SOME MATHEMATICAL TERMS:

• 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 x² = 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.
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• 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 4x², 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 7x⁵; 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: x²/a²+y²/b²=1.
• ellipsoid. A solid figure whose equation is x²/a²+y²/b²+z²/c²=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 x²/a²-y²/b²=1. or ²+y²/b²-z²/c²=-1.
• hypotenuse. The longest side of a right triangle.
• icosaedron . A polyhedron having 20 faces.
• identities..  Algebraic relationships:
•     (a + b)² = a² + 2ab + b²   
•     (a + b)(a - b ) = (a² - b²)     
•     a(b + c) = ab + ac     
•     1/a - 1/b = (b -a)/(ab) 
• 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:
•     aⁿ x a^m = a^{(n +m)}   
•     a^-n = 1/aⁿ    
•     a^1/n = ⁿÖa     
•     (aⁿ)^m = a^nm  
• 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 i² = -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.
• 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, ax² + 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: a₁, a₂, a₃, a₄, ...
• 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:
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• 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.