N
n-dimensions
n-dimensions is the property of space that indicates that n mutually perpendicular directions for movement of any particle in that space is possible.
Natural Domain
It is an alternative term for domain. It is the range within which the function exists or has definite values. The term natural domain is used to signify that the domain is not restricted.
Natural Logarithm
When the logarithm of a number is taken with respect to the base e, then the logarithm is said to be natural logarithm. The natural logarithm is represented as ln a, where a is the number.
Natural Numbers
All integers greater than 0 are called natural numbers.
Negative Direction
The negatively associated data is often described in the form of a scatterplot. This way of describing natural numbers is known as negative direction.
Negative Exponent
A negative exponent is used to describe the reciprocal of the number. For example, 5-2=1/52
Negative Number
Any real number less than 0 is called a negative number.
Negative Reciprocal
The process of taking the reciprocal of a number and then its negative is called the negative reciprocal. For example the negative reciprocal of ¼ is -4.
Negatively Associated Data
If in a set of paired data, the value of one side increases with the decrease in the other, then the data is referred to as the negatively associated data.
Neighborhood
The neighborhood of any number a is the open interval containing the number. For example, the neighborhood of a can be written as (a + d, a - d).
n – gon
A polygon with n number of sides is called n – gon. For example, a hexagon can also be called 6-gon.
Not Adjacent
Two angles or lines are said to be not adjacent to each other, if they are not near to each other.
Nonagon
A polygon having nine sides is called a nonagon.
Noncollinear
The points that do not lie in a single line are said to be noncollinear points.
Non-Euclidean Geometry
To understand Non-Euclidean geometry we need to understant the parallel postulate. The paraller postulate states that for an given point say P and a line l, not passing through P, there is exactly one line that passes through P, which is parallel to l. The Non-Euclidean Geometry, thus refers to that branch of geometry that does not obey the parallel postulate principle. The hyperobolic geometry and elliptic geometry fall in the class of Non-Euclidean Geometry.
Nonnegative
Any quantity that is not less than zero is refered as nonnegative.
Nonnegative Numbers
The set of integers starting from 0 to infinity in the positive direction of the X-axis is referred to as whole numbers.
Non-overlapping sets
Two sets of numbers which do not have a single element in common are called non-overlapping sets.
Non real number
Any complex number of the form a + bi, where b is not equal to 0 is called a non real number. In other words, any number with an imaginary part is called non real number.
Nonsingular Matrix
Nonsingular matrix is also called Invertible Matrix. Any square matrix whose determinant is not 0 is called a nonsingular matrix.
Nontrivial
The solution of an equation is said to be nontrivial, if the solution does not include zeroes.
Nonzero
Any positive or negative number is a nonzero number.
Normalizing a vector
The process of finding out a unit vector parallel to the given vector and of unit magnitude is called normalization of the vector. The process is carried out by dividing the vector with its magnitude.
n th derivative
The process of taking the derivative of a function n times is called nth derivative. If the derivative of f(x) is taken n times, then its nth derivative will be represented as fn(x).
n th Partial Sum
The sum of the first n terms in an infinite series is called the nth partial sum.
n th Root
The n th root of a number is the number which when multiplied with itself n times gives the number in question. The n th root of 5 can be represented as 51/n.
Null Set Any set with no elements in it is called a null set.
Number Line
A line representing all real numbers is called the number line.
Numerator
The top part of any fraction is called the numerator. In case of integers, the number itself is the numerator, as it is divided by 1.
n-dimensions
n-dimensions is the property of space that indicates that n mutually perpendicular directions for movement of any particle in that space is possible.
Natural Domain
It is an alternative term for domain. It is the range within which the function exists or has definite values. The term natural domain is used to signify that the domain is not restricted.
Natural Logarithm
When the logarithm of a number is taken with respect to the base e, then the logarithm is said to be natural logarithm. The natural logarithm is represented as ln a, where a is the number.
Natural Numbers
All integers greater than 0 are called natural numbers.
Negative Direction
The negatively associated data is often described in the form of a scatterplot. This way of describing natural numbers is known as negative direction.
Negative Exponent
A negative exponent is used to describe the reciprocal of the number. For example, 5-2=1/52
Negative Number
Any real number less than 0 is called a negative number.
Negative Reciprocal
The process of taking the reciprocal of a number and then its negative is called the negative reciprocal. For example the negative reciprocal of ¼ is -4.
Negatively Associated Data
If in a set of paired data, the value of one side increases with the decrease in the other, then the data is referred to as the negatively associated data.
Neighborhood
The neighborhood of any number a is the open interval containing the number. For example, the neighborhood of a can be written as (a + d, a - d).
n – gon
A polygon with n number of sides is called n – gon. For example, a hexagon can also be called 6-gon.
Not Adjacent
Two angles or lines are said to be not adjacent to each other, if they are not near to each other.
Nonagon
A polygon having nine sides is called a nonagon.
Noncollinear
The points that do not lie in a single line are said to be noncollinear points.
Non-Euclidean Geometry
To understand Non-Euclidean geometry we need to understant the parallel postulate. The paraller postulate states that for an given point say P and a line l, not passing through P, there is exactly one line that passes through P, which is parallel to l. The Non-Euclidean Geometry, thus refers to that branch of geometry that does not obey the parallel postulate principle. The hyperobolic geometry and elliptic geometry fall in the class of Non-Euclidean Geometry.
Nonnegative
Any quantity that is not less than zero is refered as nonnegative.
Nonnegative Numbers
The set of integers starting from 0 to infinity in the positive direction of the X-axis is referred to as whole numbers.
Non-overlapping sets
Two sets of numbers which do not have a single element in common are called non-overlapping sets.
Non real number
Any complex number of the form a + bi, where b is not equal to 0 is called a non real number. In other words, any number with an imaginary part is called non real number.
Nonsingular Matrix
Nonsingular matrix is also called Invertible Matrix. Any square matrix whose determinant is not 0 is called a nonsingular matrix.
Nontrivial
The solution of an equation is said to be nontrivial, if the solution does not include zeroes.
Nonzero
Any positive or negative number is a nonzero number.
Normalizing a vector
The process of finding out a unit vector parallel to the given vector and of unit magnitude is called normalization of the vector. The process is carried out by dividing the vector with its magnitude.
n th derivative
The process of taking the derivative of a function n times is called nth derivative. If the derivative of f(x) is taken n times, then its nth derivative will be represented as fn(x).
n th Partial Sum
The sum of the first n terms in an infinite series is called the nth partial sum.
n th Root
The n th root of a number is the number which when multiplied with itself n times gives the number in question. The n th root of 5 can be represented as 51/n.
Null Set Any set with no elements in it is called a null set.
Number Line
A line representing all real numbers is called the number line.
Numerator
The top part of any fraction is called the numerator. In case of integers, the number itself is the numerator, as it is divided by 1.
O
Oblate Spheroid
If we revolve an ellipse about its minor axis then the 3 dimensional sphere obtained will be of the shape called oblate spheroid. Earth is an example of oblate spheroid.
Oblique
A line or a plane that is neither horizontal nor vertical but is tilted at some specific angle is called oblique.
Oblique Cone
An oblique cone is a cone in which the center of the base of the oblique cone is not aligned (not in line) with the center of the apex of the cone.
Oblique Cylinder
If the bases of the cylinder are not aligned just one above the other, it is called the oblique cylinder.
Oblique Prism
A prism whose bases are not aligned directly one above the other is called as oblique prism.
Obtuse Angle
An angle whose measure is more than 90º but less than 180º.
Obtuse Triangle
If one of the angles of a triangle is an obtuse angle then it is called as the obtuse triangle.
Octagon
A polygon with 8 sides is called octagon. It may have equal or unequal sides.
Octahedron
Octahedron is a polyhedron with 8 faces. An octahedron appears like two square based pyramids placed on one another. All the faces of an octahedron are equilateral triangles.
Octants
The eight parts into which the three dimensional space is divided by the co-ordinate axis.
Odd/Even Identities
Trigonometric identities show whether each trigonometric function is an odd or even function.
For example:
sin(-x) = sinx
cos(-x) = cosx
tan(-x) = tanx
csc(-x) = -cscx
sec(-x) = secx
tan(-x) = tanx
cot(-x) = -cotx
Odd Function
If the graph of a function is symmetric about x axis then the function is said to be an odd function. Alternately, an odd function satisfies the condition, f(-x) = -f(x).
Odd Number
The set of integers that are not a multiple of 2. For example, {1, 3, 5, 7, 9, ...)
One Dimension
A dimension of the space where motion can take place in only two directions, either backward or forward.
One-Sided Limit
Taking the limit of a term either from the left hand side or right hand side is called the one-sided limit.
One-to-One Function
A one-one function is type of function in which every element of the range corresponds to at least one element of the domain. A one-to-one function passes both the tests, the horizontal and vertical test.
Open Interval
A set interval excluding the initial and final numbers of the domain. For example in the interval of (2, 5) , 2 and 5 are the excluded from the set of numbers while performing any mathematical operation.
Operations on Functions
The operations on functions are as follows:
Addition: (f +g)(x) = f(x) + g(x)
Subtraction: (f - g) = f(x) – g(x)
Multiplication: (fg)(x) = f(x). g(x)
Division: (f/g)(x) = f(x)/g(x)
Order of a Differential Equation
The power on the highest derivative of a differential equation is called as the order of differential equation.
Ordered Pair
Two numbers written in the form (x,y) are called as the ordered pairs.
Ordinal Numbers
The numerical words that indicate order. The ordinal numbers are first, second, third etc,
Ordinary Differential Equation
A differential equation free of partial derivative terms.
Ordinate
The y coordinate of a point is usually called as the ordinate. For example, if P is a point (5,8) then the ordinate is the 8.
Origin
The reference point of any graph indicated by (0,0) in 2-D and (0,0,0) in 3-D.
Orthocenter
The point of intersection of three altitudes of a triangle is called orthocenter.
Orthogonal
Orthogonal means making an angle of 90º
Outcome
The result of an experiment, like throwing a dice or taking out a pack of cards from a set of cards.
Overdetermined System of Equations
An equation in which there are more equations than the number of variables involved.
Oblate Spheroid
If we revolve an ellipse about its minor axis then the 3 dimensional sphere obtained will be of the shape called oblate spheroid. Earth is an example of oblate spheroid.
Oblique
A line or a plane that is neither horizontal nor vertical but is tilted at some specific angle is called oblique.
Oblique Cone
An oblique cone is a cone in which the center of the base of the oblique cone is not aligned (not in line) with the center of the apex of the cone.
Oblique Cylinder
If the bases of the cylinder are not aligned just one above the other, it is called the oblique cylinder.
Oblique Prism
A prism whose bases are not aligned directly one above the other is called as oblique prism.
Obtuse Angle
An angle whose measure is more than 90º but less than 180º.
Obtuse Triangle
If one of the angles of a triangle is an obtuse angle then it is called as the obtuse triangle.
Octagon
A polygon with 8 sides is called octagon. It may have equal or unequal sides.
Octahedron
Octahedron is a polyhedron with 8 faces. An octahedron appears like two square based pyramids placed on one another. All the faces of an octahedron are equilateral triangles.
Octants
The eight parts into which the three dimensional space is divided by the co-ordinate axis.
Odd/Even Identities
Trigonometric identities show whether each trigonometric function is an odd or even function.
For example:
sin(-x) = sinx
cos(-x) = cosx
tan(-x) = tanx
csc(-x) = -cscx
sec(-x) = secx
tan(-x) = tanx
cot(-x) = -cotx
Odd Function
If the graph of a function is symmetric about x axis then the function is said to be an odd function. Alternately, an odd function satisfies the condition, f(-x) = -f(x).
Odd Number
The set of integers that are not a multiple of 2. For example, {1, 3, 5, 7, 9, ...)
One Dimension
A dimension of the space where motion can take place in only two directions, either backward or forward.
One-Sided Limit
Taking the limit of a term either from the left hand side or right hand side is called the one-sided limit.
One-to-One Function
A one-one function is type of function in which every element of the range corresponds to at least one element of the domain. A one-to-one function passes both the tests, the horizontal and vertical test.
Open Interval
A set interval excluding the initial and final numbers of the domain. For example in the interval of (2, 5) , 2 and 5 are the excluded from the set of numbers while performing any mathematical operation.
Operations on Functions
The operations on functions are as follows:
Addition: (f +g)(x) = f(x) + g(x)
Subtraction: (f - g) = f(x) – g(x)
Multiplication: (fg)(x) = f(x). g(x)
Division: (f/g)(x) = f(x)/g(x)
Order of a Differential Equation
The power on the highest derivative of a differential equation is called as the order of differential equation.
Ordered Pair
Two numbers written in the form (x,y) are called as the ordered pairs.
Ordinal Numbers
The numerical words that indicate order. The ordinal numbers are first, second, third etc,
Ordinary Differential Equation
A differential equation free of partial derivative terms.
Ordinate
The y coordinate of a point is usually called as the ordinate. For example, if P is a point (5,8) then the ordinate is the 8.
Origin
The reference point of any graph indicated by (0,0) in 2-D and (0,0,0) in 3-D.
Orthocenter
The point of intersection of three altitudes of a triangle is called orthocenter.
Orthogonal
Orthogonal means making an angle of 90º
Outcome
The result of an experiment, like throwing a dice or taking out a pack of cards from a set of cards.
Overdetermined System of Equations
An equation in which there are more equations than the number of variables involved.
P
Pi
Pie is defined as the ratio of circumference of a circle to its diameter. It is represented by the Greek letter Π. Many great mathematicians have done pioneering work in researching on the number pi like, Archimedes, Euler, William Jones etc, to name a few.
Pi
Pie is defined as the ratio of circumference of a circle to its diameter. It is represented by the Greek letter Π. Many great mathematicians have done pioneering work in researching on the number pi like, Archimedes, Euler, William Jones etc, to name a few.
Point-Slope Equation of a Line
y – y1 = m (x – x1) is known as the point slope equation of a line, where m is the slope of the line and (x1, y1) represents a point on the line.
For example, equation of a line passing through (3,4) and making an angle of 45 degrees with the positive direction of x-axis is, y – 4 = 1(x – 3), here, (x1, y1) = (3,4) and slope = m = tan 45° = 1.
Polar Axis
The x axis is known as the polar axis.
Polar Conversion Formulas
The rules that are required to change the rectangular coordinates into polar coordinates are known as the polar conversion formulas.
Conversion Formulas
Polar to rectangular- x = rcosθ , y = rsinθ
Rectangular to polar- r2= x2 + y2
Tanθ = y/x
Polar Curves
Spirals, lemniscates and limacones are the curves that have equations in polar form. Such types of curves with equations in the polar form are known as the polar curves.
Polar Integral Formula
Polar integral formula gives the area between the graph of curve r = r(θ ) and origin and also between the rays θ= α and θ= β (where α ≤ β).
Polygon
A closed figure bounded by line segments. The name of the polygon describes the number of sides of a polygon. Triangle, pentagon,hexagon etc are the examples of polygon.
Polygon Interior
All the points enclosed by a polygon is called as the polygon interior.
Polynomial Facts
An expression of the form, p(x) = anxn + an-1xn-1 +.............+ a2 + a1x + a0 is called as the standard polynomial equation. Examples of polynomial equations are 3x + 2y2 = 5 and 5x2+ 3y = 3.
Polynomial Long Division
Polynomial long division is useful method to express a n improper rational expression as the sum of a polynomial and a proper rational expression.
Positive Number
A real number greater than zero is known as a positive number.
Positive Series
A series that consists of only positive terms.
Postulate
A postulate is just like an assumption that is accepted to be true without proof.
Power
The number or variable (called as base) that is raised to the exponent is called as power.
Power Rule
Power rule is a formula that is used to find the derivative of power of a variable.
Power Series
A series that represents a function as a polynomial and whose power goes on increasing with every term. In other it has no highest power of x.
Power series in x is given by:
n=0∑n=∞anxn + a1x+ a2x2 + a3x3 +......
Prime Numbers
A number that has one and the number itself as the factors. For example, 1, 2, 3, 5, 7, 11....
Probability
The likelihood of occurrence of an event is called as probability. It is one of the most researched areas of mathematics. There are some basic rules of probability:
- For any event A, 0≤ P(A) ≤ 1
- P = 1 for a sure event.
- P = 0 for an impossible event
- P (not A) = 1- P(A) or P(Ac) = 1 – P(A)
Proper Fraction
If the numerator of a fraction is less than the denominator then the fraction is said to be proper.
Proper Rational Expression
A rational expression having degree of the numerator less than the degree of denominator.
Pythagorean Theorem
According to Pythagoras theorem, the sum of squares of the two arms or legs of a right angled triangle is equal to the sum of the square of the hypotenuse. If AB, BC and AC are the threes side of a right angled triangle taken in same order then AC2 = AB2 + BC2 .
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If the numerator of a fraction is less than the denominator then the fraction is said to be proper.
Proper Rational Expression
A rational expression having degree of the numerator less than the degree of denominator.
Pythagorean Theorem
According to Pythagoras theorem, the sum of squares of the two arms or legs of a right angled triangle is equal to the sum of the square of the hypotenuse. If AB, BC and AC are the threes side of a right angled triangle taken in same order then AC2 = AB2 + BC2 .
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Q
Q1
Q1 or the first quartile is the median of the data which are less than the overall median. For example, consider a set of data, 3, 5, 7, 8, 9, 10. The median of this set of data is 7. 3, 5 are the only numbers less than the median. The median of the numbers 3 and 5 is 4, so the 1st quartile is 4.
Q3
Q3 or the third quartile is the median of the data which is more than the overall median. For example, if we consider a set of data, 2, 3, 5, 6, 8 the median is 5. Now, 6 and 8 are the numbers in this set that are greater than the overall median. These are called as Q3 or third quartile.
QED
QED stands for quod erat demonstrandum, which means "That which has to be proven".
Quadrangle
A polygon with four sides.
Quadrants
The four sections into which the x-y plane is divided by the x and y axis.
Quadratic
A two degree polynomial equation represented by the equation,
ax2 + bx + c = 0, where, a ≠ o.
Quadratic Polynomial
Any polynomial of degree 2.
Quadrilateral
A closed figure bounded by four lines.
Quadruple
Four times any number or a value is called as quadruple.
Quartic Polynomial
A polynomial of degree four.
Example: ax4 + bx3 + cx2 + dx + e = 0
Quintic Polynomial
A polynomial of degree 5
a5 + b3 + c
Quintiles
From a set of data, the 20th and 80th percentiles are called the quintiles.
Quintuple
Multiplying any number by a factor of 5.
Q1
Q1 or the first quartile is the median of the data which are less than the overall median. For example, consider a set of data, 3, 5, 7, 8, 9, 10. The median of this set of data is 7. 3, 5 are the only numbers less than the median. The median of the numbers 3 and 5 is 4, so the 1st quartile is 4.
Q3
Q3 or the third quartile is the median of the data which is more than the overall median. For example, if we consider a set of data, 2, 3, 5, 6, 8 the median is 5. Now, 6 and 8 are the numbers in this set that are greater than the overall median. These are called as Q3 or third quartile.
QED
QED stands for quod erat demonstrandum, which means "That which has to be proven".
Quadrangle
A polygon with four sides.
Quadrants
The four sections into which the x-y plane is divided by the x and y axis.
Quadratic
A two degree polynomial equation represented by the equation,
ax2 + bx + c = 0, where, a ≠ o.
Quadratic Polynomial
Any polynomial of degree 2.
Quadrilateral
A closed figure bounded by four lines.
Quadruple
Four times any number or a value is called as quadruple.
Quartic Polynomial
A polynomial of degree four.
Example: ax4 + bx3 + cx2 + dx + e = 0
Quintic Polynomial
A polynomial of degree 5
a5 + b3 + c
Quintiles
From a set of data, the 20th and 80th percentiles are called the quintiles.
Quintuple
Multiplying any number by a factor of 5.
Radian
It is the unit of measuring angles. For example, 180 º = Π radians, 45 º = Π/4 radians etc,
Radical
The designated symbol for the square root of any mathematical entity is called radical.
Radicand
The mathematical quantity whose nth root is taken. It is the number under the radical symbol.
Radius of a circle
The distance or the measure of the line segment between center of circle and any point on the circle is called the radius of the circle.
Range
The limit within which set of values reside. For example, the range of the function y = x2 is [0, ∞] or {y|y ≥ o}
Ratio
The resultant quantity derived by dividing one number with the other.
Rational Exponents
The exponents which are composed of rational numbers are called rational exponents.
Rational Function
Given two polynomials, one divided by another, the resultant is expressed as a function, then it is called rational equation.
Rational numbers
The set of all ratios, made up of real numbers, which do not have zero as denominator.
Rational root theorem
All possible roots of a polynomial are provided by the rational root theorem.
Rationalizing Substitution
It is a method of integration capable of transforming a fractional integrand into more than one kind of root.
Rationalizing the Denominator
The process of adjusting a fraction is such a way that denominator becomes a rational number.
Ray
A line having only one end point and extending infinitely in the other direction is called a ray.
Real numbers
It is a set of all numbers consisting of positive, negative, rational, square root, cube root etc. Real numbers form the set of all the numbers on the number line.
Reciprocal Numbers
One divided by the given number is the reciprocal of the number.
Rectangle
A rectangle is a quadrilateral having all equal angles. They are equal to 900.
Rectangle Parallelepiped
Rectangle Parallelepiped is a polyhedron where every face is a rectangle.
Recursive Formula
In a series of numbers, the next term in the series is calculated by a formula which uses previous terms in that same series. This term is called recursive term and the process is called recursive formula.
Reducing a fraction
When numerator and denominator, both have common factors, we cancel out all of them until no common factor remains.
Regular Octahedron
A polyhedron which has eight faces is called regular octahedron.
Regular Polygon
A regular polygon is one in which all angles and sides are are congruent to each other.
Regular Prism
Regular Prism is a prism in which all the face comprise of regular polygons.
Regular Pyramid
The pyramid who's base is made up of regular polygon is called regular pyramid.
Regular Right Prism
A regular right prism is one whose bases are made up of right polygons
Right Pyramid
Right Pyramid is a pyramid where base is a regular regular polygon and the apex is directly on top of the center of the base of polygon.
Regular Tetrahedron
Regular Tetrahedron is a pyramid where all the faces of the polygon are triangles.
Related Rates
The set of all the problems, where the changes in various rates are calculated by means of differentiation.
Relation
The ordered pair of entities which have some distinct abstraction between them is called a relation.
Relative Maximum
Relative maximum is a point in the graph which is at the highest point for that particular section.
Relative Minimum
Relative minimum is a point in the graph which is at the lowest point for that particular section.
Relative Prime
Those numbers which have the greatest common factors as prime numbers are called relative prime numbers.
Remainder
The number which is left over after the division as an undivided whole number is called remainder.
Residual
The measure of a line which is parallel to Y axis and one end of which is touching the data point is called residual.
Rhombus
The parallelogram having all equal sides is called rhombus.
Reimann Geometry
Reimann geometry is a type of geometry where all the lines are considered non parallel, intersecting and happening on the surface of the sphere.
Right Circular Cone
A right circular cone is a cone whose base is a circle and any radius is making right angle to the line segment from apex of the cone to center of the circle.
Right Circular Cylinder
Right circular cylinder cylinder whose bases is are circular.
Regular Hexagon
A hexagon with all sides equal to each other is called regular hexagon.
Rose Curve
The leaves of the curve which have complete symmetry over the center of the curve is called a rose curve.
Rotation
When figure is transformed according to a fixed point is called rotation (generally in same plane).
Rounding a Number
Without compromising the degree of accuracy to a large extent, the approximation of number to the nearest value is called rounding of the number
What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller... magic.com
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