QED : Abbreviation for quod erat demonstrandum, used to denote the end of a proof.
Quadrangle : A closed broken figure in the plane consisting of 4 line segments.
Quadrangular prism : A prism whose base is a quadrilateral.
Quadrangular pyramid : A pyramid whose base is a quadrilateral.
3rd Quad 4th Quad
Quadratfrie : square free
Quadrantal angles : Any of the angles nπ /2 ( n = 0,1,2,3,4,………)
Quadratic equation : An equation of the form f(x)=0 where f(x) is a second degree polynomial. That is, ax2+bx+c=0.
Quadratic Expression : A function of the form f(x) = ax2+bx+c, where a ≠ 0.
Quadratic Function : a function f(x) whose value at any value of x is given by the polynomial f(x) = ax2+bx+c. the graph of a Quadratic Function is Parabola.
Quadratic inequality : An inequality in which one side is a quadratic polynomial and the other side is zero. E.g. ax2+bx+c > 0
Quadrature : 1. The quadrature of a geometric figure is the determination of its area. 2. Quadrature means solving an integral analytically or numerically.
Quadric curve : The graph of a second degree equation in two variables.
Quadric surface : The graph of a second degree equation in three variables.
Quadrilateral : A geometric figure with four sides.
Quadrinomial : An algebraic expression consisting of 4 terms.
Quarter : indicates : one fourth = ¼ , One of the phases of moon, one fourth of a year.
Quartic : it means fourth order. A quartic number is a number which equates the fourth power of an integer. A quartic function equated to zero results in quartic equation, that is , ax4 + bx3 + cx2 + dx + e = 0 ( a ≠ 0)
Quartic polynomial : A polynomial of degree 4.
Quartic Symmetry : Symmetry in a plane figure having four axes of symmetry.
Quartile : The first quartile of a sequence of numbers is the number such that one quarter of the numbers in the sequence are less than this number.
Quintic polynomial : A polynomial of degree 5.
Quinary : Quinary is a numeral system with five as the base. In this system, five numerals from 0 to 4, are used .
Quintal : A unit for weighing mass equals to 100 kg.
Quintic Equation : An algebraic equation of 5th degree of the form , ax5 + bx4 + cx3 + dx2 + ex + f = 0 ( a ≠ 0)
Quintic function : A fifth order expression of the form (ax5 + bx4 + cx3 + dx2 + ex +f )(a≠0)
Quotient field : The set of rational numbers is afield and as any rational number is in the form a/b, where ‘a’ and ‘b’ are integers and b ≠ 0, the field of rational numbers is called quotient field.
Quotient : The number obtained by dividing one number into another. In the division sentence: 88 divided by 11 = 8, the quotient is 8
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 |an+1 / an | = 1 for the series .
n- α
Raabe’s test states that if Lim |an+1 / an | = 1
and if a positive number c exists such that
n- α
Lim[ |an+1 / an | - 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
57.3o.
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 3rd
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 + bxn-1 + cxn-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.
T
Tan :
Abbreviation of tangent.
Tangent
A line
that meets a smooth curve at a single point and does not cut across the curve.
ii) In Trigonometry, the tangent is function defined as tan x = sinx / cosx. In
a right angle triangle, the tangent of an angle θ is the ratio of the length of the sides opposite and adjacent
to the angle. Tan θ = Perpendicular / Base. Value of Tan
varies from 0 to infinity for the angles
from zero to 900
Tangent Line : The tangent line is represented a the limit of secant
line.
Tangent Plane : A Tangent plane is a plane that touches a surface defined
in 3dimensional coordinate system at a given point p. The normal vector of the
tangent plane is perpendicular to the surface at the point p. the surface
should be smooth near the surface at the
point p. the tangent plane contains all the lines tangent to a specific point
on a surface.
Tanh : Hyperbolic of tan.
Tautology : A statement
of proportional logic which can be inferred from any proposition whatsoever that is true because of its logical structure.
Taylor’s Series : According to Taylor’s series or theorem, a
polynomial f(x) can be expanded as
given below around a point ‘a’ valid for an integer n .
F(x) = f(a) + f’(a) 9 x –a) + f”(a) (x – a)2
/ 2! + f”’(a) (x – a)3 / 3! + ………+ fn(a) (x – a)n
/ n! + ……..
When a
= 0 , the series is called Maclaurin series .
Tensor : A set of quantities that obey certain
transformation laws relating the bases in one generalized coordinate system to
those of another and involving partial derivative sums . vectors are simple
tensors.
Tera : Symbol T. A prefix having meaning 1012.
Term : A mathematical expression of the form rxn,
pxnyr, where n,p,r are numbers and x and y are variable.
Terminating :To come to an end. E.g., 8.5 is a terminating
decimal, while 1.733333.. is non terminating decimal.
Terminating
continued fraction : A continuous fraction having finite
number of terms.
Terminating
decimal : A decimal that terminates is a
terminating decimal. All Terminating decimal are Rational numbers but not all rational numbers are terminating decimal
expression .
Ternary number system : A number system whose base is 3.
Terrestrial triangle : The Terrestrial triangle is formed on the earth
by the great circles connecting the pole and two palces on the earth.
Tessellation
: A Tessellation is a repeated
geometric design that covers a plane without gaps or overlaps.
Tetrahedron
: A polyhedron with four faces.
Tetromino
: A four-square polyomino.
THEOREM : A Theorem is a
statement which is stated in natural language and can be proved on the basis
explicitly states or precisely known confusions.
Theorem
of Parallel axis : The moment of inertia of any object about an axis through its
centre of mass is the minimum moment of inertia for an axis in that direction
in space. The moment of inertia about any axis parallel to the axis is given by
Ipa = Icm + Md2
Where Ipa
is moment of inertia of the body
about an axis passing through centre of mass, M is the body of mass and d is
the distance between the two axes.
Theoretical Probability : The
chances of events happening as determined by calculating results that would
occur under ideal circumstances.
Theory of Equations :
Theory of equations includes the study of equations, polynomials , algebraic expressions,
algebraic equations, separation of roots, approximation of roots and the
application of matrices and determinants for solving the equations etc.
Theory of Games : The
study of ways in which strategic interactions among rational players produce
outcomes with respect of the preferences of the players, none of which might
have been introduced by any one of them.
Theory of Indices :
Theory of indices describes the laws for multiplication and division of quantities
having same base as given below.
1.am an = am + n 2.
am /an = am - n 3.
(am )n = am n 4. (ab)n = an b n
5. (a/b)n
= an /b n
6. a0 =1 7. a-m =1/am 8.
am/n = nth root of am
Theory of Probability : A
theory of Probability is a way of understanding probability statements. A theory
of probability connects the mathematics of probability, which is the set of
consequences of axioms of probability, with real world of observation and experimentation.
Therm : A unit of energy
equal to 105.
Time series : Times
series analysis accounts for the fact that data points taken over time may have
an internal structure ( such as autocorrelation, correlation, trend or seasonal
variation ) that should be accounted for the value of the variable is generated
successively in time. A continuous graph trace is an example of continuous time
series.
Ton : 1. Long Ton – unit of weight
used in U.K., equal to 2240 lbs or 1016 kg. (2) short Ton ; unit of weight used in U.S.A., equal to 2000
pounds or 907.18 kg. (3) Metric Ton :
usually referred to as tone equal to 1000 kg.
Topological space : A
set with topology defined upon it is called a topological space .
Topology : Generally Topology is the study of those
proportions of space which are invariant under continuous deformations, that is
, deformations which do not create’tears’ or ‘holes’. More specifically, given
set X , a Topology on X is a collection of subsets of X, such that the empty
set and X itself are included in the collection, and such that the collection
is closed under the formation of finite intersection and arbitrary unions.
Torque : Symbol T, Torque
about an axis is the product of force and the distance of its line of action
from the axis
Toeplitz
matrix : A matrix in which all the elements are the same along any
diagonal that slopes from northwest to southeast.
Torus :
A geometric solid in the shape of a donut.; A surface of
revolution generated by revolution of a circle in three dimensional spaces
about an axis passing through its centre and perpendicular to the plane of the
circle and it do or not touch the circle .
Total Derivative : The
rate of change of a function of two or more variables with respect to a
paprameter on which these variables depend.
If Z =
f(x,y,t), x= θ(t) and y = Ø(t),
the total derivative of z with respect to t.
Total Differential : In
analogy with the differential of a function of one variable, the total
differential of a function Z = f( x,y) of more than one variable is
Dz = 
dx + dy
dx + dy
Totally ordered Set : A
set with total order defined on it. An order relation on a set S is a total
order exactly if, for any two elements x and y of S, either x< y , x = y or
y< x , but no two of the three.
Trace :
The trace of a matrix is the sum of the terms along the
principal diagonal.
Transcendental
Function : A function that cannot be expressed as
algebraic function. E.g. , In x, sinx, ex etc., and any function
containing them are Transcendental functions.
Transcendental
number : A real
or complex number that is not algebraic.
Transform of Element of Group : The
transform of an element ‘K’ by an element ‘X’ is X-1 is X-1
KX.
Transform of Matrix : A
matrix B related to a given matrix A by the expression B = Q-1 AQ, Q
being a non-singular matrix. Eigen values remain same.
Transformation : The
changing of an algebraic expression or equation into an equivalent one with a
different form.
Transformation of Axis : Let
the coordinate of a point be (x,y,z)
in a coordinate system of axes. The axis can be transformed in three ways. One ,
the origin is shifted keeping the axes parallel. Two , the origin is kept as it
is , but the axes are rotated. Third , the origin shifting and rotation of axes
take place simultaneously. The coordinate of the point with respect to new
coordinate axes will be different.
Transformation of Coordinate : A
coordinate transformation is conversion from one system to another, to describe
the same space. E.g. Cartesian coordinates may be converted to spherical
coordinates or vice versa.
Transitive Property : The
property that states that if a=b and b = c , then a =c .
Transitive relation : A
binary relation R over a set X is Transitive if it holds for a,b,c in X, that
is . if a is related to b and b is related to c, then a is related to c . e.g.
a>b, and b>c , then a>c ( > relation
is transitive ).
Transitive Set : A set
is called Transitive if it is equal to
its Transitive closure. That is, X is a Transitive set if whenever y is an
element of X and z is an element of Y, then z is an element of X.
Translation : A function which we obtain if we add the same constant
to each value of the variable of the given function and move the graphs of the
function by a constant distance.
Transpose: To
move a term from one side of an equation to another side , with change of sign.
Transpose of Matrix : The Transpose
of a matrix A is obtained by interchanging its rows and columns. It is usually
denoted by AT, if A is the original matrix.
Transversal : A line
that intersects two or more other lines in the same plane.
Trapezium
: A quadrilateral in which no sides are parallel.
Trapezoid
: A quadrilateral in which two sides are parallel.
Tree : A tree
is a graph with the property that there is a unique path from any vertex to any
other vertex traveling along the edges.
Triangle
: A geometric figure with three sides.
Triangular
number : A number of the form n(n+1)/2.
Triangular
prism : A polyhedron-a prism with two identical, triangular bases.
Trinomial
: An algebraic expression consisting of 3 terms.
Tromino
: A three-square polyomino.
Truncated
pyramid : A section of a pyramid between its base and a plane parallel to
the base.
Twin
primes : Two prime numbers that differ by 2. For example, 11 and 13 are
twin primes.
V : Roman Symbol for 5
Value , Absolute : The absolute value of real no is its numerical value without regard to sign. The absolute value of a number can be considered as the distance between zero and that number.
Value of Expression : An expression consists of a set of operators, functions or keywords and its value is the outcome obtained after performing operations.
Value of Function : Value of function is the outcome obtained after assigning suitable value to the independent variable.
Vanish : A function vanishes when its value becomes zero.
Variable : A quantity usually represented by x that can take different values. An integer variable can have only integral values whereas a real variable can have only fractional value also. In y = f(x) , x is independent variable and y is dependent variable.
Variance : In Statistics, variance is a measure of variability; the mean square deviation from the mean, that is , the mean of the squares of the differences between individual values of x and the mean value . The variance in a population is given by
Variate : A random variable with a numerical value that is defined on a given sample space.
Variation : Deviation of a variable from the mean value.
Variation of Function : In an interval [a,b] , the variation of function takes place as the value of independent variable changes. For a function of constant value, there will not be any change in the value of the function.
Variable : A symbol whose value can change.
Vector : Any quantity which has both magnitude and direction at each point in space , as opposed to a scalar which has only magnitude. We represent a vector geometrically by an arrow of length proportional to its magnitude , pointing in the assigned direction. Any vectors can be represented in terms of its components along the coordinate axes XS, Y, and Z. a vector drawn from the origin to a given point is called position vector and is usually symbolized by r in rectangular Cartesian coordinates as r = xi + yj + zk.
Vector, Parallelogram of : A Parallelogram that is constructed in order to add two vectors, by drawing them to scale so that they form two adjacent sides of the parallelogram.
Vector analysis : A branch of Mathematics dealing with vectors, their relations and applications.
Velocity : The rate of change of position. Velocity is a vector quantity.
Velocity = displacement / time
Velocity of Light : Usually denoted by c . its value is 3 x 1010 m/s.
Venn Diagram : The Venn diagram is made up of two or more overlapping circles and it is used to show relationship between sets. Different sets are shown as circles in a big rectangle represent ting the universal set. Intersecting circles denote intersecting sets. Separate circles show disjoint set.
Vertex, Vertices : 1. A corner of a polygon. 2. A node in a graph. 3. A local extreme point of curvature.
Vertical Line : A line which points to or away from the centre of the earth. A vertical line is perpendicular to a horizontal line.
Vertex : Point where surfaces meet-corner.
Vertical Opposite angles : The angles that are formed when two lines intersect each other and angles opposite to each other are equal as shown below; A= B
B
Vigesimal : related to intervals of 20.
Vitali Set : A set of real numbers such that no two real numbers of the set have a difference which is rational number and each real number is equal to a rational number plus a number of the set.
Vinculum : The horizontal bar in a fraction separating the numerator from the denominator.
Volume : The measure of space occupied by a solid body.
Vulgar fraction : A common fraction.
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