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**COMMON TERMS IN
MATHEMATICS**

** **

**Dilara KORKMAZ ****(DORAK)**** &
Mehmet Tevfik DORAK**

** **

**See also** '**Common Concepts in Statistics****'
and 'CTK
Glossary of Mathematical Terms’**

**[Please note that the best
way to find an entry is to use the Find option from the Edit menu, or CTRL + F]**

**Absolute value****: The
magnitude of a number. It is the number with the sign (+ or -) removed and is
symbolised using two vertical straight lines ( |5| ). Also called modulus. **

**Abstract number****: A
number with no associated units.**

**Acute angle****: An angle
with degree measure less than 90. See **__MathWorld__**: **__Geometry__**: **__Trigonometry__**: **__Angles__**. **

**Addition****: The process
of finding the sum of two numbers, which are called ***addend*** and the ***augend*** (sometimes
both are called the addend). **

**Algorithm****: Any
mathematical procedure or instructions involving a set of steps to solve a
problem. **

**Arctan**: The inverse of the trigonometric function **tangent** shown
as arctan(x) or tan^{-1}(x). It is useful in vector conversions and
calculations. See **Wikipedia**:** Mathematics**: **Trigonometric Functions**.

**Arithmetic mean**: M = (x_{1} + x_{2}
+ .... x_{n}) / n (n = sample size).

**Arithmetic sequence****: A sequence of numbers in which each term (subsequent to
the first) is generated by adding a fixed constant to its predecessor.**

**Associative property****: A binary operation (*) is defined associative if, for
a*(b*c) = (a*b)*c. For example, the operations addition and multiplication of
natural numbers are associative, but subtraction and division are not.**

**Asymptote****: A straight
line that a curve approaches but never meets or crosses. The curve is said to
meet the asymptote at infinity. In the equation y = 1/x, y becomes infinitely
small as x increases but never reaches zero.**

**Axiom****: Any
assumption on which a mathematical theory is based. **

**Average****: The sum of
several quantities divided by the number of quantities (also called mean). **

**Avogadro's number**: The number of molecules in one
mole is called Avogadro’s number (approximately 6.022 × 10^{23}
particles/mole).

**Binary operation****: An
operation that is performed on just two elements of a set at a time.**

**Brownian motion****: See
an article (by Lee & Hoon) and an animation and a second one.. **

**Butterfly effect****: In a
system when a small change results in an unpredictable and disproportionate
disturbance, the effect causing this is called a butterfly effect.**

**Calculus****: Branch of
mathematics concerned with rates of change, gradients of curves, maximum and
minimum values of functions, and the calculation of lengths, areas and volumes.
It involves determining areas (integration) and tangents (differentiation),
which are mutually inverse. Also called **__real
analysis__**. See also **__Dr. Vogel's Gallery of Calculus Pathologies__**; ****MathWorld****: **__Calculus__**; **__Wikipedia__**:**** Mathematics**

**Cartesian coordinates****: Cartesian coordinates (x,y) specify the position of a
point in a plane relative to the horizontal x and the vertical y axes. The x
and y axes form the basis of two-dimensional Cartesian coordinate system.**

**Chaos:**** Apparent
randomness whose origins are entirely deterministic. A state of disorder and
irregularity whose evolution in time, though governed by simple exact laws, is
highly sensitive to starting conditions: a small variation in these conditions
will produce wildly different results, so that long-term behaviour of chaotic
systems cannot be predicted. This sensitivity to initial conditions is also
known as the ****butterfly effect**** (when a butterfly flaps its wings in Mexico, the result
may be a hurricane in Florida a month later). **

**Chord**: A straight line joining two points on a curve or a circle. See
also **secant line**.

**Circle**: A circle is defined as the set of points at a given distance
(or radius) from its centre. If the coordinates of the centre of a circle on a
plane is (a,b) and the radius is r, then (x-a)^{2} + (y-b)^{2}
= r^{2}. The equation that characterises a circle has the same
coefficients for x^{2} and y^{2}. The area of a circle is A = pr^{2}
and circumference is C = 2pr. A circle with centre (a,b) and radius r has parametric
equations: x = a + r.*cos ***q**
and
y = b + r.*sin ***q** (0 ≤
**q** ≤ 2p). A
‘tangent’ is a line, which touches a circle at one point (called the point of
tangency) only. A ‘normal’ is a line, which goes through the centre of a circle
and through the point of tangency (the normal is always perpendicular to the
tangent). A straight line can be considered a circle; a circle with infinite
radius and centre at infinity. See a **Lecture Note**, **BBC Bitesize**: **Circle**; **Wikipedia**:** Mathematics**: **Circle**; ** MathWorld**:

**Circumference****: A
line or boundary that forms the perimeter of a circle. **

**Closure property****: If
the result of doing an operation on any two elements of a set is always an
element of the set, then the set is closed under the operation. For example,
the operations addition and multiplication of natural numbers (the set) are
closed, but subtraction and division are not.**

**Coefficient****: A number or
letter before a variable in an algebraic expression that is used as a
multiplier. **

**Common denominator****: A denominator that is common to all the fractions within
an equation. The smallest number that is a common multiple of the denominators
of two or more fractions is the ****lowest (or least) common
denominator**** (LCM). **

**Common factor****: A
whole number that divides exactly into two or more given numbers. The largest
common factor for two or more numbers is their ****highest
common factor**** (HCF). **

**Common logarithm****:
Logarithm with a base of 10 shown as log _{10} [log_{10}10^{x}
= x].**

**Common ratio****: In a
geometric sequence, any term divided by the previous one gives the same common
ratio.**

**Commutative property****: A binary operation (*) defined on a set has the
commutative property if for every two elements, a and b, a*b = b*a. For
example, the operations addition and multiplication of natural numbers are
commutative, but subtraction and division are not.**

**Complementary angles****: Two angles whose sum is 90 ^{o}. See also **

**Complex numbers****: A
combination of real and imaginary numbers of the form ***a*** + ***bi*** where ***a*** and ***b*** are real numbers and ***i*** is the square root of -1 (see ****imaginary
number****). While real numbers can be represented as
points on a line, complex numbers can only be located on a plane. See Types of Numbers.**

**Composite number****: Any
integer which is not a prime number, i.e., evenly divisible by numbers other
than 1 and itself. **

**Compound fraction****: In a
fraction when both numerator and denominator are fractions, it is a compound
fraction. The value of a compound fraction is what the division of the
numerator by the denominator yields. **

**Congruent****: Alike in all
relevant respects.**

**Constant****: A quality of
a measurement that never changes in magnitude. **

**Coordinate****: A set of
numbers that locates the position of a point usually represented by*** (x,y***) values. **

**Cosine law**: For any triangle, the side lengths a, b, c
and corresponding opposite angles A, B, C are related as follows: a^{2}
= b^{2} + c^{2} - 2bc cosA etc. The law of cosines is useful to
determine the unknown data of a triangle if two sides and an angle are known. See ** Wikipedia**:

**Counting number****: An
element of the set C = {1,2,3,...}. **

**Cube root****: The factor
of a number that, when it is cubed (i.e., x ^{3}) gives that number. **

**Cubic equation****:
Graphs of equations in which the highest power of x is x ^{3}.**

**Curve****: A line that
is continuously bent.**

**Decimal****: A fraction having
a power of ten as denominator, such as 0.34 = 34/100 (10 ^{2}) or 0.344
= 344/1000 (10^{3}). In the continent, a comma is used as the decimal
point (between the unit figure and the numerator). **

**Degree of an angle**: A unit of angle equal to one
ninetieth of a right angle. Each degree ( ^{0 }) may be further
subdivided into 60 parts, called *minutes**
(60’)*, and in turn each minute may be subdivided into another 60
parts, called *seconds*
(60’’). Different types of angles are called acute (<90^{0})<
right (90^{0}) < obtuse (90^{0}-180^{0}) < reflex
(180^{0}-360^{0}). See also **radian **(the SI unit of
angle).

**Denominator****: The bottom
number in a fraction.**

**Derivative****: The
derivative at a point on a curve is the gradient of the tangent to the curve at
the given point. More technically, a function (***f'***(***x _{0}*

**Differential Equations**: Equations containing one or
more derivatives (rate of change). As such these equations represent the
relationships between the rates of change of continuously varying quantities.
The solution contains constant terms (constant of integration) that are not
present in the original differential equation. Two general types of
differential equations are ordinary differential equations (ODE) and partial
differential equations (PDE). When the function involved in the equation
depends upon only a single variable, the differential equation is an ODE. If
the function depends on several independent variables (so that its derivatives
are partial derivatives) then the differential equation is a PDE. See **Internet Resources for Differential Equations**;
**S.O.S
Mathematics Review: Differential
Equations.**

**Diameter****: A straight
line that passes from side to side thorough the centre of a circle.**

**Differential calculus****: Differentiation is concerned with rates of change and
calculating the gradient at any point from the equation of the curve,*** y = f(x)***. **

**Differential equation****: Equations involving total or partial differentiation
coefficients and the rate of change; the difference between some quantity now
and its value an instant into the future. See also ****Wikipedia**:** Mathematics**:** Differential Equations; and Differential
Equation Applet.**

**Digit****: In the
decimal system, the numbers 0 through 9.**

**Dimension****: Either the
length and/or width of a flat surface (two-dimensional); or the length, width,
and/or height of a solid (three-dimensional).**

**Distributive property****: A binary operation (*) is distributive over another
binary operation (^) if, a*(b^c) = (a*b)^(a*c). For example, the operation of
multiplication is distributive over the operations of addition and subtraction
in the set of natural numbers.**

**Division****: The
operation of ascertaining how many times one number, the ***divisor***, is contained in another, the ***dividend***. The result is the ***quotient***, and any number left over is called the ***remainder***. The dividend and divisor are also called the ***numerator*** and ***denominator***, respectively. **

**Dynamics****: The branch
of mathematics, which studies the way in which force produces motion. **

*e***: Symbol for
the base of natural logarithms (2.7182818285...), defined as the limiting value
of (1 + 1/m) ^{m}.**

**Equilibrium****: The state of
balance between opposing forces or effects. **

**Even number****: A natural
number that is divisible by two. **

**Exponent**** (****power****, ****index****): A number denoted by a small numeral placed above and to
the right of a numerical quantity, which indicates the number of times that
quantity is multiplied by itself. In the case of X ^{n}, it is said that
X is raised to the power of n. When a and b are non-zero real numbers and p and
q are integers, the following rules of power apply:**

a^{p}
x a^{q}
= a^{p+q}; (a^{p})^{q} = a^{pq}; (a^{1/n})^{m}
= a^{m/n}; a^{1/2} x b^{1/2} = (ab)^{1/2}.

**Exponential function****: A function in the form of f(x) = a ^{x} where x is
a real number, and a is positive and not 1. One exponential function is f(x) = **

**Extrapolation**: Estimating the value of a
function or a quantity outside a known range of values. See also **interpolation**.

**Factorial****: The product
of a series of consecutive positive integers from 1 to a given number (n). It
is expressed with the symbol ( ! ). For example, 5! = 5x4x3x2x1 = 120. As a
rule (n!+n) is evenly divisible by n. **

**Factor****: When two or
more natural numbers are multiplied, each of the numbers is a factor of the
product. A factor is then a number by which another number is exactly divided
(a divisor). **

**Factorisation:****
Writing a number as the product of its factors which are prime numbers.**

**Fermat's little theorem:**** If p is a prime number and b is any whole number, then b ^{p}-b
is a multiple of p (2^{3 }- 2 = 6 and is divisible by 3). **

**Fermat prime****: Any prime
number in the form of 2 ^{2n} + 1 (see also **

**Fibonacci sequence****: Sequence of integers, where each is the sum of the two
preceding it. 1,1,2,3,5,8,13,21,... The number of petals of flowers forms a
Fibonacci series. **

**Fractals****: Geometrical
entities characterised by basic patterns that are repeated at ever decreasing
sizes. They are relevant to any system involving self-similarity repeated on
diminished scales (such as a fern's structure) as in the study of chaos.**

**Fraction****: A type of
number written as a numerator over a denominator. The term usually applies only
to ratios of integers (like 2/3, 5/7). Fractions less than one are called ***common***, ***proper*** or ***vulgar*** fractions;
and those greater than 1 are called ***improper*** fraction. Because a quotient is the result of a division
operation, a fraction can also be called a quotient. **

**Function ( f)**

**Geometry** in **Wikipedia**
& **Geometry** in **MathWorld**.
See also **Geometric Fallacies**.

**Geometric mean**: G = (*x*_{1}.*x*_{2}...*x*_{n})^{1/n}
where n is the sample size. This can also be expressed as antilog ((1/n) S log *x*).
See **Applications of the Geometric Mean; Spizman, 2008: Geometric Mean in Forensic Economy**.

**Geometric sequence****: A sequence of numbers in which each term subsequent to the
first is generated by multiplying its predecessor by a fixed constant (the ****common
ratio****).**

**Goldbach conjecture****: Every even number greater than 4 is the sum of two odd
primes (32 = 13 + 19). Every odd number greater than 7 can be expressed as the
sum of three odd prime numbers (11 = 3 + 3 + 5).**

**Gradient****: The slope of
a line. The gradient of two points on a line is calculated as rise (vertical
increase) divided by run (horizontal increase), therefore, the gradient of a
line is equal to the tangent of the angle it makes with the positive x-axis
(y/x). See Curve Bank: Slope.**

**Greek alphabet****: For
list of Greek letters follow the link.**

**Harmonic mean**: Of a set of numbers (y_{1}
to y_{i}), the harmonic mean is the reciprocal of the arithmetic mean
of the reciprocal of the numbers [H = N / S (1/y)]. See also ** Wikipedia**:

**Hierarchy of operations****: In an equation with multiple operators, operations
proceed in the following order: (brackets), exponentiation,
division/multiplication, subtraction/summation and from left to right.**

**Highest common factor (HCF)****: The greatest natural number, which is a factor of two or
more given numbers. **

**Hypotenuse****: The longest
side of a right triangle, which lies opposite the vertex of the right angle.**

*i***: The square
root of -1 (an ****imaginary number****). **

**Identity element****: The
element of a set which when combined with any element of the same set leaves
the other element unchanged (like zero in addition and subtraction, and 1 in
multiplication or division).**

**Imaginary number****: The
product of a real number*** x*** and ***i***, where ***i*^{2}** + 1 = 0. A
complex number in which the real part is zero. In general, imaginary numbers are
the square roots of negative numbers. See Types of Numbers.**

**Improper fraction****: A
fraction whose numerator is the same as or larger than the denominator; i.e., a
fraction equal to or greater than 1, or, a fraction that represents a number
that contains a whole number in it.**

**Infinite****: Having no
end or limits. Larger than any quantified concept. For many purposes it may be
considered as the reciprocal of zero and shown as an 8 lying on its side (****∞****). **

**Infinitesimal****: A
vanishingly small part of a quantity. It equals almost zero. **

**Integer****: Any whole
number: positive and negative whole numbers and zero.**

**Integral calculus****: This
is the inverse process to differentiation; i.e., a function which has a given
derived function. For example, x ^{2} has derivative 2x, so 2x has x^{2}
as an integral. A classic application of integral is to calculate areas. **

**Integration****: The process
of finding a function given its derived function.**

**Intersection****: The
intersection of two sets is the set of elements that are in both sets. **

**Intercept**: A part of a line/plane cut off by another
line/plane. In mathematics, an intercept is the point where a line cuts
the y-axis (y-intercept).

**Interpolation**: Estimating the value of a
function or a quantity from known values on either side of it.

**Inverse function**: A function which 'does the
reverse' of a given function. For example, functions with the prefix arc are
inverse trigonometric functions; e.g. arcsin x for the inverse of sin(x). See
also **Wikipedia**:**
Mathematics**: **Inverse
Functions**** and Logarithmic Inverse Functions.**

**Irrational number****: A
real number that cannot be expressed as the ratio of two integers, and
therefore that cannot be written as a decimal that either terminates or
repeats. The square root of 2 is an example because if it is expressed as a
ratio, it never gives 2 when multiplied by itself. The numbers ****p**** = 3.141592645..., and ***e*** = 2.7182818... are also irrational numbers. See also ****transcendental
numbers****, ****real
numbers****, and Types of Numbers.**

**Iteration****: Repeatedly performing
the same sequence of steps. Simply, solving an algebraic equation with an
arbitrary value for the unknown and using the result to solve it again, and
again. **

**Law of indices****: The
laws of indices are: a ^{m} × a^{n} = a^{m+n}; a^{m}
÷ a^{n} = a^{m−n} if m is bigger than n; a^{m} ÷
a^{n} = 1/a^{n}-^{m}, if n is bigger than m^{ };
(a^{m})^{n} = a^{mn}; a^{1} = a; a^{0}
= 1.**

**Least squares method**: A method of fitting a straight
line or curve based one minimisation of the sum of squared differences
(residuals) between the predicted and the observed points. Given the data
points (x_{i}, y_{i}), it is possible to fit a straight line using a formula, which
gives the y=a+bx. The gradient of the straight line b is given by [S(x_{i} - m_{x})(y_{i}-m_{y})] / [(S(x-m_{x}))^{2}], where
m_{x} and m_{y} are the means for x_{i} and y_{i}. The intercept
a is obtained by m_{y} - bm_{x}. See **Wikipedia**: **Least
Squares**.

**Linear****: A model or function
where the input and output are proportional.**

**Linear expression**: A polynomial expression with
the degree of polynomial being 1, i.e., that does not include any terms as the power
of a variable. It will be something like, f(x)=2x^{1}+3, but not x^{2}+2x+4
(the latter is a **quadratic expression**). Linear equations are closely
related to a straight line.

**Literal numbers****:
Letters representing numbers (as in algebraic equations).**

**Logarithm****: The
logarithm of a number N to a given base b is the power to which the base must
be raised to produce the number N. Written as log _{b} N. Naturally, log_{b}
b^{x} = x. In any base, the following rules apply: log (ab) = log a + log b; log
(a/b) = log a - log b; log (1/a) = -log a; log a^{b} = b log a; log 1 =
0 and log 0 is undefined. See**

**Logistic model (map, sequence)**: **Wikipedia**:
**Logistic
Map**; **Cut-the Knot**: **Logistic Model**.

**Lowest term****: The terms
which a fraction has when it cannot be reduced further. For example, 1/5 have
the lowest terms for 5/25. **

**Matrix**: A matrix (plural: matrices) is a rectangular table of data.
See **Basics of Matrix Algebra**; **Linear Algebra Review**; ‘**Introduction
to Matrix Algebra’ Book**; **Matrix Algebra Tool** and **Interactive
Exercises**.

**Mechanics: Study of the
forces acting on bodies, whether moving (dynamics) or stationary (statics). **

**Mersenne prime****: A
Mersenne number, M _{p}, has the form 2^{p}-1, where p is a prime.
If M_{p} itself a prime, then it is called a Mersenne prime. There are
32 such primes known (i.e., not all primes yield a Mersenne prime). (See also **

**Mixed number****: A number
that contains both a whole number and a fraction (like 2****1/2****). **

**Mode****: Together
with mean and median, the mode is one of the measures of centrality of a
distribution. The mode is the value which occurs the most in the set. **

**Modulus****: The absolute
value of a number regardless of its sign, shown as | ***x*** | or mod ***x***. For a vector ***u***, the modulus | ***u*** | is used to indicate its magnitude calculated using Pythagoras’ theorem: | **

**Multiplication****: The
process of finding the ***product*** of two quantities that are called the ***multiplicand*** and the ***multiplier***.**

**Natural logarithm****:
Logarithm with a base of ***e***, usually abbreviated ***ln*** (***ln*** e ^{x }= x). **

**Natural number****: Any
element of the set N = {0,1,2,3,...} (positive integers). The inclusion of zero
is a matter of definition. See Types of Numbers.**

**Numerator****: The top
number in a fraction.**

**Obtuse angle****: An angle
with a degree measure between 90 and 180. See MathWorld:
Geometry: Trigonometry: Angles: Obtuse Angle.**

**Odd number****: A natural
number that is not divisible by 2. **

**Odds**: The odds of a success is defined to be the ratio of the probability
of a success to the probability of a failure (p/(1-p)). When the probability of
success if 50%, the odds is 1.

**Ordinate****: The vertical
coordinate on a plane.**

**Origin: The point on a graph that
represents the point where the x and y axes meet: (x,y) = (0,0).
**

**Parabola****: The graph
results from a ****quadratic function****.**

**Parallel****: Lines or
planes that are equidistant from each other and do not intersect. **

**Perfect number****: A
number which is equal to the sum of its proper divisors. 6, 28, and 496 are the
three of seven known perfect numbers. [6 is a perfect number because its proper
divisors (1,2, and 3) total 6.] See Types of Numbers.**

**Permutation****: A permutation
of a sequence of objects is just a rearrangement of them. **

**Perpendicular****: At
right angles to a line or plane.**

**Pi (****p****)****: The ratio of the circumference of a circle to its
diameter. The value of ****p**** is 3.1415926, correct to seven decimal places. The sum of
the three angles of a triangle is ****p**** radians. **

**Poisson distribution**: The probability distribution of
the number of occurrences of random (usually rare and independent) events in an
interval or time or space. See a **Lecture Note**.

**Polar equation**: A system which describes a point
in the plane not by its Cartesian coordinates (x,y) but by its polar
coordinates: angular direction (**q**) and
distance r from the origin (r, **q****)**.

**Polygon****: A geometric
figure that is bound by many straight lines such as triangle, square, pentagon,
hexagon, heptagon, octagon etc. **

**Polynomial****: An algebraic
expression of the form a _{0}x^{n} + a_{1}x^{n-1}
+ ... + a_{n}, where a_{0}, a_{1}, ..., a_{n} are
members of a field (or ring), and n is the degree of the polynomial. See Wikipedia:
Polynomial.
**

**Precalculus**: A foundational mathematical discipline.
Pre-calculus intends to prepare students for the study of calculus.
Pre-calculus typically includes a review of algebra, as well as an introduction
to exponential, logarithmic and trigonometric functions as preparation for the
study of calculus. See ** Wikipedia**:

**Prime factors****: Prime
factors of a number are a list of prime numbers the product of which is the
number concerned. When n=1, for example, f(x)=2x ^{1}+3, this is a linear
expression. If n=2, it is quadratic (for example, x^{2} + 2x + 4); if
n=3, it is cubic, if n=4, it is quartic and if n=5, it is quintic.**

**Prime number****: A natural
number other than 1, evenly divisible only by 1 and itself. The numbers
2,3,5,7,11,13,17,19,... Apart from 2, all primes are odd numbers and odd primes
fall into two groups: those that are one less than a multiple of four
(3,7,11,19) and those one more than a multiple of four (5,13,17). Every natural
number greater than 1 may be resolved into a product of prime numbers; eg 8316
= 2 ^{2} x 3^{3} x 7 x 11. See Types of Numbers, Prime
Numbers.**

Probability
distributions: See **Gallery of Probability Distributions** in **Engineering Statistics Handbook**.

**Product****: The result
of a multiplication problem.**

**Proper divisor****: Any
number divides another without leaving a remainder. **

**Proper fraction****: A
fraction in which the numerator is smaller than the denominator, i.e., a
fraction smaller than 1.**

**Proportion****: A type of
ratio in which the numerator is included in the denominator. It is the ratio of
a part to the whole (0.0 ≤ ****p**** ≤ 1.0) that may be expressed as a decimal fraction
(0.2), vulgar fraction (1/5) or percentage (20%). **

**Pythagoras’ Theorem**: For any right-angled triangle,
the square on the hypotenuse equals the sum of the squares on the other two
sides. See . ** Wikipedia**:

**Quadratic equation**: An algebraic equation of the
second degree (having one or more variables raised to the second power). The general quadratic equation is ax^{2} + bx + c = 0 (in
standard form), in which a, b, and c are constants (or parameters) and ‘a’ is
not equal to 0. The factored form gives the roots (where the parabola curs the y=zero
line on the x-axis). Quadratic formula is used to calculate the
roots of a quadratic function. The term quadratic comes from the Latin word quadratum,
which means ‘square’. See **Quadratic Calculator**.

**Quadratic functions/graphs**: Functions (and their graphs) of equations in which the highest
power of x is x^{2}. The resulting curve is called a parabola. If there
is no calculable solution, i.e., no roots that are the points on x axis where
the graph hits it, that means the graph does not touch the x axis. While a quadratic
(squared) function has variables at most at the second degree |(i.e., squared),
there are also cubic, fourth degree and higher degree polynomials (functions).

**Quotient****: The result
obtained from a division operation, i.e., the result given by dividing a
dividend by a divisor See ****HMH****). **

**Radian (rad)**: The SI unit for measuring an angle formally
defined as ‘the angle subtended at the centre of a circle by an arc equal in
length to the radius of the circle’ (the angle of an entire
circle is 2p radians;
p radians
equal 180^{0} (sum of the three angles of a triangle); this is the
basis of circumference of a circle formula 2pr). Sum of angles of a triangle
equals p radians.
See **an Animation of Radian**.

**Radius****: The distance
between the centre of a circle and any point on the circle's circumference. **

**Range****: A measure of
the spread of data. Standard deviation (SD) and inter-quartile range (IQR) are
the other commonly used measures of spread.**** **

**Rate****: The relationship
between two measurements of different units such as change in distance with
respect to time (miles per hour). **

**Ratio****: The
relationship between two numbers or measurements, usually with the same units
like the ratio of the width of an object to its length. The ratio a:b is
equivalent to the quotient a/b.**

**Rational number****: A
number that can be expressed as the ratio of two integers, e.g., 6/7. The set
of rational numbers is denotes as ‘****Q****’ for quotient. See Types of Numbers.**

**Real number****: ****Rational**** (fractions) and ****irrational**** (numbers with non-recurring decimal representation)
numbers. The set of real numbers is denoted as ‘****R****’ for real. In computing, any number with a fractional (or
decimal) part. Basically, real numbers are all numbers except imaginary numbers
(such as the square root of -1). See Types of Numbers. **

**Reciprocal****: The
multiplicative inverse of a number (i.e., 1/x). It can be shown with a negative
index (x ^{-1}).**

**Reducing a fraction****: Simplifying a fraction to its ****lowest
terms**** like converting (reducing) 5/25 to 1/5,
where it can no longer be simplified. Reduction is, therefore, rewriting a fraction
(or even a function) in a simpler form. **

**Reflex angle****: An angle
with a degree measure between 180 and 360. See MathWorld:
Geometry: Trigonometry: Angles: Reflex Angle.**

**Repeating decimal****: A
decimal that can be written using a horizontal bar to show the repeating
digits. **

**Right angle****: An angle
with a degree measure 90. An angle which is not an right angle is called
oblique angle. See MathWorld: Geometry: Trigonometry: Angles: Right
Angle. **

**Root**: If, when a number is raised to the power of n gives the answer
a, then this number is the n^{th} root of a (a^{1/n}).

**Rounding****: To give a close
approximation of a number by dropping the least significant numbers. For
example, 15.88 can be rounded up to 15.9 (or 16) and 15.12 can be rounded down
to 15.1 (or 15). In R, ceiling() and floor() functions are used for these
purposes.**

**Scalar****: A real
number and also a quantity that has magnitude but no direction, such as mass
and density. See Wikipedia:
Scalar.
**

**Scientific notation (exponential notation, standard form**): One
way of writing very small or very large numbers. In this notation, numbers are
shown as (0<N<10) x 10^{q}. An equivalent form is N.Eq. For
example; 365,000 is 3.65x10^{5} or 3.65E5. See **Wikipedia**:
**Scientific Notation**.

**Secant line**: A line that intersects a curve. The **intercept**
is a **chord** of the curve. ** Wikipedia**:

**Sequence****: An ordered set
of numbers derived according to a rule, each member being determined either
directly or from the preceding terms. See Real Analysis Glossary: Sequences & Context.**

**Sigma (S, s )****:
Represents ****s****ummation (****S****, ****s****). See Greek Letters.**

**Significant figure (s.f.)**: The specific degree of accuracy
denoted by the number of digits used. For example 434.64 has five s.f. but at 3
s.f. accuracy it would be shown as ‘435 (to 3 s.f.)’. From the left, the first
nonzero digit in a number is the first significant figure, after the first
significant number, all digits, including zeros, count as significant numbers
(Both 0.3 and 0.0003 have 1 s.f.; both 0.0303 and 0.303000 have 3 s.f.). If a
number has to be reduced to a lower s.f., the usual rounding rules apply
(2045.678 becomes 2046 to 4 s.f. and 2045.7 to 5 s.f.). The final zero even in
a whole number is not a s.f. as it only shows the order of magnitude of the
number (2343.2 is shown as 2340 to 3 s.f.).

**Sine law**: For any triangle, the side lengths a, b, c
and corresponding opposite angles A, B, C are related as follows: sin A / a =
sin B / b = sin C / c. The law of sines is useful for computing the lengths of
the unknown sides in a triangle if two angles and one side are known. See **Wikipedia**:
**Law
of Sines**.

**Skew lines****: Two lines in
three-dimensional space, which do not lie in the same plane (and do not
intersect). **

**Stationary point****: Point
at which the derivative of a function is zero. Includes maximum and minimum
turning points, but not all stationary points are turning points. **

**Straight line**: A straight line is
characterised by an equation (y = mx + c), where (0, c) is the intercept and m
is the gradient/slope. One of the methods for fitting a straight line is the **least
squares method**.

**Subtend****: To lie
opposite and mark out the limits of an angle.**

**Subtraction****: The inverse
operation of addition. In the notation a - b = c, the terms a, b, and c are
called the ***minuend***, ***subtrahend*** and ***difference***, respectively.**

**Supplementary angles****: Two angles whose sum is 180 ^{o}. See also **

**Tangent**: The tangent of an angle in a right-angled
triangle is the ratio of the lengths of the side opposite to the side adjacent
[tan(x) = sin(x) / cos(x)]. A tangent line is a line, which touches a given
curve at a single point. The slope of a tangent line can be approximated by a
secant line. See **Wikipedia**:
**Tangent**;
**MathWorld**:
**Tangent**.

**Tangent law**: For any triangle, the side lengths a,
b, c and corresponding opposite angles A, B, C are related as follows: (a+b) /
(a-b) = {tan[1/2(A+B)]} / {tan[1/2(A-B)]}. See **Wikipedia**:
**Law
of Tangents**.

**Taylor Expansions**: A special
kind of power series used as a basis of approximation. A **Taylor expansion**
(series) is the sum of functions based on continually increasing derivatives
(till one gets a zero value) if they exist. The accuracy of the approximation
improves as the order of the approximation is increased (like fourth derivative
or fifth). As the nonlinearity of the function increases the higher order terms
become more important (i.e., the error increases as fewer terms of the Taylor
series are included in the approximation). The main use of Taylor polynomial
approximations is not to estimate the value of a function at a given point
(this can be done by a calculator) but to approximate functions over an
interval (representing complicated nonlinear functions as series ‘infinite
polynomials’ makes life easier; see for example: **Applications of Taylor
Series**). **Maclaurin’s expansion** is a special case of Taylor’s
expansion. **Wikipedia**: **Taylor
Series**; **MathWorld**: **Taylor
Series**; a Lecture Note on **Taylor Expansions by Luca Sbano**; **Taylor Polynomials Quizzes**;
**Taylor Series Applet**; **Taylor
Polynomials Applet**; and **Taylor Polynomials**.

**Transcendental number****: A real number that does not satisfy any algebraic
equation with integral coefficients, such as x ^{3} - 5x + 11 = 0. All
transcendental numbers are irrational and most irrational numbers
(non-repeating, non-terminating decimals) are transcendental. Transcendental
functions (such as exponential, sine and cosine functions) can burst into chaos
under certain circumstances. See Types of Numbers. **

**Triangle****: A
three-sided figure that can take several shapes. The three inside angles add up
to 180 ^{o}. Triangles are divided into three basic types: obtuse, right
and acute; they are also named by the characteristics of their sides:
equilateral, isosceles, and scalene. The area of a triangle is 1/2 x
perpendicular height x base.**

**Trigonometry**: The branch of mathematics that is concerned
with the trigonometric functions. Trigonometric identities are the results that
hold true for all angles. Sin, Cos and Tan are trigonometric ratios; Cosec, Sec
and Cot are reciprocal of trigonometric ratios; Arcsin (sin^{-1}),
Arccos (cos^{-1}) and Arctan (tan^{-1}) are inverse of
trigonometric functions. See **Syvum Math**: **Trigonometric Functions**; **CTK:
Trigonometric Functions**; **Trigonometry Realms**; **S.O.S. Math**:
**Trigonometric Identities Table**; ** Wikipedia**:

**Union****: The union of
two sets is the set of elements that are in either of the two sets (compare
with intersection).**

**Unit****: A standard
measurement. **

**Variable****: An amount
whose value can change. **

**Vector**: A quantity characterised by a magnitude and a direction
represented by (1) column form: two numbers (components) in a 2x1 matrix; (2)
geometric form: by arrows in the (x,y)-plane; or (3) component form: the
Cartesian unit vectors ** i** (x-axis unit vector) and

**Vertex****: The point
where lines intersect.**

**Whole number****: Zero or any
positive number with no fractional parts.**

**Links to Mathematics and
Statistics Sites**

**MathWorld:
Algebra - Calculus
- Geometry - Probability
- Animated GIFs
**

**MathWay: Basic Math - Pre-Algebra - Algebra – Trigonometry - Precalculus - Calculus - Statistics - Graphing**

**Cut-the-Knot Math
Glossary** **Real Analysis
Glossary** **MathWords**

**Paul's Online Math Notes
Mr Mathematics: Math
Lessons Dr Nic’s Maths
& Stats **

**IB Math Tuition** **NCTM Classroom Resources**
**Interactive Mathematics**:
**AI-based Problem
Solver** **BBC Bitesize**: **Maths**

**S.O.S
Mathematics Review:** **Algebra** - **Trigonometry** - **Calculus**

** Simulations: Math /
Chemistry
/ Biology
**

** Wikipedia**:

**Maths Apps: Microsoft Math Solver (online and App)
NaNSolvers
Math Solver PhotoMath Geometry Pad **

**Open Source Math Software: Sage R (RMath / Math with
R / Mathematics)
Phyton (Python Math / Mathematical
Python) **

** MathCad
Wolfram Mathematica
Matlab Maple **

*Compiled
by ***Dilara DORAK (KORKMAZ) & ****Mehmet Tevfik DORAK**

** **

*Last updated on 25
August 2023*

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