E
e
e is a transcendental number that has a value approximately equal to 2.718. It is frequently used while working with logarithms and exponential functions.
Eccentricity
A number that indicates the shape of a curve. It is represented by the small letter 'e' (This e is in no ways related to the exponential e = 2.718). In conic section, the eccentricity of the curves is a ratio between the distance from the center to focus and either the horizontal or vertical distance from the center to the vertex.
Echelon Form of a Matrix
An echelon matrix is used to solve a system of linear equations.
Edge of a Polyhedron
One of the line segments that together make up the faces of the polyhedron.
Element of a Matrix
The numbers inside the matrix in the form of rows and columns is called as the element of matrix.
Element of a Set
Any point, line, letter, number etc. contained in a set is called as the element of the set.
Empty Set
A set that doesn't contains any element. The empty set is represented by {} or Ø.
Equality Properties of Equation
The equality properties of algebra that are used to solve the algebraic equations. The mathematical definitions of these equality properties are as follows
x = y means, x is equal to y and y ≠ x means y is not equal to x. The operations of addition, subtraction, multiplication and division all hold true for equality properties of equation.
Reflexive Property- x = x;
Symmetric Property- If x = y then y = x;
Transitive Property- If x = y and y = z then x = z
Equilateral Triangle
An equilateral triangle has all its three sides equal and the measure of each angle is 60º.
Equivalence Relation
Any equation that is reflexive, symmetric and transitive.
Equivalent Systems of Equation
Two sets of simultaneous equations that have same solution.
Essential Discontinuity
It is a type of discontinuity in the graph that cannot be removed by simply adding a point. Mathematically, at the point of essential discontinuity the limit of the function doesn't exist.
Euclidean Geometry
The geometrical study of lines, points, angles, quadrilaterals, axioms, theorems and other branches of geometry is called the Euclidean geometry. Euclidean geometry is named after Euclid, one of the greatest Greek mathematicians and known as the 'Father of Geometry'.
e
e is a transcendental number that has a value approximately equal to 2.718. It is frequently used while working with logarithms and exponential functions.
Eccentricity
A number that indicates the shape of a curve. It is represented by the small letter 'e' (This e is in no ways related to the exponential e = 2.718). In conic section, the eccentricity of the curves is a ratio between the distance from the center to focus and either the horizontal or vertical distance from the center to the vertex.
Echelon Form of a Matrix
An echelon matrix is used to solve a system of linear equations.
Edge of a Polyhedron
One of the line segments that together make up the faces of the polyhedron.
Element of a Matrix
The numbers inside the matrix in the form of rows and columns is called as the element of matrix.
Element of a Set
Any point, line, letter, number etc. contained in a set is called as the element of the set.
Empty Set
A set that doesn't contains any element. The empty set is represented by {} or Ø.
Equality Properties of Equation
The equality properties of algebra that are used to solve the algebraic equations. The mathematical definitions of these equality properties are as follows
x = y means, x is equal to y and y ≠ x means y is not equal to x. The operations of addition, subtraction, multiplication and division all hold true for equality properties of equation.
Reflexive Property- x = x;
Symmetric Property- If x = y then y = x;
Transitive Property- If x = y and y = z then x = z
Equilateral Triangle
An equilateral triangle has all its three sides equal and the measure of each angle is 60º.
Equivalence Relation
Any equation that is reflexive, symmetric and transitive.
Equivalent Systems of Equation
Two sets of simultaneous equations that have same solution.
Essential Discontinuity
It is a type of discontinuity in the graph that cannot be removed by simply adding a point. Mathematically, at the point of essential discontinuity the limit of the function doesn't exist.
Euclidean Geometry
The geometrical study of lines, points, angles, quadrilaterals, axioms, theorems and other branches of geometry is called the Euclidean geometry. Euclidean geometry is named after Euclid, one of the greatest Greek mathematicians and known as the 'Father of Geometry'.
Euler's Formula
Euler's formula is given by eiπ + 1= 1. It is a widely used formula in complex number analysis.
Euler's Formula in Polyhedron
For any polyhedron, the following relation holds true:
[Number of faces(n)] – [number of vertices(v)] – [number of edges(e)] = 2.
This formula holds true for all convex and concave polyhedron.
Even Function
A function whose graph is symmetric about y-axis. Also, f(-x) = f(x).
Even Number
The set of all integers that are divisible by 2. E= {0, 2, 4, 6, 8......}
Explicit Differentiation
The derivative of an explicit function is called as the explicit differentiation. For example, y = x3 + 2x2 - 3x. Differentiating it gives,
y'= 3x2 + 4x – 3.
Explicit Function
In an explicit function, the dependent variable can be totally expressed in terms of independent variable. For example, y= 5x2 - 6x.
Exponent Rules
The exponential rules are as follows.
Euler's formula is given by eiπ + 1= 1. It is a widely used formula in complex number analysis.
Euler's Formula in Polyhedron
For any polyhedron, the following relation holds true:
[Number of faces(n)] – [number of vertices(v)] – [number of edges(e)] = 2.
This formula holds true for all convex and concave polyhedron.
Even Function
A function whose graph is symmetric about y-axis. Also, f(-x) = f(x).
Even Number
The set of all integers that are divisible by 2. E= {0, 2, 4, 6, 8......}
Explicit Differentiation
The derivative of an explicit function is called as the explicit differentiation. For example, y = x3 + 2x2 - 3x. Differentiating it gives,
y'= 3x2 + 4x – 3.
Explicit Function
In an explicit function, the dependent variable can be totally expressed in terms of independent variable. For example, y= 5x2 - 6x.
Exponent Rules
The exponential rules are as follows.
| Serial Number | Exponential Formula |
| 1 | anam = an+m |
| 2 | (a.b)n = an. bn |
| 3 | a0 = 1 |
| 4 | (am)n = amn |
| 5 | am/n = n√am |
| 6 | a-m = 1/a-m |
| 7 | (am/an )= a(m-n) |
Extreme Value Theorem
According to this theorem, there is always at least one absolute maximum and one absolute minimum for any continuous function over a closed interval.
Extreme Value of a Polynomial
The graph of a polynomial of degree n has at most n-1 extreme values (either maxima or minima)
F
Face of Polyhedron
Polygonal outer boundary of a solid object having no curved surfaces.
Factor of an integer
If the given integer is divided evenly by another integer then the resultant is called factor of an integer. For example: 2, 4, 8, 16 etc, are the factors of 32.
Factor of polynomial
Polynomial P(x) is completely divided into Polynomial R(x) by Q(x) then Q(x) is called Factor of polynomial. For example: P(x)= x2+6x+8, Q(x)=x+4 then P(x)/Q(x)= x+2. Q(x)=x+4 is the factor.
Factor theorem
When x-a is factor of P(x), the value x in P(x) is replaced with a, then if the resultant value is 0, such a theorem is called Factor theorem. For example: P(x)= x2+6x+24. Q(x)= x-(-4). If x is replaced with a, that is -4, then P(x)= 0.
Factorial
The product of the an integer with all the consecutive smaller integers is called a factorial. It is represented as "n!". For example: 5! = 5*4*3*2*1= 120.
Factoring Rules
These are the formulas that govern the factorization of a polynomial. For example
Face of Polyhedron
Polygonal outer boundary of a solid object having no curved surfaces.
Factor of an integer
If the given integer is divided evenly by another integer then the resultant is called factor of an integer. For example: 2, 4, 8, 16 etc, are the factors of 32.
Factor of polynomial
Polynomial P(x) is completely divided into Polynomial R(x) by Q(x) then Q(x) is called Factor of polynomial. For example: P(x)= x2+6x+8, Q(x)=x+4 then P(x)/Q(x)= x+2. Q(x)=x+4 is the factor.
Factor theorem
When x-a is factor of P(x), the value x in P(x) is replaced with a, then if the resultant value is 0, such a theorem is called Factor theorem. For example: P(x)= x2+6x+24. Q(x)= x-(-4). If x is replaced with a, that is -4, then P(x)= 0.
Factorial
The product of the an integer with all the consecutive smaller integers is called a factorial. It is represented as "n!". For example: 5! = 5*4*3*2*1= 120.
Factoring Rules
These are the formulas that govern the factorization of a polynomial. For example
- x2-(a+b)x +ab= (x-a)(x-b).
- x2+2(a)x+a2=(x+a)2
- x2-2(a)x +a2=(x-a)2
Fibonacci series
It is a series of numbers where the next number is found by adding the previous two numbers in the series. The first two numbers of the series are 0 and 1. The series is 0,1,2,3,5,8...
Finite
The term is used to describe a set in which all the elements can be counted using natural numbers.
First Derivative
A function F(a), which governs the slope of the curve at any given point or the slope of the line drawn tangent to the curve from that point in the plane is called the first derivative. It is represented as F'. For F(x)= 5x2. F'(x)=10x will be the slope of the curve.
First Derivative test
A Technique which is used to determine the capacity of inflection point.(minimum, maximum or neither)
First Order of the differential equation A differential equation P(a) who's order is 1. For example: P(a)=3a, here the order of a is 1.
Flip
It is also known as axis of reflection. It is a line which divides the plane or a geometric figure into two halves that are mirror images of each other.
Floor Function (Greatest Integer Function)
It is a function F(x) which is responsible for finding the greatest integer less that the actual value of P(x). For example: P(x)= 5.5, here the greatest integer less than 5.5 is 5. The function which gives F(x)=5 becomes floor function.
Foci of the Ellipse
They are the fixed two points inside the ellipse such that the vertical curve is governed according to the equation L1+L2= 2a and horizontal curve according to equation L1+L2=2b where L is the distance between the focal point and the curve, a is the horizontal radius and b is the vertical radius.
Foci of hyperbola
They are fixed two points inside of the curve of hyperbola such that the determinant of the L1-L2 is always constant. L1 and L2 are the distances between point P (which is the curve) and respective focus of the curve.
Focus
The curves of the conic sections are governed according to distances from a special point called focus.
Focus of Parabola
In a Parabola, the distance between a point P on the curve and an arbitrary point inside parabola which is equal to the distance between the same point P and directrix of the curve. Such an arbitrary point is called Focus of the Parabola.
FOIL method
FOIL is an acronym for First Outer Inner Last. It is method by which binomials are multiplied. The Multiplication order is
- First terms of Binomials
- Outer terms of Binomial
- Inner terms of binomials
- Outer terms of Binomials.
For example: (a+b)(a-b)= a.a+a.(-b)+b.a +b.(-b)
Formula
The relationship between various Variables (sometimes expressed in the form of an equation) depicted using symbols. For example: a+b=7
Fractal
When every part of the figure is similar to every other part of other figure, then the figure is called fractal.
Fraction
It is a ratio between two numbers. For example: 9/11.
Fraction Rules
The rules of algebra used for uniting various the fractions.
Fractional Equation
The expression in the form of A/B on both the sides of equal sign is called fractional equation. For example: x/6= 4/3.
Function Operation
Various Operations such as additions, subtractions, multiplications, divisions and compositions which have a combining effect on various functions. For example: F(a/b)= F(a)/F(b).
Fundamental theorem of Algebra
Every polynomial characterized by single variable having complex coefficients, will have a minimum of at least one root which is also complex in nature.
Fundamental Theorem of Arithmetic
The statement that the factors of a prime number are always distinct and unequal is the fundamental theorem of arithmetic.
Fundamental Theorem of Calculus
Differentiation and integration are two most basic operations of the calculus. The theorem that establishes a relationship between them is called Fundamental theorem of Calculus.
Formula
The relationship between various Variables (sometimes expressed in the form of an equation) depicted using symbols. For example: a+b=7
Fractal
When every part of the figure is similar to every other part of other figure, then the figure is called fractal.
Fraction
It is a ratio between two numbers. For example: 9/11.
Fraction Rules
The rules of algebra used for uniting various the fractions.
Fractional Equation
The expression in the form of A/B on both the sides of equal sign is called fractional equation. For example: x/6= 4/3.
Function Operation
Various Operations such as additions, subtractions, multiplications, divisions and compositions which have a combining effect on various functions. For example: F(a/b)= F(a)/F(b).
Fundamental theorem of Algebra
Every polynomial characterized by single variable having complex coefficients, will have a minimum of at least one root which is also complex in nature.
Fundamental Theorem of Arithmetic
The statement that the factors of a prime number are always distinct and unequal is the fundamental theorem of arithmetic.
Fundamental Theorem of Calculus
Differentiation and integration are two most basic operations of the calculus. The theorem that establishes a relationship between them is called Fundamental theorem of Calculus.
G
Gauss-Jordan Elimination
A method of solving a system of linear equations. In this process the augmented form of the matrix system is reduced into row echelon form by means of row operations.
Gaussian Elimination
A method of solving a system of linear equations. In Gauss elimination method, the augmented form of matrix is reduced to row echelon form and then the system is solved by back substitution.
Gaussian Integer
Gaussian integers are the integers in the complex numbers that are represented by a + bi. For example, 3 + 2i, 5i and 6i + 5 are called Gaussian integers.
GCF
The largest integer that divides a certain set of numbers. Also called as Greatest Common Factor. For example, the GCF of 20, 30 and 60 is 10.
General Form for the Equation of a Line
The general form of equation of a line is represented by the equation-
Ax + By + C = 0, where, A, B and C are integers.
Geometric Figure
A geometric figure is a set of points on the plane or space that leads to the formation of figure.
Geometric Mean
Geometric mean is a method of finding the average of certain set of numbers. For example, if there are numbers a1, a2, a3,........anthen multiply the numbers and take the nth root of the product.
Geometric Mean = (a1, a2, a3,........an)½
Geometric Progression
A geometric progression is a mathematical sequence whose terms are in a constant ratio with the previous terms. For example, 2, 4, 8, 16, 32.....128 are the terms of a geometric progression. Here the common ratio is 2. (as 4/2 = 8/4 = 16/8....)
Geometric Series
Geometric series is a mathematical series whose successive terms are in a constant ratio. An example of geometric series is 2, 4, 8, 16, 32........
Geometry
The study of geometric figures in two and three dimensions is called as geometry.
Greatest lower bound
The greatest of all lower bounds of a set of numbers is called as the GLB or greatest lower bound. For example, in the set [2,7], the GLB is 2.
Glide Reflection
A transformation in which a figure has to go through a combination of steps of translation and reflection.
Global Maximum
The highest point on the graph of a function or a relation (in the domain of the function). The first and second derivative tests are used to find the maximum values of a function. It is also called as global maximum, absolute maximum and relative maximum.
Global Minimum
The lowest point on the graph of a function or a relation. The first and second derivative tests are used to find the minimum values of a function. It is also called as the global minimum, absolute minimum or global minimum.
Golden Mean
The ratio (1 + √5)/2 ≈ 1.61803 is called as the golden mean. The unique property of golden mean is that the reciprocal of golden mean is about 0.61803. Hence, the golden mean is one plus its reciprocal.
Golden Rectangle
If the ratio of length and breadth of a rectangle is equal to the golden mean then the rectangle is called as the golden rectangle. It is believed that this rectangle is most pleasing to the eyes.
Golden Spiral
A spiral that can be drawn inside the golden rectangle.
Googol
The number 10100 is called as googol.
Googolplex
Googolplex can be written as 10100100.
Graph of an Equation or Inequality
The graph obtained by plotting all the points on the coordinate system.
Graphic Methods
The use of graphical methods to solve the mathematical problems.
Great Circle
A circle that is drawn on the surface of the sphere and shares a common center with the circle.
Greatest Integer Function
The greatest integer function of any number (say x) is an integer 'less than or equal to x'. The greatest integer function is represented as [x]. For example, [3.4] = 3 and [-2.5] = 3
Gauss-Jordan Elimination
A method of solving a system of linear equations. In this process the augmented form of the matrix system is reduced into row echelon form by means of row operations.
Gaussian Elimination
A method of solving a system of linear equations. In Gauss elimination method, the augmented form of matrix is reduced to row echelon form and then the system is solved by back substitution.
Gaussian Integer
Gaussian integers are the integers in the complex numbers that are represented by a + bi. For example, 3 + 2i, 5i and 6i + 5 are called Gaussian integers.
GCF
The largest integer that divides a certain set of numbers. Also called as Greatest Common Factor. For example, the GCF of 20, 30 and 60 is 10.
General Form for the Equation of a Line
The general form of equation of a line is represented by the equation-
Ax + By + C = 0, where, A, B and C are integers.
Geometric Figure
A geometric figure is a set of points on the plane or space that leads to the formation of figure.
Geometric Mean
Geometric mean is a method of finding the average of certain set of numbers. For example, if there are numbers a1, a2, a3,........anthen multiply the numbers and take the nth root of the product.
Geometric Mean = (a1, a2, a3,........an)½
Geometric Progression
A geometric progression is a mathematical sequence whose terms are in a constant ratio with the previous terms. For example, 2, 4, 8, 16, 32.....128 are the terms of a geometric progression. Here the common ratio is 2. (as 4/2 = 8/4 = 16/8....)
Geometric Series
Geometric series is a mathematical series whose successive terms are in a constant ratio. An example of geometric series is 2, 4, 8, 16, 32........
Geometry
The study of geometric figures in two and three dimensions is called as geometry.
Greatest lower bound
The greatest of all lower bounds of a set of numbers is called as the GLB or greatest lower bound. For example, in the set [2,7], the GLB is 2.
Glide Reflection
A transformation in which a figure has to go through a combination of steps of translation and reflection.
Global Maximum
The highest point on the graph of a function or a relation (in the domain of the function). The first and second derivative tests are used to find the maximum values of a function. It is also called as global maximum, absolute maximum and relative maximum.
Global Minimum
The lowest point on the graph of a function or a relation. The first and second derivative tests are used to find the minimum values of a function. It is also called as the global minimum, absolute minimum or global minimum.
Golden Mean
The ratio (1 + √5)/2 ≈ 1.61803 is called as the golden mean. The unique property of golden mean is that the reciprocal of golden mean is about 0.61803. Hence, the golden mean is one plus its reciprocal.
Golden Rectangle
If the ratio of length and breadth of a rectangle is equal to the golden mean then the rectangle is called as the golden rectangle. It is believed that this rectangle is most pleasing to the eyes.
Golden Spiral
A spiral that can be drawn inside the golden rectangle.
Googol
The number 10100 is called as googol.
Googolplex
Googolplex can be written as 10100100.
Graph of an Equation or Inequality
The graph obtained by plotting all the points on the coordinate system.
Graphic Methods
The use of graphical methods to solve the mathematical problems.
Great Circle
A circle that is drawn on the surface of the sphere and shares a common center with the circle.
Greatest Integer Function
The greatest integer function of any number (say x) is an integer 'less than or equal to x'. The greatest integer function is represented as [x]. For example, [3.4] = 3 and [-2.5] = 3
H
Half Angle identities
The identities of trigonometry that are used to calculate the value of sine, cosine, tangent etc. of half of a given angle.
The trigonometric identities are as follows:
sin2x = (1 – cos2x)/2
cos2x = (1 + cos2x)/2
Half Closed Interval/Half Open Interval
It is a set of all numbers containing only one end point.
Harmonic Mean
The inversion of the summation of the reciprocals of a set of numbers. For example: (1, 2, 3) are in a set then their harmonic mean is 1/(1+ ½+ ⅓ )
Harmonic Progression
It is a sequence in which every term is the reciprocal of the natural number. For example 1, ½, ⅓, ¼.
Harmonic Series
The summation of all the terms in harmonic progression. For example: 1+ ½+ ⅓+ ¼
Height
The least measurable distance between the base and the top of a geometric figure is called as the height. The top can be the opposite vertex, or an apex or even another base of the figure.
Height of the Cone
The distance between the center of the circular base and the vertex of the cone can be called as the height of the cone.
Height of Cylinder
The distance between the centers of the circular bases of the cylinder is the height of the cylinder.
Height of a Parallelogram
The perpendicular distance between the parallel sides of a parallelogram (i.e. the base to the opposite side).
Height of a Prism
The length of the shortest line segment between the bases of the prism.
Height of a Pyramid
The shortest distance between the vertex and extended base of the pyramid.
Height of a Triangle
The length of the shortest line segment between a vertex and the opposite side of the triangle.
Helix
It is a spiral shape curve in three dimensional space.
Heptagon
A heptagon can be called as a polygon which has seven sides. It's other name is septagon, but heptagon is widely used.
Hero's Formula
Suppose all the three sides of the triangle are known. The formula used to calculate the area of the triangle in this scenario is called Hero's formula. For example: √[s(s-a)(s-b)(s-c)]
Hexagon
It is a special geometric figure which has six sides and angles.
Hexahedron
A solid which has no curved surfaces and the number of surfaces are equal to six.
Higher Derivative
The derivative of first derivative or the derivative of second derivative that have degree more than 1 are called as higher derivatives.
Homogeneous Equations
When two or more linear equations have their constant term as zero, then such a set of equations are called homogeneous equations.
Horizontal Line Equation
It is an equation which is used to describe a line parallel to Y-axis.
Horizontal Line Test
If a horizontal line intersects a graph twice [graph is made by the function F(x)], then the function is said be not one on one. This test to check one to one of function is called horizontal line test.
Horizontal Reflection
A geometric figure situated in first or fourth quadrant, the reflection of which is present in second or third quadrant along X-axis and vice or versa is called horizontal reflection.
Hyperbola
A hyperbola is a geometric figure, which is a locus of two points called as foci, where the difference between the distances to each point is constant.
Hyperbolic Geometry
Given two entities, a point and a line, there can be infinitely many lines passing through the point and are parallel to first point. This is called Hyperbolic geometry.
Hyperbolic Trigonometry
The trigonometric functions sine cosine tangent etc. who's values are calculated using 'e'. Mathematical definitions of hyperbolic trigonometry are as follows:
sinhx = (ex - e-x)/2,
coshx = (ex + e-x)/2
tanhx = (sinhx/coshx) = (ex - e-x)/(ex + e-x)/2
Hypotenuse
The hypotenuse is longest side of right angled triangle.
Hypotenuse-leg Congruence
Two different right angle triangles are said to be congruent when their hypotenuse and one of the corresponding legs are equal in length.
Hypotenuse-leg Similarity
In two right angled triangles when the ratio of the corresponding sides have equal ratios, then such triangles are having HL Similarity.
Half Angle identities
The identities of trigonometry that are used to calculate the value of sine, cosine, tangent etc. of half of a given angle.
The trigonometric identities are as follows:
sin2x = (1 – cos2x)/2
cos2x = (1 + cos2x)/2
Half Closed Interval/Half Open Interval
It is a set of all numbers containing only one end point.
Harmonic Mean
The inversion of the summation of the reciprocals of a set of numbers. For example: (1, 2, 3) are in a set then their harmonic mean is 1/(1+ ½+ ⅓ )
Harmonic Progression
It is a sequence in which every term is the reciprocal of the natural number. For example 1, ½, ⅓, ¼.
Harmonic Series
The summation of all the terms in harmonic progression. For example: 1+ ½+ ⅓+ ¼
Height
The least measurable distance between the base and the top of a geometric figure is called as the height. The top can be the opposite vertex, or an apex or even another base of the figure.
Height of the Cone
The distance between the center of the circular base and the vertex of the cone can be called as the height of the cone.
Height of Cylinder
The distance between the centers of the circular bases of the cylinder is the height of the cylinder.
Height of a Parallelogram
The perpendicular distance between the parallel sides of a parallelogram (i.e. the base to the opposite side).
Height of a Prism
The length of the shortest line segment between the bases of the prism.
Height of a Pyramid
The shortest distance between the vertex and extended base of the pyramid.
Height of a Triangle
The length of the shortest line segment between a vertex and the opposite side of the triangle.
Helix
It is a spiral shape curve in three dimensional space.
Heptagon
A heptagon can be called as a polygon which has seven sides. It's other name is septagon, but heptagon is widely used.
Hero's Formula
Suppose all the three sides of the triangle are known. The formula used to calculate the area of the triangle in this scenario is called Hero's formula. For example: √[s(s-a)(s-b)(s-c)]
Hexagon
It is a special geometric figure which has six sides and angles.
Hexahedron
A solid which has no curved surfaces and the number of surfaces are equal to six.
Higher Derivative
The derivative of first derivative or the derivative of second derivative that have degree more than 1 are called as higher derivatives.
Homogeneous Equations
When two or more linear equations have their constant term as zero, then such a set of equations are called homogeneous equations.
Horizontal Line Equation
It is an equation which is used to describe a line parallel to Y-axis.
Horizontal Line Test
If a horizontal line intersects a graph twice [graph is made by the function F(x)], then the function is said be not one on one. This test to check one to one of function is called horizontal line test.
Horizontal Reflection
A geometric figure situated in first or fourth quadrant, the reflection of which is present in second or third quadrant along X-axis and vice or versa is called horizontal reflection.
Hyperbola
A hyperbola is a geometric figure, which is a locus of two points called as foci, where the difference between the distances to each point is constant.
Hyperbolic Geometry
Given two entities, a point and a line, there can be infinitely many lines passing through the point and are parallel to first point. This is called Hyperbolic geometry.
Hyperbolic Trigonometry
The trigonometric functions sine cosine tangent etc. who's values are calculated using 'e'. Mathematical definitions of hyperbolic trigonometry are as follows:
sinhx = (ex - e-x)/2,
coshx = (ex + e-x)/2
tanhx = (sinhx/coshx) = (ex - e-x)/(ex + e-x)/2
Hypotenuse
The hypotenuse is longest side of right angled triangle.
Hypotenuse-leg Congruence
Two different right angle triangles are said to be congruent when their hypotenuse and one of the corresponding legs are equal in length.
Hypotenuse-leg Similarity
In two right angled triangles when the ratio of the corresponding sides have equal ratios, then such triangles are having HL Similarity.
I
i
In complex number analysis, the letter i denotes iota. Mathematically, iota is given by negative square root of 1, that means √-1. = i
Icosahedron
Icosahedron is a polyhedron with 20 faces. In the case of a regular icosahedron, the faces are all equilateral triangles.
Identity (Equation)
An equation that is true for any values of the variable. For example, the identity, sin2θ + cos2θ = 1 is true for all values of θ.
Identity Function
The function f(x) = x is called as the identity function.
Identity Matrix
A square matrix that has 1 as its element in the principal diagonal and rest all elements are zero.
Image of a Transformation
The image obtained after performing the operations of dilation or rotation or translation.
Imaginary Numbers
A complex number like 7i, that is free of the real part is called as the complex number.
Imaginary Part
Consider a complex number -7 + 8i, the coefficient of i called as the imaginary part of the complex number.
Implicit Function or Relation
A function in which the dependent variable can't be exactly expressed as a function of the independent variable.
Implicit Differentiation
Differentiating an implicit function. For example, consider 4x2 + 5y5 - 6x = 1. Here, y can't be written explicitly as a function of x.
Impossible Event
An event that is impossible to happen or an event whose probability is zero.
Improper Fraction
A fraction that has denominator greater than its numerator.
Improper Integral
A integration in which the bounds of integration has discontinuities in the graph. They can also have limits between ∞ and -∞. The discontinuities between the bounds of integration makes the use of limits necessary in evaluating improper integrals.
Improper Rational Expression
If the degree of a numerator polynomial is more than or equal to the degree of a denominator polynomial than the rational expression is called as the improper rational expression.
Incenter
The center of a circle inscribed in a triangle or a polygon. Geometrically, incenter is the point of intersection of the angle bisectors of a triangle.
Incircle
The largest possible circle that can be drawn inside a plane figure. All triangles and regular polygons have incircle.
Inconsistent System of Equations
A system of equations that has no solutions.
Increasing Function
A function whose value increases continuously as we move from left to right of its graph is called increasing function. A line with positive slope is a perfect example of increasing function where the value of the function increases as we proceed on the x-axis. If the increasing function is differentiable then its derivative at all points (where the function is increasing) will be negative.
Indefinite Integral
I = a∫bf(x) dx, is known as the improper integral
Indefinite Integral Rules
Independent Events
If the occurrence or non-occurrence of two events is independent of each other it is called as the independent event.
Independent Variable
The quantity in an equation whose values can be freely chosen in an equation without taking into consideration the values of the other variables.
Indeterminate Expressions
An undefined expression that cannot be assigned any value. There are various forms of indeterminate expressions:
i
In complex number analysis, the letter i denotes iota. Mathematically, iota is given by negative square root of 1, that means √-1. = i
Icosahedron
Icosahedron is a polyhedron with 20 faces. In the case of a regular icosahedron, the faces are all equilateral triangles.
Identity (Equation)
An equation that is true for any values of the variable. For example, the identity, sin2θ + cos2θ = 1 is true for all values of θ.
Identity Function
The function f(x) = x is called as the identity function.
Identity Matrix
A square matrix that has 1 as its element in the principal diagonal and rest all elements are zero.
Image of a Transformation
The image obtained after performing the operations of dilation or rotation or translation.
Imaginary Numbers
A complex number like 7i, that is free of the real part is called as the complex number.
Imaginary Part
Consider a complex number -7 + 8i, the coefficient of i called as the imaginary part of the complex number.
Implicit Function or Relation
A function in which the dependent variable can't be exactly expressed as a function of the independent variable.
Implicit Differentiation
Differentiating an implicit function. For example, consider 4x2 + 5y5 - 6x = 1. Here, y can't be written explicitly as a function of x.
Impossible Event
An event that is impossible to happen or an event whose probability is zero.
Improper Fraction
A fraction that has denominator greater than its numerator.
Improper Integral
A integration in which the bounds of integration has discontinuities in the graph. They can also have limits between ∞ and -∞. The discontinuities between the bounds of integration makes the use of limits necessary in evaluating improper integrals.
Improper Rational Expression
If the degree of a numerator polynomial is more than or equal to the degree of a denominator polynomial than the rational expression is called as the improper rational expression.
Incenter
The center of a circle inscribed in a triangle or a polygon. Geometrically, incenter is the point of intersection of the angle bisectors of a triangle.
Incircle
The largest possible circle that can be drawn inside a plane figure. All triangles and regular polygons have incircle.
Inconsistent System of Equations
A system of equations that has no solutions.
Increasing Function
A function whose value increases continuously as we move from left to right of its graph is called increasing function. A line with positive slope is a perfect example of increasing function where the value of the function increases as we proceed on the x-axis. If the increasing function is differentiable then its derivative at all points (where the function is increasing) will be negative.
Indefinite Integral
I = a∫bf(x) dx, is known as the improper integral
Indefinite Integral Rules
Independent Events
If the occurrence or non-occurrence of two events is independent of each other it is called as the independent event.
Independent Variable
The quantity in an equation whose values can be freely chosen in an equation without taking into consideration the values of the other variables.
Indeterminate Expressions
An undefined expression that cannot be assigned any value. There are various forms of indeterminate expressions:
- 0/0
- ±∞/±∞
- 00
- 1∞
- ∞0
- ∞ - ∞
Induction
A method of proving a mathematical problem by the help of a series of steps. Mathematical induction is used to prove complex mathematical problems.
Independent Events
Two or more events are said to be independent events if the occurrence or non-occurrence of any of these events doesn't affect the occurrence or non-occurrence of others. By the principle of probability, if A and B are two independent events, then P(A|B) = P(A).
Independent Variable
Independent variables are those whose value can be chosen without any restriction. For example, in the equation Y = 2x2 + 3x, y is the dependent variable and x is the independent variable.
Indirect Proof
Proving a statement or a fact by the method of contradiction is known as indirect proof. This means that the conjecture is taken to be false and then it is proved that the statement contradicts the assumption made at the beginning of solving the problem.
A method of proving a mathematical problem by the help of a series of steps. Mathematical induction is used to prove complex mathematical problems.
Independent Events
Two or more events are said to be independent events if the occurrence or non-occurrence of any of these events doesn't affect the occurrence or non-occurrence of others. By the principle of probability, if A and B are two independent events, then P(A|B) = P(A).
Independent Variable
Independent variables are those whose value can be chosen without any restriction. For example, in the equation Y = 2x2 + 3x, y is the dependent variable and x is the independent variable.
Indirect Proof
Proving a statement or a fact by the method of contradiction is known as indirect proof. This means that the conjecture is taken to be false and then it is proved that the statement contradicts the assumption made at the beginning of solving the problem.
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