A Dictionary of Mathematical Terms

A

abacus an oriental (far east) counting device and calculator.

abelian or Hyperelliptic Function is a generalisation of an elliptic function. It is a function of two variables with four periods. In a similar way to an elliptic function it can also be regarded as the inverse function to certain integrals ( called abelian or hyperelliptic integrals ) of this form where R is a polynomial of degree greater than 4.

abscissa the x-coordinate in a normal two-dimensional coordinate system. The abscissa of the point (a, b) is 'a'.

absolute value The symbol for absolute value is usually a pair of vertical lines containing the number. The symbolism |4| is read as "The absolute value of four". The absolute value of a real number is its distance from zero, so |4| = |-4| = 4 ... which is the distance of the number from zero. The positive value.

abundant number is an integer for which the sum of its proper divisors is greater than the number itself. i.e., the proper divisors of 12 are 1, 2, 3, 4, 6 which sum to 16. See also: perfect number deficient number

acceleration the rate of change, the derivative of velocity. If position is represented by s(t), then velocity is s'(t) and the acceleration is s"(t). The change in velocity divided by the change in time. See Acceleration, compare units used.

acute angle a positive angle that measures less than 90 degrees ... an angle in the range of 0 degrees to 90 degrees. See complementary

acute triangle a triangle in which each of its angles measures less than 90 degrees ... a triangle in which all the angles are acute.

additive identity The number zero is called the additive identity because when you add it to a number, N, the result you get is the same number, N ... 0 + 5 = 5.

additive inverse the additive inverse of a number, N, is the number that when you add it to N, the result that you get is zero.  The additive inverse of 7 is -7 ... 7 + -7 = 0.

adjacent angles two angles that share both a common side and vertex.

altitude the perpendicular distance measured from the base of a figure to the highest point of the figure.  

Amicable numbers are a pair of numbers a, b for which the sum of the proper divisors of a equals b and the sum of the proper divisors of b is equal to a.

amplitude half the difference between the largest and smallest function value of a periodic function.

Analytic number theory is number theory studied using methods like infinite series, convergence, etc. taken from analysis and especially from Complex analysis. It contrasts with algebraic number theory.

angle the union of two rays which have a common endpoint (starting point).

antecedent the hypothesis of conditional statement.  The "if" part of an "if-then" statement.

antiderivative the antiderivative of a function, f(x), is a function, F(x), whose derivative is f(x). Also called the indefinite integral.

apogee is the point where a heavenly body is furthest away from the centre of its orbit. The nearest point is called the perigee.

apothem the perpendicular distance from the center to a side of a regular polygon.

apotome is one of Euclid's categories of irrational numbers. A number of the form (A - B) is called a apotome. The corresponding number with a + sign is called a binomial

area The general term for the measurement of the amount of surface space that is occupied or covered by a two dimensional figure ... from Latin.

arc the set of points on a circle that lie in the interior of a central angle.

arc length given by the following:

arccos If x = cos y, then y = arccos x.  The inverse of the cosine function.

arccsc If x = csc y, then y = arccsc x.  The inverse of the cosecant function.

arccot If x = cot y, then y = arccot x.  The inverse of the cotangent function.

arcsec If x = sec y, then y = arcsec x.  The inverse of the secant function.

arcsin If x = sin y, then y = arcsin x.  The inverse of the sine function.

arctan If x = tan y, then y = arctan x.  The inverse of the tangent function.

argument The independent variable in a function.

arithmetic mean The sum of a set of numbers divided by the number of numbers. Also called the average.

arithmetic sequence a sequence of numbers of the form a, a + b, a + 2b, a + 3b, ... , a + (n - 1)b. There is a constant 'adder' between two terms; there is a constant 'difference' between two terms.  Ex: 4, 7, 10, 13, 16, 19, 22, 25, ...

arithmetic series the sum of an arithmetic sequence.  Ex: Given the arithmetic sequence 3, 5, 7, 9, 11 ... the arithmetic series would be 3 + 5 + 7 + 9 + 11.

Ascension The rising of a star above the horizon

associative property of addition (a + b) + c = a + (b + c)

associative property of multiplication (a * b) * c = a * (b * c)

asymptote a straight line that is a close approximation to a curve as the curve is drawn; in other words, a line that a curve or function gets close to but never crosses. The two most common types of asymptotes are horizontal and vertical.

average same as arithmetic mean.

axiom a statement that is assumed to be true without proof.   Postulate.

axis of symmetry a line that passes through a figure in such a way or image of the part of the figure on the other side of the line. that the part of the figure on one side of the line is a mirror reflection

azimuth The azimuth is the arc of the horizon between the meridian (the direction North) and a vertical circle passing through a heavenly body.

B

Bernoulli Numbers were defined by Jacob Bernoulli in connection with evaluating sums of the form can be generated using the formula: The sequence B₀ , B₁ , B₂ ,... x/(e^x - 1) = (B_nxⁿ)/n!     though various different notations are used for them. The first few are: B₀ = 1 , B₁ = -¹/₂ , B₂ = ¹/₆ , B₄ = -¹/₃₀ , B₆ = ¹/₄₂ , ... They occur in many diverse areas of mathematics including the series expansions of tan(x).

beta function B (m, n) is defined to be the integral:     It can be defined in terms of the gamma function by:     Many integrals can be reduced to the evaluation of Beta functions.

Bieberbach Conjecture is the conjecture which states that if f is a complex function given by the series f (z) = a₀ + a₁z + a₂z² + a₃z³ + ...
which maps the unit disc conformally in a one-one way then |a_n|n |a₁| for each n. It can be expressed as: The nth coefficient of a univalent function can be no more than n.

binary number system the number system that uses only 0's and 1's.  The places in the binary numbers are:   ... 2ⁿ ... 2⁵=32, 2⁴=16, 2³=8, 2²=4, 2¹=2, 2⁰=1. See Number Base

binomial an algebraic expression that is the sum of two terms (two monomials).

binomial coefficients are the coefficients of powers of x in the expansion of (1 + x)ⁿ.
We have
where the binomial coefficient is the number of ways of choosing an (unordered) subset of size k from a set of size n.
The binomial coefficients are the entries in the Pascal triangle.

binomial theorem the theorem that tells shows the expansion of the general expression (a + b)ⁿ ... the binomial (a + b) raised to the n^th power: :
(x + y)ⁿ = xⁿ + a_n-1x^n-1y + a_n-2x^n-2y² + ... + yⁿ Where there is a descending power of the first term ... and an ascending power of the second term ...... with numeric values of Pascal's Triangle.

biquadratic residue A number m is a biquadratic residue modulon if m = r⁴ modulo n for some r.

bisect to cut or divide something in half.

Boolean algebra is an algebra in which the binary operations are chosen to model the union and intersection operations in Set Theory. For any set A, the subsets of A form a Boolean algebra under the operations of union, intersection and complement.

brachistochrone is a curve such that a particle descending along the curve under gravity will travel from one point to any other point in minimum time. The cycloid is such a curve, the stright line is the trial example.

C

cartesian coordinates a system whereby points on a plane are identified by an ordered pair of numbers, representing the distances to two or three perpendicular axes. The standard "x-y" coordinate system used in high school algebra is a Cartesian Coordinate System ... with points in the plane having cartesian coordinates (x, y).

catenary A catenary is the curve in which a heavy uniform chain hangs. Its equation is:
y = cosh(x) = ¹/₂ (e^x + e^-x) = 1 + x²/₂ + x⁴/₂₄ + .........

center the point that is the same distance from all the points on a circle. The point that is the same distance from all the points on a sphere. The point inside an ellipse where the major and the minor axes intersect. The center of a circle that can be inscribed in a regular polygon.

central angle an angle that has its vertex at the center of a circle.

centroid the center of mass of an object. The point where the object would balance if supported by a single support. The point in a triangle where the three medians intersect.

chain rule dy/dx = dy/du * du/dx.

chord a line segment that connects two points on a curve.

circle the set of points in a plane that are a fixed distance from a given point.

circular functions same as trigonometric functions.

circumcenter the point in a triangle that is the center of the circle that can be circumscribed about the triangle. The intersection of the perpendicular bisectors of the triangle.

circumference the distance around a closed curve. The circumference of a circle is 2*pi*r where r is the radius of the circle.

circumscribed a circle is said to be circumscribed to a triangle or other polygon if the vertices of the polygon lie on the circle. The polygon is than said to be inscribed in the circle. The (unique) circle circumscribed to a triangle is called the circumcircle and its centre is the circumcentre.

circumscribed circle a circle that passes through all of the vertices of a regular polygon.

closed interval an interval that contains its endpoints.  

coefficient a constant that multiplies a variable. In Ax + By = C, A and B are coefficients of x and y.

cofunction the cofunction of a trigonometric function, f(x), is equal to f(pi/2 - x). The cofunction of the sine is the cosine. The cofunction of the secant is the cosecant. The cofunction of the tangent is the cotangent.

collinear points are collinear if they lie on the same line.

commutative property a + b = b + a.   a*b = b*a.

complementary angles two angles are complementary if their sum is 90 degrees.See acute.

completing the square the method of adding an expression to both sides of an equation so that one side becomes a perfect square trinomial.

complex fraction a fraction that contains a fraction in its numerator and/or denominator.

complex number the sum of an imaginary number and a real number written in the form a + bi or r(cos x + isin x).

component the components in the vector (a, b, c) are a, b, and c.

composite function a function that consists of two functions arranged in such a way that the output of one function becomes the input of the other function.

composite number a natural number that is not prime.

concave a figure is concave if a line segment can be drawn so that it goes in, out, then back into the figure.

conclusion the part of an if - then statement that follows the word "then". Consequent.

conditional statement an 'if - then' statement.

cone  the union of all line segments that connect a point and a closed curve in a different plane from the point.

congruent shapes or angles are congruent if you could put one on top of the other, and they would look like just one shape. Equal.

conic section parabola, hyperbola, ellipse, circle. Formed by the intersection of a plane with a right circular cone.

conjecture a statement that seems to be true, but has not yet been proven.

conjugate the conjugate of a complex number is formed by reversing the sign on the imaginary part of the number. The conjugate of a + bi is a - bi.

conjunction a statement that is really two statements joined by the word AND. Both parts must be true for the statement to be considered true. (Concept of set intersection.)

consequent the part of an "if - then" statement that follows the "then". Conclusion.

constant a value that does not change.  

continuous a function is continuous if you can draw it without lifting your pencil off the paper. y = f(x) is continuous at a if: 1. f(a) exists. 2. lim as x-->a f(x) exists. And 3.  lim as x-->a of f(x) = f(a).

contrapositive the contrapositive of A-->B is Not B---->Not A.

convergent series an infinite series that has a finite sum is called convergent.  

converse the statement made by interchanging the hypothesis and the conclusion of a statement.

convex a set of points such that for any two points in the set, the line segment that connects them is also in the set.

coordinates a set of numbers that identifies the location of a point.

coplanar points that lie within the same plane are called coplanar.

corollary  a statement that can be easily proven once a theorem is proved.

cosecant csc x = 1/sin x

cosine In a triangle, the cosine of an angle = (length of the adjacent side)/(hypotenuse)

cotangent cot x = 1/tan x

coterminal angles angles whose measures are 2kpi apart.

counting numbers natural numbers. The numbers you use to count.

critical point the point on a curve where the first derivative equals zero. Extremum.

cube a solid figure with six square faces.

cubic a polynomial of degree 3.

cylinder the union of all line segments that connect corresponding points on congruent circles in parallel planes.

D

decagon a polygon with ten sides.

decimal numbers the numbers in the base 10 number system.

decreasing function a function is considered to be decreasing if f(b) < f(a) when b > a.

Declination the angular distance to a point on a celestial object, measured north or south from the celestial equator.

deduction a conclusion arrived at by reasoning.

deficient number is an integer for which the sum of its proper divisors is less than than the number itself. i.e., the proper divisors of 8 are 1, 2, 4, which sum to 7. See also perfect number, abundant number.

definite integral the definite integral of f(x) between a and b represents the area under the curve y = f(x) , above the x - axis, to the right of the line x = a, and to the left of the line x = b. The definite integral of f(x) = F(b) - F(a) where F is an antiderivative function for f(x).

degree 1/360 of a full rotation. There are 360 degrees in a circle. Unit of measure of an angle.

denominator the bottom part of a fraction.

dependent variable the output or matched value of a function.

derivative the rate of change (speed, slope, velocity) of a function. The derivative at x of f(x) is the slope of the tangent line at (x, f(x)). y' = f '(x) =the limit as delta approaches zero of [f(x + delta x) - f(x)] / delta x.

determinant the determinant | a b | ad -bc | c d |

diagonal the line segment connecting two nonadjacent vertices in a polygon.

diameter the line segment joining two points on a circle and passing through the center.

difference the result of subtracting two numbers.

differentiable a function is differentiable over an interval if it is continuous over the interval and if the derivative exists everywhere on the interval.

differential an infinitesimally small change in a variable, represented by d, as in dx, or dy.

differentiation the process of finding a derivative.

digit the ten symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are digits. Example: the number 365 has three digits: 3, 6, and 5.

dimension The dimension of a space is the number of coordinates needed to identify a location in that space.

directly proportional y is directly proportional to x if y = kx.

discriminant the discriminant of a quadratic equation, ax2 + bx + c = 0 is b2 - 4ac. The discriminant tells how many roots there are for the equation and the nature of the roots.

disjoint having no elements in common.

disjunction an OR statement. (concept of set union.)

distributive property a(b + c) = ab + ac

divergent series a series whose sum is infinite.

dividend In a / b = c, a is the dividend.

division the opposite operation of multiplication.

divisor In a / b = c, b is the divisor.

dodecahedron a polyhedron with twelve faces.

domain the set of all possible values of the argument of a function.

E

e

  2.718281828.....  The base of the natural logarithm function.  e can be found from the infinite series:
of course taken to infinity.

eccentricity    A number that indicates the shape of a conic section.   The eccentricity of an ellipse is given by e  =  sqrt(a² - b²) / a

element   a member of a set.

ellipse  the set of all points in a plane such that the sum of the distances to two fixed points is a constant. The equation of an ellipse with center at the origin is: x² + y² = 1

ellipsoid   a solid of revolution formed by rotating an ellipse about one of its axes.

empty set   a set that contains no elements.

equation   a mathematical statement that says that two expressions have the same value.

equilateral triangle   a triangle that has three equal sides.

equivalent equations   two equations whose solutions are the same.   For example: x + 3y = 10,   and   2x + 6y = 20.

even function  a function that satisfies the property that f(x) = f(-x).

even number  a natural number that is divisible by 2.

event  in probability, a set of outcomes.

evolute The evolute of a curve is the envelope of the normals to the curve. This can also be thought of as the locus of the centres of curvature.

exponent  a number that indicates the operation of repeated multiplication.

exponential function  a function of the form f(x) = ax, where a is a constant known as the base.

extremum  a point where a function reaches a maximum or a minimum.

F

factor  one of two or more expressions that are multiplied together.

factor theorem  If P(x) is a polynomial, then if P(r) = 0, then (x - r) is a factor of P(x).

factorial factorial of an integer n is the product 1.2.3. ... .n It is denoted by n!
Generalised to non-integers, it is the Gamma function.

Fibonacci Sequence  1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377....   The sequence in which every number is the sum of the two preceding numbers. See Fibonacci.

field is a ring in which non-zero elements have multiplicative inverses. Among the most important fields are the Real numbers R, the complex numbers C and various finite fields which are used in Number Theory and Combinatorics.

Fourier analysis is the process by which one may write a periodic function on (say) the interval [0, 2] as the sum of multiples of the functions sin(nx) and cos(nx). Where: f x) = a₀ + a₁cos(x) + b₁sin(x) + a₂cos(2x) + b₂sin(2x) + ... This is called the Fourier series of f and the numbers a_i and b_i are called the Fourier coefficients.

G

geometric mean   the geometric mean of two numbers is the square root of the product of the numbers.    The geometric mean of n numbers is the nth root of the product of the numbers.

geometric sequence   a sequence of numbers of the form   a, ar, ar2, ar3,....., arn-1.

geometric series  the sum of a geometric sequence.

Guldin's Theorem If a plane figure is rotated about an axis in its plane then the volume of the solid body formed is equal to the product of the area with the distance travelled by the centre of gravity.

graph   the graph of an equation is the set of points that make the equation true.

great circle   the circle formed by the intersection of a plane passing through the center of a sphere.

greatest common factor   the greatest common factor of two numbers, a and b, is the largest  number that divides both a and b evenly.

H

half plane   the set of all points in a plane that lie on one side of a line in the plane.

harmonic sequence   a sequence is a harmonic sequence if the reciprocals of the numbers in the sequence form an arithmetic sequence.

heptagon   a polygon with seven sides.

Heron's formula   a formula for the area of a triangle: A = sqrt[(s(s - a)(s - b)(s - c))] where a, b, and c are the lengths of the sides of the triangle, and s is half the perimeter. Area

hexadecimal number   a number written in base sixteen.

hexagon  a polygon with six sides.

hexahedron  a polyhedron with six faces.   A regular hexahedron is a cube.

hyperbola   the set of all points in a plane such that the difference of the distances to two fixed points is a constant.    The general equation for a hyperbola is:

hyperbolic functions   the hyperbolic functions are defined as follows:

1. hyperbolic cosine   cosh x = (1/2)(e^x + e^-x)
2. hyperbolic sine       sinh x = (1/2)(e^x - e^-x)
3. hyperbolic tangent   tanh x =    sinh x/cosh x

hypotenuse  the longest side of a right triangle.   The side opposite the right angle in a right triangle.

hypothesis  a proposition that is being investigated, it has yet to be proven.

I

i

  the basic unit for the imaginary number: i2 = -1.

icosohedron  a polyhedron with 20 faces.

identity an equation that is true for all values of the variable.

identity element   If * is an operator, then the identity element, I, for * is the number such that I * a = a.   The identity for addition is zero, and the identity for multiplication is 1.

identity matrix    a square matrix with ones along the diagonal and zeros everywhere else. If I is an identity matrix, then IA = A.

imaginary number   a number of the form ni, where n is a real number, and i2 = -1.

implication   a conditional statement.

improper fraction  a fraction with a numerator that is greater than the denominator.

incenter  the center of a circle that is inscribed in a triangle.   The intersection of the angle bisectors of the triangle.

incircle   the circle that can be inscribed in a triangle.

increasing function  a function is increasing if f(a) > f(b) when a > b.

increment  a small change, usually indicated by the greek letter delta.

indefinite integral  the sum of the antiderivative of a function and an arbitrary constant.

independent variable  the input number to a function.

infinity  a limitless quantity.

inflection point  a point on a curve such that the curve is concave up on one side of the point, and concave down on the other side of the point.

inscribed polygon  a polygon placed inside a circle so that each vertex of the polygon touches the circle.

integers  the set of numbers containing zero, the natural numbers, and all the negatives of the natural numbers.

integral   If  dF(x)/dx = f(x), then F(x) is an integral of f(x).   The area under the curve of a function above the x - axis.

integrand  a function that is to be integrated.

integration  the process of finding an integral.

intercept  the x-intercept of a curve is the point where the curve crosses the x - axis, and the y - intercept of a curve is the point where the curve crosses the y - axis.

inversely proportional   y is inversely proportional to x if y = k/x.

irrational number  a number that cannot be expressed as the ratio of two integers.

isometry  a transformation of a figure that does not change the distances of any two points in the figure.

isosceles triangle  a triangle with at least two equal sides.

J

joint variation  y varies jointly as x and z if y = kxz.

K

K informal abbreviation for thousand, used in expressions where the base unit is understood, such as "10K run" (10 kilometers) or "700K disk" (700 kilobytes or kibibytes). Note that "K" is also the symbol for the kelvin. Also note that the symbol for the metric prefix kilo- (1000) is actually k-, not K-.

L

latus rectum  the chord through the focus of a parabola parallel to the directrix. The chord through a focus of an ellipse perpendicular to the major axis.

Laplace transform of a function f is defined by the integral:

law of cosines    c² = a² + b² - 2abCosC

law of sines   a/sin A = b/sin B = c/sin C

least common denominator   the least common denominator of two fractions, a/b and c/d, is the smallest number that contains both b and d as factors.

least common multiple   the least common multiple of two numbers, a and b, is the smallest  number that contains both a and b as factors.

lemma  a theorem that is proved mainly as an aid in proving another theorem.

like terms  two terms each of whose parts, with the exception of their coefficients, is the same.

line   a straight set of points that extends off into infinity in both directions.

line segment  two points on a line, and all the points between those two points.

logarithm  if y = b^x, then log_b y = x.

logic  the study of sound reasoning.

M

magnitude  the magnitude of a vector is its length.

major arc  an arc of measure greater than 180 degrees.

major axis   the line segment connecting the two vertices that are farthest apart in an ellipse.

matrix  a table of numbers arranged in rows and columns.

maxima  the points on a curve where the value is greater than that of the surrounding points.

mean  average,  arithmetic mean.

median   the number in a group of numbers such that there are an equal number of numbers in the set greater than the number as are less than the number.

midpoint  a point, M, on a line segment, AB, such that AM = MC.

minima  the points on a curve where the value is less than that of the surrounding points.

minor arc  an arc on a circle that is less than 180 degrees.

minor axis  the shortest distance across an ellipse through the center.

minute  the unit of measure of an angle that is 1/60 of a degree.

mode  the number that occurs most frequently in a set of data.

modulus  the absolute value of a complex number.

monomial  an algebraic expression that does not involve any additions or subtractions.

multiplicand   in the equation ab = c, a and b are multiplicands.

multiplication  the operation of repeated addition.

multiplicative identity  the number 1 is the multiplicative identity because 1 * a = a for all a.

multiplicative inverse  the number, b, that when multiplied by a number, a, gives a result of 1. Reciprocal.   b = 1/a.

N

natural logarithm   the logarithm with the base of e.   Written:   ln x.

natural numbers  the counting numbers.   

negative number   a real number less than zero.

normal  perpendicular.

null set  same as empty set.  A set with no elements.

number line   a line on which every point represents a real number.

numeral   a symbol that stands for a number.

numerator  the top of a fraction.

O

obtuse angle  an angle whose measure is greater than 90 degrees.

obtuse triangle  a triangle with an obtuse angle.

octagon   a polygon with 8 sides.

octahedron   a polyhedron with 8 faces.

octal number   a number in base 8.

odd function   a function that satisfies the property that f(-x) = -f(x).

odd number   a whole number that is not divisible by 2.

open interval   an interval that does not contain both its endpoints.

ordered pair    a set of two numbers in which the order has an agreed upon meaning. Such as the cartesian coordinates (x, y), where it is agreed that the first coordinate represents the horizontal position, and the second coordinate represents the vertical position.

ordinate   the second coordinate of a cartesian ordered pair.

origin  the point (0, 0) on a Cartesian Coordinate System.

orthocenter   the point in a triangle where the three altitudes intersect.

orthogonal    perpendicular.

P

parabola   the set of all points in a plane that are equally distant from a fixed point (called the focus) and a fixed line, (called the directrix).   

paraboloid  a surface that is formed by rotating a parabola about its axis.

parallel   two lines are parallel if they are in the same plane and never intersect.

parallelepiped   a solid figure with six faces such that the planes containing two opposite faces are parallel.    Each face is a parallelogram.

parallelogram   a quadrilateral with opposite sides parallel.

pentagon   a five sided polygon.

percent   a fraction in which the denominator is assumed to be 100.

perfect number is an integer for which the sum of its proper divisors is equal to the number itself. For example, 6 and 28 are both perfect numbers.
See also: abundant number, deficient number.

perimeter   the sum of the lengths of the sides of a polygon.

period   the measure of how often a function repeats its same values.

periodic function  a function that keeps repeating the same values.

permutation   the permutation of n things taken j at a time is: n! / (n-j)!

perpendicular   two lines are perpendicular if the angle between them is 90 degees.

pi

   the ratio of the circumference of a circle to its diameter. See pi, this page explaining the magical relation of this number.

phi

   the ratio of the succesive numbers of the fibonacci series. 1.61803398501736 See phi, this page explaining the magical relation of this number.

plane   a flat surfaces that stretches off into infinity.

polar coordinates   a coordinate system of ordered pairs in which the first number of the pair represents distance from the origin, and the second number of the pair represents the angle of inclination from the horizontal axis.

polygon   the union of several line segments that are joined together so as to completely enclose an area.

polyhedron   a solid that is bounded by plane polygons.

polynomial   an algebraic expression of the form:Example: axn + bx(n-1) + .......+ cx3 + dx2 + ex + k

positive number   a real number greater than zero.

postulate   a fundamental statement that is assumed to be true without proof.

power  a number that indicates the operation of repeated multiplication.

prime number   a number whose only factors are itself and 1.

product   the result of two numbers being multiplied.

proper fraction   a fraction whose numerator is less than its denominator.

proportion:   an equation of fractions in the form a/b = c/d

proportional   If y = kx, then y is said to be proportional to x.

protractor  a device for measuring angles.

pyramid   the union of all line segments that connect a given point and the points that lie on a given polygon.

Pythagorean Theorem   the theorem that relates the three sides of a right triangle: a² + b² = c²

pythagorean triple   three natural numbers that satisfy the pythagorean theorem.

Q

quadrant   one of the quarters of the plane of the Cartesian coordinate system

quadratic equation   an equation involving the second power, but no higher power of an unknown.   The general form of a quadratic equation in two unknowns is: Ax² + Bxy + Cy² + Dx + Ey + F = 0.

quadratic formula   the formula that says that the solution to a 2nd degree (quadratic) equation is as follows:

quadrilateral   a polygon with 4 sides.

quartic   a polynomial of degree 4.

quintic   a polynomial of degree 5.

quotient   the answer to a division problem.

R

R   abbreviation for the real numbers.

radian   the ratio of an arc of a circle to the radius of the circle.   On a unit circle, a full rotation around the circle is 2pi radians.   On any circle, a full rotation is 2pi r radians.

radius   the distance from the center to a point on a circle.   The line segment from the center to a point on a circle.

range   the set of all possible values for the output of a function.

ratio   the ratio of two real numbers, a and b, is a/b.

rational number  a number that can be expressed as the ratio of two integers.

real numbers   the union of the set of rational numbers and irrational numbers.

reciprocal   the reciprocal of a number, a, is 1/a, (a cannot be zero).

rectangle   a quadrilateral with four 90 degree angles.

rectangular coordinates  same as Cartesian Coordinates.

reflection   mirror image.

reflexive property   x = x for all x.  Every number equals itself.

regular polygon  a polygon in which all the angles are equal and all of the sides are equal.

regular polyhedron   a polyhedron whose faces are congruent, regular polygons.

relation   a set of ordered pairs.

remainder  if m = nq + r, then m/q has quotient q and remainder r.

repeating decimal  a decimal in which the digits endlessly repeat a pattern.

rhombus   a quadrilateral with four equal sides.

right angle  an angle whose measure is 90 degrees.

right circular cone  a cone whose base is a circle located so that the line connecting the vertex to the center of the circle is perpendicular to the plane containing the circle.

right circular cylinder  a cylinder whose bases are circles and whose axis is perpendicular to its bases.

right triangle  a triangle that contains a right angle.

root  the root of an equation is the same as the solution to the equation.

S

saros a unit of time used in astronomy, mostly in predicting solar and lunar eclipses. The saros is equal to 6585.32 days (6585 days 7 hours 23 minutes), which is exactly 223 lunar months. (This is either 10 or 11 days more than 18 years, depending on the number of leap years during the period.) Astronomers in ancient times discovered that the saros is very nearly equal to 19 eclipse years (6585.78 days). This means that one saros after an eclipse the Sun, Moon, and Earth return almost exactly to the same position and another, very similar eclipse occurs. However, because of the 7 hours 23 minutes included, the Earth has turned about one third of a revolution and the new eclipse occurs about 116° of longitude west of the preceding one. After 3 saros, the eclipse returns nearly to its original location. Thus eclipses at a particular location tend to repeat with a period of 3 saros or 54 years 1 month. Thus the last total solar eclipse in North Carolina, on March 7, 1970, will repeat on April 8, 2024 and again on May 11, 2078. See saros

scalar  a quantity that has size but no direction.

scalene triangle  a triangle with three unequal sides.

secant  a line that intersects a circle or a curve in two places.

secant  the reciprocal of the cosine.

second  the unit of measure of an angle that is 1/60 of a minute.

sector  a region bounded by two radii of a circle and the arc whose endpoints lie on those radii.

segment  the union of a point, A, and a point, B, and all the points between them.

series  the sum of a sequence.

set   a well defined group of objects.

similar  two polygons are similar if their corresponding sides are proportional.

simulataneous equations  a group of equations that are all true at the same time.

sine  in a right triangle, the length of a side opposite an angle divided by the length of the hypotenuse of the triangle.

skew   two lines that are not in the same plane.

slope   the slope of a line is the change in the vertical coordinates/the change in the horizontal coordinates of any two points on the line.

solid   a three dimensional object that completely encloses a volume of space.

sphere   the set of all points in space that are a fixed distance from a given point.

square   a quadrilateral with four equal sides and four 90 degree angles.

square root   of a number, x, is the number that, when multiplied by itself gives the number, x.

subset   A set, B, is a subset of another set, A, if every element in B is also an element of A.

sum   the result of adding.

supplementary  two angles are supplementary if their sum is 180 degrees.

symmetric   two points are symmetric with respect to a third point if the segments joining them to the third point are equal.   Two points are symmetric with respect to a line if the line is the perpendicular bisector of the segment joining the points.

T

tangent   a line that intersects a circle in one point.

tangent   in a triangle,     (the side opposite an angle) / (the side adjacent the same angle).

term   a part of a sum in an algebraic expression.

terminating decimal  a fraction whose decimal representation contains a finite number of digits.

tetrahedron   a polyhedron with four faces.

theorem   a statement that has been proven.

trajectory   the path that a body makes as it moves through space.

transitive property   the property that states that if a = b, and b = c, then a = c.

translation   a shift of the axes of the Cartesian Coordinate System.

transit The passage of a celestial body across the observer's meridian. The passage of a smaller celestial body or its shadow across the disk of a larger celestial body.

transversal   a line that intersects two other lines.

trapezoid  a quadrilateral that has exactly two sides parallel.

triangle   a three sided polygon.

trinomial   a polynomial with exactly three terms.

U

union  the union of two sets, A and B, is the set of all elements that are either in A, or in B, or in both A and B.

unit vector  a vector of length 1.   It is customary to designate i as the unit vector in the x direction, j as the unit vector in the y direction, and k is the unit vector in the z direction.

V

variable  a symbol used to represent a value.

vector  a quantity that has both magnitude and direction.

velocity   the rate of change of position.    The first derivative of the position function.

vertex  the point on an angle where the two sides intersect.

volume  measurement of space.

W

whole numbers  the set of numbers that includes zero and all of the natural numbers.

X

x-axis

  the horizontal axis in a Cartesian Coordinate System.

x-intercept

   the value of x at the point where a curve crosses the x-axis.

Y

y-axis

   the vertical axis in a Cartesian Coordinate System.

y-intercept

   the value of y at the point where a curve crosses the y-axis.

Z

zero

   the additive identity.   The number that when you add it to a number, n, you will net n as a result.