Quick Reference

Glossary of Mathematics | Measurement | Areas and Volumes

Mathematics is the group of sciences concerned with the study of number, quantity, shape and space and their relationships with each other. The four main divisions of mathematics are arithmetic, algebra, geometry and calculus.

algebra. The substitution of symbols and letters for numerical variables and constants. These symbols can be manipulated in the same way as numbers and form the basis for most mathematical calculations.

abscissa. The x-coordinate of a point in a 2-dimensional coordinate system.

absolute value. The positive value for a real number, disregarding the sign. Written |x|. For example, |3|=3, |-4|=4, and |0|=0.

algebraic equation. An equation of the form
*f*(x)=0 where f is a polynomial.

algebraic number. A number that is the root
of an algebraic polynomial. For example, sqrt(2) is an algebraic number
because it is a solution of the equation *x*^{2} = 2.

angles. The inclination of one line to another. Angles are measured in degrees or radians. One revolution of a circle = 360° = 2pi radians.

annulus. The region enclosed by two concentric circles.

arithmetic. The manipulation of numbers by addition, subtraction, multiplication, division and extraction of roots.

arithmetic mean. The arithmetic mean of n numbers is the sum of the numbers divided by n.

average. Typically this refers to the arithmetic mean.

base. The number of single digit numerals
in a counting system. The decimal system has base 10 (0,1,2,...,9) and the
binary system base 2 (0 and 1). In the expression x^{y}, x is called
the base and y is the exponent.

binary number. A number written to base 2.

binary operation. A binary operation is an operation that involves two operands. For example, addition and subtraction are binary operations.

binomial. An expression that is the sum of
two terms such as *a + b* or *a - b*.

binomial coefficient. The coefficients of
x in the expansion of (x+1)^{n}.

bisect. To cut in half.

calculus. The study of continuous change in functions. The two branches of calculus are differentiation and integration. Differentiation is the determination of the rate of change in a function. Integration is the summation of the changes in a function, normally regarded as the area under a curve.

catenary. A curve whose equation is y = (a/2)(e
^{x/a }+ e ^{-x/a}). A chain suspended from two points forms
this curve.

central angle. An angle between two radii of a circle.

chord. The line joining two points on a curve is called a chord.

circle. The set of points equidistant from a given point (the center). A circle is the path proscribed by point that rotates about a fixed origin.

circular cone. A cone whose base is a circle.

circumcenter. The circumcenter of a triangle is the center of the circumscribed circle.

circumcircle. The circle circumscribed about a figure.

coefficient. The number part of an algebaric
term: in 4*x*², 4 is the coefficient.

complementary angles. Two angles whose sum
is 90^{o}.

complex number. The sum of a real number and an imaginary number, for example 3+4i where i=sqrt(-1).

concave. Curved from the inside.

congruent figures. two geometric figures that are identical in size and shape.

conic section. The cross section of a right circular cone cut by a plane. An ellipse, parabola, and hyperbola are conic sections.

coordinate geometry. System of geometry where points, lines, shape and surfaces are represented by algebraic expressions. These expressions can be presented as graphical solutions (graphs) in two of three dimensions.

cubic equation. A polynomial equation of degree 3.

decimal number. A number written to the base 10.

deficient number. A positive integer that is larger than the sum of its proper divisors.

degree. The degree of a term in one variable
is the exponent of that variable. For example, the degree of 7x^{5};
is 2.

denominator. In the fraction x/y, x is called the numerator and y is called the denominator.

diagonal. In a polygon, the line segment joining a vertex with another (non-adjacent) vertex is called a diagonal.

diameter. The longest chord of a figure. In a circle, a diameter is a chord that passes through the center of the circle.

differential calculus. That part of calculus that deals with the opeation of differentiation of functions.

digit. In the decimal system, one of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

dihedral angle. The angle formed by two planes meeting in space.

dividend. In the expression "a divided by b", a is the divident and b is the divisor.

divisor. In the expression "a divided by b", a is the divident and b is the divisor.

dodecaedron . A solid having 12 plane faces.

domain. The domain of a function f(x) is the set of x values for which the function is defined.

duodecimal number system. The system of numeration with base 12.

elementary function. one of the functions: rational functions, trigonometric functions, exponential functions, and logarithmic functions.

ellipse . A closed plane curve generated
by a point moving in such a way that the sums of its distances from two
fixed points is a constant: a plane section of a right circular cone that
is a closed curve. A plane figure whose equation is: x^{2}/a^{2}+y^{2}/b^{2}=1.

ellipsoid. A solid figure whose equation
is x^{2}/a^{2}+y^{2}/b^{2}+z^{2}/c^{2}=1.

equation. A set of mathematical symbols split by an equals sign (=). Terms are symbols that are added or subtracted. Factors are symbols that are multiplied or divided.

equilateral polygon. A polygon all of whose sides are equal.

equilateral triangle. A triangle with three equal sides.

even number. An integer that is divisible by 2.

exponent. In the expression x^{y},
x is called the base and y is called the exponent. See also index.

exponential function. The function f(x)=e^{x}.

expoential function to base a. The function
f(x)=a^{x}.

factor. The integer divisors of a number. 1, 2 and 7 are the factors of 14.

factorial. n! (read n factorial) is equal to the product of the integers from 1 to n.

Fermat number. A number of the form 2^{(2n)}+1.

Fibonacci number. A member of the sequence 0, 1, 1, 2, 3, 5,... where each number is the sum of the previous two numbers.

formula. A concise statement expressing the symbolic relationship between two or more quantities.

fraction. An expression of the form a/b.

frequency. The number of times a value occurs in some time interval.

frustum. For a given solid figure, a related figure formed by two parallel planes meeting the given solid. In particular, for a cone or pyramid, a frustum is determined by the plane of the base and a plane parallel to the base. NOTE: this word is frequently incorrectly misspelled as frustrum.

Gaussian curve. A normal curve.

geometry. The study of two and three dimensional space.

geometric progression. A sequence in which the ratio of each term to the preceding term is a given constant.

geometry. The branch of mathematics that deals with the nature of space and the size, shape, and other properties of figures as well as the transformations that preserve these properties.

golden ratio. (1+Sqrt[5])/2.

graph. A graph is a set of points (called vertices) and a set of lines (called edges) joinging these vertices.

great circle. A circle on the surface of a sphere whose center is the center of the sphere.

greatest common divisor/factor. The greatest common divisor of a sequence of integers, is the largest integer that divides each of them exactly.

hexagon . A plane figure having six sides and six angles.

hyperbola. A plane curve generated by a point
so moving that the difference of the distances from two fixed points is
a constant: a curve formed by the intersection of a double right circular
cone with a plane that cuts both halves of the cone. A curve with equation
x^{2}/a^{2}-y^{2}/b^{2}=1. or ^{2}+y^{2}/b^{2}-z^{2}/c^{2}=-1.

hypotenuse. The longest side of a right triangle.

icosaedron . A polyhedron having 20 faces.

identities.. Algebraic relationships:

imaginary number. A complex number of the form xi where x is real and i=sqrt(-1).

imaginary part. The imaginary part of a complex number x+iy where x and y are real is y.

index. A superscript indicating the number of times a number is multiplied by itself. Examples of indexes are:

inequality. The statement that one quantity is less than (or greater than) another.

infinitesimal. A variable that approaches 0 as a limit.

inflection. A point of inflection of a plane curve is a point where the curve has a stationary tangent, at which the tangent is changing from rotating in one direction to rotating in the oppostie direction.

integer. One of the numbers ..., -3, -2, -1, 0, 1, 2, 3, ... A whole number.

irrational number. Any real number that is
not rational, that is it cannot be written as a terminating or repeating
decimal. These include p, *e* and Ö2.

isosceles tetrahedron. A tetrahedron in which each pair of opposite sides have the same length.

isosceles triangle. A triangle with two equal sides.

isosceles trapezoid. Ain which the two non-parallel sides have the same length.

least common multiple. The least common multiple of a set of integers is the smallest integer that is an exact multiple of every number in the set.

linear function. A function of the form y=ax+b.

line segment. The part of a line between two given distinct points on that line (including the two points).

logarithm. A logarithm is the exponent of
a number to a specified base. If *bn = x* then *n* is the logarithm
of *x* to the base *b*.

lowest common denominator. The smallest number that is exactly divisible by each denominator of a set of fractions.

major axis. The major axis of an ellipse is it's longest chord.

maximum. The largest of a set of values.

mensuration. The act of measuring. Geometry applied to the computation of lengths, areas, or volumes from given dimensions or angles.

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.

multiple. The integer b is a multiple of the integer a if there is an integer d such that b=da.

natural number. Any one of the numbers 1, 2, 3, 4, 5, ... .

negative number. A number smaller than 0.

normal. perpendicular

numbers. Numbers are either real or complex.
Real numbers are those used for counting and range from - to + . Complex
numbers are those that contain Ö-1 , usually
denoted *i* so that *i*^{2} = -1.

number line. A line on which each point represents a real number.

numerator. In the fraction x/y, x is called the numerator and y is called the denominator.

oblique angle. an angle that is not 90^{o}

oblique triangle. A triangle that is not a right triangle.

obtuse angle. an angle larger than 90^{o}
but smaller than 180^{o}

obtuse triangle. A triangle that contains an obtuse angle.

octagon . A plane figure having eight angles and eight sides.

octoedron . A solid bounded by eight plane faces.

odd number. An integer that is not divisible by 2.

ordinate. The y-coordinate of a point in the plane.

origin. The point in a coordinate plane with coordinates (0,0).

parabola . A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line: the intersection of a right circular cone with a plane parallel to an element of the cone.

parallel . Lying or extending alongside of one another and always at the same distance apart; continuously equidistant: said of two or more lines, surfaces, or concrete things.

parallelogram . A four-sided rectilineal figure whose opposite sides are parallel but the internal angles are greater or less than 90 degrees.

percentage. A number represented as a fraction of 100. Percentages may be written as a proper fraction or as a decimal fraction, ie: 48% is 48/100 or 0.48.

perfect number. A positive integer that is equal to the sum of its proper divisors. For example, 28 is perfect because 28=1+2+4+7+14.

perpendicular . Situated at right angles to the plane of the horizon, or directly up or down; vertical.

prime. A prime number is an integer larger than 1 whose only positive divisors are 1 and itself.

Pythagorean triangle. A right triangle whose sides are integers.

platonic solids (polyhedrons). Solids with
faces of equal shape. There are only five:

Tetrahedron - 4 triangular faces Cube - 6 square faces
Octahedrons - 8 triangular faces Dodecahedron - 12 pentagonal faces
Icosahedron - 20 triangular faces

polygons. Figures with sides of equal length
and equal internal angles. The first 10 are:

Triangle - 3 sides Quadrangle - 4 sides Pentagon -
5 sides Hexagon - 6 sides Heptagon - 7 sides Octagon -
8 sides Nonagon - 9 sides Decagon -10 sides
Dodecagon - 12 sides Icosagon - 20 sides

power. A general term for squares, cubes etcetera. See index.

primes. Numbers whose only factors are 1 and itself. Unity (1) is not a prime. The first seven primes are: 3, 5, 7, 11, 13, 17 and 19.

probability. The likelyhood that something will happen.

Pythagoras' Theorem. For any right-angled
triangle, the square of the longest side (*R*) is equal to the sum
of the squares of the other two sides (*x* and *y*)

QED. Abbreviation for quod erat demonstrandum, used to denote the end of a proof.

quadrangular prism. A prism whose base is a quadrilateral.

quadrangular pyramid. A pyramid whose base is a quadrilateral.

quadrant. Any one of the four portions of the plane into which the plane is divided by the coordinate axes.

quadratic equation. An equation of the form
f(x)=0 where f(x) is a second degree polynomial. That is, *ax ^{2}
+ bx + c = 0*.

quadrilateral. A geometric figure with four sides.

quotient. The result of a division.

radians. Circular measure where the circumference
of a circle is divided in to a number of arcs each equal in length to the
radius. There are 2pi radians in 1 revolution. One radian =
180/pi degrees. One radian is approximately 57.3^{o}.

ratio. quotient of two numbers.

rational number. A rational number is a number that is the ratio of two integers. All other real numbers are said to be irrational. All rational numbers can be written as a terminating or repeating decimal.

real part. The real number x is called ther eal part of the complex number x+iy where x and y are real and i=sqrt(-1).

reciprocal. A number divided into 1. The reciprocal of 7 is 1/7.

reflex angle. An angle between 180^{o}
and 360^{o}.

rhombus. A parallelogram with four equal sides.

right angle. an angle formed by two perpendicular
lines; a 90^{o} angle.

right triangle. A triangle that contains a right angle.

scalene triangle. A triangle with unequal sides.

secant. A straight line that meets a curve in two or more points.

sequence. A collection of numbers in a prescribed
order: a_{1}, a_{2}, a_{3}, a_{4}, ...

series. The sum of a finite or infinite sequence

similar figures. Two geometric figures are similar if their sides are in proportion and all their angles are the same.

spherical trigonometry. The branch of mathematics dealing with measurements on the sphere.

square. A quadrilateral with 4 equal sides and 4 right angles.

square number. A number of the form n^2.

supplementary. Two angels are supplementary
of they add up to 180^{o}.

tangent. A line that meets a smooth curve at a single point and does not cut across the curve.

torus. A geometric solid in the shape of a donut.

transcendental number. A number that is not algebraic.

trapezium. A quadrilateral in which no sides are parallel.

trapezoid. A quadrilateral in which two sides are parallel.

triangle. A geometric figure with three sides.
The sum of the internal angles of any triangle is 180 . The four
basic triangle types are:

right-angled - one angle equal to 90^{o} isosceles
- two sides of equal length equilateral -all sides of equal
length scalene -no equality in any of the sides.

trigonometry. The branch of mathematics exploiting the properties of right angled triangles. The trigonometric identities are: sine, cosine and tangent and are determined as follows:

truncated pyramid. A section of a pyramid between its base and a plane parallel to the base.

twin primes. Two prime numbers that differ by 2. For example, 11 and 13 are twin primes.

unilateral surface. A surface with only one side, such as a Moebius strip.

unit circle. A unit circle is a circle with radius 1.

unit cube. A cube with edge length 1.

unit fraction. A fraction whose numerator is 1.

unit square. A unit square is a square of side length 1.

unity. one

volume. The measure of spce occupied by a solid body.

vulgar fraction. A common fraction.

whole number. A natural number.

x-axis. The horizontal axis in the plane.

x-intercept. The point at which a line crosses the x-axis.

y-axis. The vertical axis in the plane.

y-intercept. The point at which a line crosses the y-axis.