R

R

Raabe’s Theorem :  This is extension of the ratio test for testing convergence of a series. The ratio test is inconclusive when the

Lim |a_n+1 / a_n | = 1 for the series .

n- α

Raabe’s test states that if  Lim |a_n+1 / a_n | = 1 and if a positive number c exists such that

                                n- α

Lim[ |a_n+1 / a_n | - 1 ] = -1- c, then the series will be absolutely convergent.

n- α

Radian

A unit of angular measurement such that there are 2 pi radians in a complete circle. One radian = 180/pi degrees. One radian is approximately 57.3^o.

Radical axis : The radical axis of two circles is the  locus of points of equal power with respect to both circles.

Radical center : The radical center of three circles is the common point of intersection of the radical axes of each pair of circles.

Radical Expression : An expression in which radical sign appears and radicand is a number or expression inside the radical symbol.  represents the 3^rd root .

Radical Plane : A radical Plane is the locus of the points which have equal powers with respect to two spheres S and S’. the radical plane of two given spheres is always perpendicular to the line joining the centres of the two spheres .

Radicand : Radicand is a number or expression inside the radical symbol.

Radii : Plural of radius.

Radius : The length of a straight line drawn from the center of a circle to a point on its circumference. In case of sphere , it is the distance between the centre and the surface.

Radius of Curvature : Radius of curvature of acurve at a point is the radius of the osculating circle at that point. It is also reciprocal of curvature.

Radius Vector : A vector representing the position of an object in space with respect to an arbitrary inertial frame of reference.

Radix  point : The generalization of decimal point to bases of numeration other than base 10.

Random : Having no specific pattern, purpose or objective

Random Sampling : A sampling procedure assuring that each element in the population has an equal chance of being selected.

Random Variable : A random Variable is a function that that associates a unique numerical value with every outcome of an experiment. A random Variable has either an associated probability distribution or probability density function.

Range : The set of values taken on by a function. ; The difference of the largest and the smallest value in a data collection process in a statistical experiment.

Rank : The rank of set is defined inductively as the smallest ordinal number greater than the rank of any member of the set, where the rank of empty set is zero.

Rate : A way of comparing two quantities.

Ratio : Quotient of two numbers. ; The ratio of two quantities p and q  is p/q. this is called p to q ratio.

Ratio of Simplitude : The ratio of the lengths of corresponding sides of similar figures .

Rational Expression : The quotient of two polynomials is called a rational expression. Rational expression are to polynomials what rational number are to integers.

Rational Function : A rational function is basically a division of two polynomial functions, that is , it is a polynomial divided by another polynomial. In formal notation, a rational function would be f(x)  = p(x) / q(x) , where  p(x)  and q(x)  are polynomial functions and q(x) not equal to zero .

Rational number : A rational number is a number that is the ratio of two integers. All other real numbers are said to be irrational.

Real Axis : An Axis on which only real numbers can be represented. ; The x-axis of an Argand diagram.

Real Valued Functions : A function whose range is in the real numbers is said to be real valued function.  

Real Variable :  A variable which can take only real values in the form of real numbers.

Ream : A ream is 500 sheets of paper.

Reciprocal : The reciprocal of a quantity is equal to 1 divided by the quantity itself.

Rectangle : A rectangle is a quadrilateral with 90⁰ angles and its opposite sides are equal and parallel. The larger side is called length and smaller side is called width. Area  of rectangle is length multiply width.

Rectangular coordinates : The rectangular coordinate system is based on a grid, and every point on the plane can be identified by unique x and y coordinates. Coordinates axes are perpendicular and , hence, the coordinates on them are called rectangular coordinates. These are also called Cartesian coordinates.

Rectangular form of Complex numbers : A complex number represented in the form  ( x + iy ).

Rectangular Hyperbola :  see Hyperbola section of www.mathsdictionary.in

Rectangular Parallelepiped : A Parallelepiped with bases as rectangles, all perpendicular to its lateral faces, also known as cuboids.

Rectification :  Rectification means determining the length of an arc of a curve.

Rectilinear figure : Rectilinear figures are those which are contained by straight lines.

Recurring Decimal ; A repeating decimal e.g. 1.3333333333….

Reduction form : The reduced form of the equation

axⁿ + bx^n-1 + cx^n-2 ……. = 0 is

Xⁿ + b/a x ^n-1  + c/a x ^n-2 ………  = 0

Reduction formula in Integration : see integration section of www.mathsdictionary.in

Reduction formula in Trigonometry : see Trigonometry section of www.mathsdictionary.in

Reflection : A map that transforms an object into its mirror image.

Reflex Angle : An angle greater than 180⁰ but less than 360⁰.

Reflexive property : X= X for all X. every number equals itself.

Region : Domain, an open connected set, ; The union of such set and some or all of its boundary points.

Regression Lines : if the data is given in pairs, then the scatter diagram of the data is just the points plotted on x-y plane. The scatter plot is used to identify relationship between the first and the second entries of paired data. If points follow a linear, we can represent them by a line, called regression line.

Regular polygon : A polygon which is equiangular and equilateral .

Regular Polyhedron : A polyhedron whose faces are regular polygons all alike and is assembled in the same way around each vertex.

Relation : A property that associates two quantities in a definite order, as equality or inequality.

Relative error : There are two types of errors, that is , absolute error and relative error. Absolute error is the amount of physical error in a measurement. Relative error gives an indication of how good a measurement is relative to the size of the same thing being measured. It is ratio of error to the mean of measurement. On being multiplied by 100, we get % error.

Relative Error  = Absolute Error / Value of thing being measured

Relaxation Method : A method of solving simultaneous equations by guessing a solution and then reducing the errors that result by successive approximation until the error is less than some predefined value.

Remainder : if ‘a’ and ‘b’ are integers, with b not equal zero , then remainder is an integer r such that a = bq + r for some integer q , and with 0  

Remainder theorem : Let there be a polynomial p(x) , where “p(x)” just means that the variable in the polynomial in x. according to this theorem , if p(a) = 0, then ( x- a) is factor of the polynomial p(x) .

Repeated Root : If a polynomial f(x) is divisible by (x –a)ⁿ, then the equation f(x) = 0 supposed to have n times repeated root at x =a.

Repeating decimal : same as recurring decimal

Representative fraction :  The representative fraction is a simple ratio that informs the reader how many units of length on the actual ground surface are represented by, or contained within, the same unit of length on the map.

Residue Class : The residue classes of a function mode n are all possible values of the residue f(x) (mod n).

Residue Theorem :  It is a strong tool in complex analysis to evaluate line integrals of analytic functions over closed curves. It is also used to evaluate real integrals. It generalizes the Cauchy Integral Theorem.  For evaluating real integrals , integrand is extended to the complex  plane. A part of the real axis is extended to a closed curve by attaching a half circle in the upper or lower half plane.  We can evaluate the integral over the curve by using residue theorem.

Real part : The real number x is called the real part of the complex number  x+iy where x and y are real and i=sqrt(-1).

Real variable : A variable whose value ranges over the real numbers.

Reflective symmetry : Line symmetry means reflection. If we were to draw a line through a shape to represent a mirror, the shape could be folded along that line and both sides would both fit exactly together.

Repdigit  : An integer all of whose digits are the same.

Repeating decimal : A decimal whose digits eventually repeat.

Repunit  : An integer consisting only of 1's.

 Rhombus  : A parallelogram with four equal sides.

 Right angle : an angle formed by two perpendicular lines; a 90o angle.

Right triangle :  A triangle that contains a right angle.

Roman numerals : A system of numeration used by the ancient Romans.

Root of unity :  A solution of the equation xⁿ=1, where n is a positive integer.

Round-off error  : The error accumulated during a calculation due to rounding intermediate results.

Rounding  :  The process of approximating a number to a nearby one.

Ruled surface  : A surface formed by moving a straight line (called the generator).

Rusty compass : A pair of compasses that are fixed open in a given position.