M
Mach Number : The ratio of the speed of an object to the speed
of sound in the surrounding.
Maclaurin Series : when a function f(x) is differentiable
coninuousely at x =0 , the function can be expressed as given below :
F(x) = f(0) + f’(0)x + f”(0) x2 / 2! + ………..
Magic square
A
magic square of n is a arrangement of n2 numbers , generally different numbers, in a square,
so that the n numbers all rows, coloumns, and both diagonals sum to the same
number.(known as the magic sum). Example of magic square of order 3
| 8 |
1 |
6 |
15 |
| 13 |
5 |
7 |
15 |
| 4 |
9 |
12 |
15 |
| 15 |
15 |
15 |
15 |
Magic tour
If
a chess piece visits each square of a chessboard in succession, this is called
a tour of the chessboard. If the successive squares of a tour on an n X n
chessboard are numbered from 1 to n^2, in order, the tour is called a magic
tour if the resulting square is a magic square.
Magnitude : 1.
The magnitude of avector is its length,
2. The absolute value of areal or
complex number.
Main diagonal
In
the matrix [aij], the elements a11, a22, ..., ann.
Major , Minor arcs of a Circle : An
arc which is greater or less than half of the circumference of a circle.
Major, Minor axis :
The line segment connecting the two farthest
vertices in an ellipse is its major axis and the line perpendicular to the
major axis is minor axis.
The
major axis of an ellipse is it's longest chord.
Major , Minor sector of a
Circle : A sector of a circle is a region enclosed by two radii and an
arc. The larger sector is called the major sector . The smaller sector is called the minor sector.
Mandelbrot Set : A
set of points in the complex plane forming a fractal. Mathematically , we
defined Mandelbrot set as the set of complex C values for which the orbit 0
under iteration of the quadratic map x2 + C remains bounded.
Mantissa : The
positive fractional part of a real number. For example, for x = 3.1234, the
mantissa is 0.1234.
Mapping : A
rule of correspondence established between sets that associates each element of
a set with an element in the same or another set.
Malfatti circles
Three
equal circles that are mutually tangent and each tangent to two sides of a
given triangle.
Mathematical Induction : A
method of mathematical proof typically used to establish that a given statement
is true for all natural numbers. This method works by first proving that the
statement is true for a starting value, and then by proving that the statement
is true for another value also.
Mathematical Programming : A
method or process of finding out maximum or minimum values of an objective
function under the given constraints( may be in form of equalities or
inequalities ).
Mathieu’s
differential equation : The canonical form for Mathieu’s differential equation
is
d2y/dx2 + [ a –
2q cos (2x)] y = 0
Maximum
The
largest of a set of values.
Matrix
A
rectangular array of real or complex numbers , organized into rows and columns
. when specifying the size of a matrix, the number of rows is stated first. The
numbers in a matrix are called elements. And are specified by the row and the column
in which they appear.
Matroid : A
collection of subsets of a set so that any subset of a member of the collection
belongs to the collection.
Mean
The
average arithmetic mean of x1,x2,x3,…xn
is (x1+x2+x3+…+xn ) / n
Medial triangle
The
triangle whose vertices are the midpoints of the sides of a given triangle.
Median
The
median of a triangle is the line from a vertex to the midpoint of the opposite
side.
Median
When
a set of numbers is ordered from smallest to largest, the median number is the
one in the middle of the list.
Mersenne number
A
number of the form 2p-1 where p is a prime.
Mersenne prime
A
Mersenne number that is prime.
Midpoint
The
point M is the medpoint of line segment AB if AM=MB. That is, M is halfway
between A and B.
Minor axis
The
minor axis of an ellipse is its smallest chord.
Minimum
The
smallest of a set of values.
Mode
The
most frequently occurring value in a sequence of numbers.
Modulo
The
integers a and b are said to be congruent modulo m if a-b is divisible by m.
Monomial
An
algebraic expression consisting of just one term.
Monotone : A sequence is monotone if its terms are
increasing or decreasing.
Monic polynomial : A polynomial in which the
coefficient of the term of highest degree is 1.
Monochromatic triangle : A triangle whose vertices are
all colored the same.
Multinomial : An algebraic expression
consisting of 2 or more terms.
Multiple: The integer b is a multiple of the
integer a if there is an integer d such that b=da.
Multiplication : The basic arithmetical
operation of repeated addition.
N
Nabla Squared : The Laplacian written as V2
Nadir
The point on the celestial sphere in the direction downwards of
the plumb-line. The Zenith , the observer and the nadir are always in a
straight line.
Native set theory : Set is defined as
collection of objects or container of objects. In this sense, ‘set’ is an undefined
concept. Similarly when we say an object ‘ belongs to’ or ‘ is a member of’ a
set without rigorously defining what it means. This approach to set theory is
called “ Native Set Theory” as opposite to “ Axiomatic Set Theory “.
Nano
: Prefix having meaning 10-9. E.g. 1 nanometer = 10-9 meter .
Napier, John : (
1550-1667 ) : Philosopher and Mathematician inventor of logarithms and
decimal point. His other mathematical contributions include a mnemonic for
formulas used in solving spherical triangles and two formulas known as Napier’s analogies.
Napierian logarithm
: A logarithm to the base e ( 2.71828). for example, In 10 = loge 10
= 2.30, also called natural logarithm.
Napier’s bones ( Rods)
: are numbered rods used to perform multiplication or division. These can be
assumed to be predecessor to slide rule. ( u can see TLM related to this on www.mathsworld.in maths tlm section )
Napier’s formulae : Suppose a spherical triangle having sides a
. band c and angles opposite to these sides are α , β and γ respectively. We have
the following relationships, called Napier’s formulae.
Napier’s rules of Circular parts : These are related to the right spherical triangle. Using
Napier’s rule of circular parts, any quantity can be calculated if only two
quantities are known.
Nappe :
One of the two pieces of a double cone, that is, two cones placed such that
their vertices touch each other .
Nagel point
In a triangle, the lines from the vertices to the points of
contact of the opposite sides with the excircles to those sides meet in a point
called the Nagel point.
Natural Base : The
base in natural logarithm.
Natural cubic spline : Splines are smooth functions with which to fit data, and when used for
interpolation, they don’t have the oscillatory behavior, that is the
characteristic of high degree polynomial interpolation.
Natural logarithm : Same as Napier’s logarithm. Also known as hyperbolic logarithm , is the
logarithm to the base e (2.71828).
Natural number
Numbers used for counting objects. Any one of the numbers 1, 2,
3, 4, 5, ... .zero ( 0) is not included
.
Nautical Mile :
A nautical mile was developed to be a distance equal to one minute of arc (
1/60 of a degree ) distance along a
great circle and is equal to 6076 feet. 1 knot = 1 nautical mile pe hour =
0.5144 m/sec.
Necker Cube
: Wire frame drawing of a cube in isometric perspective , which means that the
parallel edges of the cube are drawn as parallel lines in the picture.
Needle Problem
: Also called Buffon’s needle problem. It involves dropping a needle on a lined
sheet of paper and determining the probability of the needle crossing one of
the lines on the page. The remarkable result is that the probability is
directly related to the value of π.
Negative number
A number smaller than 0.
Number line …….-5,-4,-3,-2, -1,0,1,2,3,4,5,…………..
Nine point center
In a triangle, the circumcenter of the medial triangle is called
the nine point center.
Nine point circle
In a triangle, the circle that passes through the midpoints of
the sides is called the nine point circle.
Nomograph
A graphical device used for computation which uses a straight
edge and several scales of numbers.
Nonagonal number : A number of the form
n(7n-5)/2.
Nonary : associated with 9
Normal : perpendicular
Null hypothesis
The null hypothesis is the hypothesis that is being tested in a
hypothesis-testing situation.
Null set: the empty set
Number line : A line on which each point
represents a real number.
Number sentence : An arrangement of
numbers and symbols; for example, an addition sentence: 3 + 7 = 10; a
subtraction sentence: 12 – 4 = 8; a multiplication sentence: 5 x 7 = 35; a
division sentence: 48 ÷ 6 = 8
Number theory : The study of integers.
Numeral : A symbol that stands for a
number.
Numerator : In the fraction x/y, x is
called the numerator and y is called the denominator.
Numerical analysis : The study of methods for
approximation of solutions of various classes of mathematical problems
including error analysis.
O
Oblate spheroid : An ellipsoid produced by
rotating an ellipse through 360o about its minor axis.
Oblique angle : An angle that is not 90o
Oblique coordinates : A coordinate system in
which the axes are not perpendicular.
Oblique triangle : A triangle that is not a
right triangle.
Oblique Solid : A slant solid
geometrical figure such as a cone, pyramid or prism having axis that is not
perpendicular to the base.
Oblique spherical Triangle : A spherical triangle having no right angle.
Obtuse angle : An angle larger than 90o
but smaller than 180o
Obtuse triangle : A triangle that contains
an obtuse angle.
Octagon: A polygon with 8 sides.
Octahedron : A polyhedron with 8 faces.
Octal System : A
number system having the base 8 number system, and uses the digits from 0 to 7.
Other commonly used number system are decimal and binary system.
Octant : Anyone of the 8 portions of
space determined by the 3 coordinate planes.
Odd function: A function f(x) is called an
odd function if f(x)= -f(-x) for all x in other words f(-x) = -f(x). in such
functions , the left half of the plane looks like the mirror image of the right
half of the plane, only upside down .
Odd number : An integer that is not
divisible by 2.
Oersted : The unit of magnetizing
field strength in the CGS electromagnetic system. One oersted = 1000/ 4 π
ampere-turns/meter.
One to one : A function f is said to be one
to one if f(x)=f(y) implies that x=y.
Onto : A function f is said to map A
onto B if for every b in B, there is some a in A such f(a)=b.
Open Curve : A
curve whose ends do not meet. E.g. Parabola and Hyperbola curve.
Open set : A
set U is called open if we can change any point x in U by a small amount in any
direction and still be inside U.
Operator : A
mathematical function such as addition, subtraction etc.
Opposite angles , sides
of polygon : Two
angles , sides , vertices having equal numbers of sides between them around a
polygon.
Open interval : An interval that does not
include its two endpoints.
Ordered pair “ A pair of numbers in which one
number is distinguished as the first number and the other as the second number
of the pair
Order of Derivative : It
indicates the number of times a variable is differentiated. E.g. d3x
/ dx3 is derivative of third order.
Order of Determinant : Determinant
of an n x n square array is an nth order determinant.
Order of Differential
equation: The number of the highest derivative in a differential equation.
Order of Group : The
number of elements in a finite group is called the order of the group.
Order of Matrix: The
order of matrix is the number of rows and columns.
Order of Root : An
equation may have repeated root and order of the root is the number of times
the root repeats.
Order relation : A
relation, that is a criterion of comparison between objects, which satisfies
the properties of reflexivity, anti-symmetry and transitivity.
Ordered Pair : A
collection of two not necessarily distinct objects, one of which is
distinguished as the first coordinate and the other as the second coordinate. (
a, b ) is the common notation.
Ordered Set : A
set in which the binary relation is antisymmetric, transitive and also total.
Ordered Triple : The
pair of numbers giving the location of a point. In three dimensional coordinate
system, three numbers written in the form (x,y,z) shows the location of a
point.
Ordinal number : A number indicating the
order of a thing in a series
Ordinate ; The y-coordinate of a point in
the plane.
Origin : The point in a coordinate plane
with coordinates (0,0).
Orthic triangle : The triangle whose
vertices are the feet of the altitudes of a given triangle.
Orthocenter : The point of intersection of
the altitudes of a triangle.
Orthogonal : 1.Two
geometrical objects are orthogonal if they meet at right angle.
2. It is also related to
a matrix whose transpose equals its inverse,
3. Also related to a linear transformation that preserves the
length of vectors.
Orthogonal Circle : Two circles intersecting
at right angle are called orthogonal circle.
Orthogonal projections: A
two dimensional graphic representation of an object in which the projecting
lines are at right angles to the phase of the projection.
Orthogonal Spheres : Two Spheres intersecting
at right angles.
Orthogonal trajectory: A family of curve in the
plane that intersects a given family of curves at right angles.
Orthogonal Vectors : Two
perpendicular vectors are orthogonal vectors and their dot product is zero.
Osculation : A point on a curve where
two branches have a common tangent.
Ounce : 1.
A unit of mass equal to 28.35 grams. 2. A unit of capacity called fluid ounce =
1/20 of a pint.
Oval : A
curve having the shape of a section of an egg.
Overdraft : Indicates
the negative balance in a current account in a bank.
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