey prime if hey have no common factors other than 1. For example, 16 and 21 are relativly prime. 15 and 21 are not relatively prime, since 3 is a divisor of both.

**remainder 余数; 余式**

- The amount left over when one quantity cannot be exactly divided by another
- Another name for difference, the difference between a function or a number and an approximation to it.

**revolution 公转**

Orbital motion about a point, especially as distinguished from axial rotation: the planetary revolution about the sun.

**rhombus 菱形**

A flat shape with four equal sides and four angles which are not 90˚.

**right angle 直角**

An angle of 90˚.

**right-angled triangle 直角三角形**

A triangle one angle of which is a right angle. US and Canadian name: right triangle.

**rigid 静止**

Not moving or flexing.

**rise 上升**

- To assume a standing position after lying, sitting, or kneeling.
- To increase in size, volume, or level.

**Roman Numerals 罗马数字**

1~9: I, II, III, IV, V, VI, VII, VIII, IX

The common basic symbols are I (=1), V (=5), X (=10), L (=50), C (=100), D (=500), and M (=1000).

One of the numerals in the ancient Roman system of notation, still used for certain limited purposes, as in some pagination, dates on buildings, etc. A bar over a letter multiplies it by 1000; thus, X̅ equals 10,000. Integers are written according to these two rules: If a letter is immediately followed by one of equal or lesser value, the two values are added; thus, XX equals 20, XV equals 15, VI equals 6. If a letter is immediately followed by one of greater value, the first is subtracted from the second; thus, IV equals 4, XL equals 40, CM equals 900. Examples: XLVII(=47), CXVI(=116), MCXX(=1120), MCMXIV(=1914). Roman numerals may be written in lowercase letters, though they appear more commonly in capitals.

**root 根**

- A number that when multiplied by itself an indicated number of times forms a product equal to a specified number. For example, The number 2 is the square root of 4, the cube root of 8, and the fourth root of 16. A fourth root of 4 is √2. Also called nth root.
- A number that reduces a polynomial equation in one variable to an identity when it is substituted for the variable.
- A number at which a polynomial has the value zero.

**rotation 回转**

- The action of an object moving in a circle around a central fixed point or an axis.
- A transformation of a coordinate system in which the new axes have a specified angular displacement from their original position while the origin remains fixed.

**rotational symmetry 旋转对称**

Also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn. An object’s degree of rotational symmetry is the number of distinct orientations in which it looks the same.

**rounding 四舍五入; 舍入**

- The number is first truncated to one or two digits more than is desired; then the last one or two digits are adjusted in a specified way in order to reflect the magnitude of the original number. In rounding the final digits, 0–4 are simply dropped, 6–9 are dropped after the preceding digit is increased by 1, and 5 is handled in various ways depending on the surrounding digits and the particular convention being followed. Such as 2.43 → 2.4, 2.48 → 2.5
- Replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation, or approximating an irrational number by a fraction. Expression √2 with 1.414, π by 22/7.

**row 行**

A series of objects placed next to each other, usually in a straight line.

**ruler 尺子**

A straightedged strip, as of wood or metal, for drawing straight lines and measuring lengths.