MOL Math Glossary

A
·B
·C
·D
·E
·F
·G
·H
·I
·J
·K
·L
·M

·N
·O
·P
·Q
·R
·S
·T
·U
·V
·W
·X
·Y
·Z

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

**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.

**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.

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

**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.

**affine cipher : **Affine ciphers use linear functions to scramble
the letters of secret message.

**alternate exterior angles:** Angles located outside a set of parallel
lines and on opposite sides of the transversal.

**alternate interior angles:** Angles located inside a set of parallel
lines and on opposite sides of the transversal.

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

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

**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.

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

**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**: s = integral (sqrt (1 + (dy/dx)2)) dx.

**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.

**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**: It is better to avoid this sometimes vague term. It
usually refers to the (arithmetic) mean, but it can also signify the median,
the mode, the geometric mean, and weighted means, among other things

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

**axioms of probability:** There are three axioms of probability:
1. Probability is always more than zero 2. The chance that something happens
is 1,or 100% 3. If two events cannot both occur at the same time, the chance
that either one occurs is the sum of the chances that each occurs.

**axis of symmetry**: a line that passes through a figure in such
a way that the part of the figure on one side of the line

is a mirror reflection or image of the part of the figure on the other
side of the line.

**average expected payoff:** An estimate of the amount that will
be gained in a game of chance, calculated by multiplying the probability
of winning by the number of points won each time.

**bar graph:** A diagram showing a system of connections or interrelations
between two or more things by using bars.

**bell curve:** See normal distribution.

**between**: point B is between points A and C if AB + BC = AC.

**biconditional statement**: a compound statement that says one sentence
is true if and only if the other sentence is

true.

**bimodal:** Having two modes, which are the most frequently occurring
number in a list.

**binary number system**: the number system that uses only 0's and
1's. The places in the binary numbers are .......

2^n ....... 2^5=32 , 2^4=16 , 2^3=8, 2^2=4, 2^1=2, 2^0=1.

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

**binomial theorem**: the theorem that tells how to expand the expression
(a + b)^n ... the binomial (a + b) raised to the

nth power. There is a descending power of the first term ... an ascending
power of the second term ... with numeric

values from Pascal's Triangle.

**bisect**: to cut or divide something in half.

**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).

**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.

**center of mass**: centroid.

**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.

**chaos:** Chaos is the breakdown of predictability, or a state of
disorder.

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

**cipher:** Ciphers are codes for writing secret messages. Two simple
types are shift ciphers and affine ciphers.

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

**class interval:** In plotting a histogram, one starts by dividing
the range of all values into non-overlapping intervals, called class intervals,
in such a way that every piece of data is contained in some class interval.

**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.

**combinatorics:** The science that studies the numbers of different
combinations, which are groupings of numbers. Combinatorics is often part
of the study of probability and statistics.

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

**complementary angles**: two angles are complementary if their sum
is 90 degrees.

**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.

**concave up:** A line is "concave up" when it is a concave shape,
meaning curved like the inside of a hollowed out ball, with the two ends
of the line pointing down.

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

**conditional probability:** Conditional probability is the probability
of an event occurring given that another event also occurs. It is expressed
as P(A/B). It reads "Probability of Event A on condition of Event B." P(A/B)
= P(A and B)/P(B), where P(B) is the probability of event B and P(A and
B) is the joint probability of A and B.

**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:** In math, things that do not change: for example distance,
volume, mass, are called constants. The things that do change are called
variable.

**constant functions:** Functions that stay the same no matter what
the variable does are called constant functions.

**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.

**coordinate plane (Cartesian):** A plane with a point selected as
an origin, some length selected as a unit of distance, and two perpendicular
lines that intersect at the origin, with positive and negative direction
selected on each line. Traditionally, the lines are called x (drawn from
left to right, with positive direction to the right of the origin) and
y (drawn from bottom to top, with positive direction upward of the origin).
Coordinates of a point are determined by the distance of this point from
the lines, and the signs of the coordinates are determined by whether the
point is in the positive or in the negative direction from the origin.

**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.

**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.

**deduction**: a conclusion arrived at by reasoning.

**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.

**discontinuous graph:** A line in a graph that is interrupted, or
has breaks in it forms a discontinuous graph.

**discriminant**: the discriminant of a quadratic equation, ax^2
+ 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.

**disjoint events:** Two events are disjoint if they can't both happen
at the same time (in other words, if they have no outcomes in common).
Equivalently, two events are disjoint if their intersection is the empty
set.

**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.

**domain of the function f :** The set of numbers x for which f(x)
is defined

**e:** 2.718281828..... The base of the natural logarithm
function. e can be found from the series 2 + 1/2! + 1/3! + 1/4!

+ 1/5! + ...........

**eccentricity:** A number that indicates the shape
of a conic section. The eccentricity of an ellipse is given
by e = sqrt(a^2 – b^2) / 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: x^2/a^2
+ y^2/ b^2 = 1

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

**empty set:** a set that contains no elements.

**end point convention:** In histograms, one needs to decide where
to count values that are on the exact boundary between two intervals: either
in the left or in the right interval. Let readers of the histogram know
which side is chose

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

**equally likely:** In probability, when there are the same chances
for more than one event to happen, the events are equally likely to occur.
For example, if someone flips a coin, the chances of getting heads or tails
are the same. There are equally likely chances of getting heads or tails

**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.

**escapees:** Values for C in the Julia Set or Mandelbrot set where
at each iteration the resulting value grows larger and larger, approaching
infinity.

**estimate:** The best guess arrived at after considering all the
information given in a problem.

**Euclidean algorithm:** The method for finding remainders by multiplying
the divisor by the quotient and subtracting that amount from the number
being divided. For example, when finding the remainder for 25 divided by
4, the quotient is 6, so one multiplies 6 times 4 (giving 24) and then
subtracts 25 from 24, leaving 1 as the remainder.

**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.

**expected value:** The amount that is predicted to be gained, using
the calculation for average expected payoff.

**experimental probability:** The chances of something happening,
based on repeated testing and observing results. For example, to find the
experimental probability of winning a game, one must play the game many
times, then divide the number of games won by the total number of games
played.

**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.

**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: ** the product of all the integers from 1 up to
the integer in question. The (!) exclamation point is used to mean
factorial.

**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.

**fractal** : Term coined by Benoit Mandelbrot in 1975, referring
to objects built using recursion, where some aspect of the limiting object
is infinite and another is finite, and where at any iteration, some piece
of the object is a scaled down version of the previous iteration.

**fraction:** A rational number of the form a/b where a is called
the numerator and b is called the denominator.

**frequency:** The number of items occurring in a given category.

**frequency view:** An approach taken by mathematicians and
scientists to determine the chances of an event happening by repeating
the experiment many times and using the results to calculate the probability.

**function:** A function f of a variable x is a rule that assigns
to each number x in the function's domain a single number f(x). The word
"single" in this definition is very important.

**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.

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

**graph of the function f:** The set of all the points on the
coordinate plane of the form (x, f(x)) with x in the domain of f.

**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.

**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.

**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.

**histogram:** A bar graph such that the area over each class
interval is proportional to the relative frequency of data within this
interval.

**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 x2 /a2 - y2 /b2 = 1

**hyperbolic functions:** the hyperbolic functions are
defined as follows:

hyperbolic cosine: cosh x = (1/2)(ex + e-x)

hyperbolic sine: sinh x = (1/2)(ex - e-x)

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**: the basic unit for the imaginary number: I^2 = -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.

**indefinitely:** An unspecified amount, having no exact limit.

**independent variable:** the input number to a function.

**independent events:** Two events A and B are independent
if the probability that they happen at the same time is the product of
the probabilities that each occurs individually; i.e., if P(A & B)
= P(A)P(B). In other words, learning that one event occurs does not give
any information about whether the other event occurred too: the conditional
probability of A given B is the same as the unconditional probability of
A, i.e., P(A/B) = P(A).

**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.

**input:** The number or value that is entered, for example,
into a function machine. The number that goes into the machine is the input.

**irregular fractals:** Complex fractals whose dimension is
often difficult to determine and in some cases is unknown.

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

**isosceles triangle:** A triangle that has at least two congruent
sides.

**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.

**item:** The things or objects that are the subject of a bar
graph.

**intersection of sets:** The intersection of two or more sets
is the set of elements that all the sets have in common; in other words,
all the elements contained in every one of the sets. The mathematical symbol
for intersection is an inverted "u".

**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.

**iteration:** Repeating a set or rules or steps over and over.
One step is called an iterate.

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

**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.

**law of cosines:** c^2 = a^2 + b^2 - 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 graph:** A diagram showing a system of connections or
interrelations between two or more things by using lines.

**linear function:** A function of the form f(x) = mx + b where
m and b are some fixed numbers. The names "m" and "b" are traditional.
Functions of this kind are called "linear" because their graphs are straight
lines.

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

**logarithm:** if y = bx, then logb y = x.

**logarithm:** The exponent of the power to which a base number
must be raised to equal a given number. An example: 2 is the logarithm
of 100 to the base 10. One can look at this way: 10 * 10 = 100, which is
the same as 102, and 2 is the exponent referred to above.

**logic:** the study of sound reasoning.

**Mandelbrot set:** Discovered much later than Julia sets,
it is generated by taking the set of all functions f(Z)=Z^2+C, looking
at all of the possible C points and their Julia sets, and assigning colors
to the points based on whether the Julia set is connected or dust

**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.

**mixed numbers:** Numbers that have both whole numbers and
decimals, such as 4.56.

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

**modular arithmetic:** A method for finding remainders where
all the possible numbers (the numbers less than the divisor) are put in
a circle, and then by counting around the circle the number of times of
the number being divided, the remainder will be the final number landed
on.

**modulus:** the absolute value of a complex number.

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

**multimodal distribution:** A distribution with more than
one mode. The histogram of a multimodal distribution has more than one
"bump"

**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.

**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.

**normal distribution:** Also called "bell curve," the normal
distribution is the curved shape of a graph that is highest in the middle
and lowest on the side.

**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.

**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.

**optical illusion:** A drawing or object that appears to have
an effect that it does not really have, such as when a flat painting seems
to have three-dimensional dept

**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.

**outcome: ** Any one of the possible results of an experiment.

**outcome space:** The outcome space is the set of all possible
outcomes of a given experiment.

**output: ** The number or value that comes out from a process.
For example, in a function machine, a number goes in, something is done
to it, and the resulting number is the output

**palindrome:** Words, numbers and phrases that can be read
the same backwards as forwards. Some examples include: "mom", "racecar",
"34543", or the phrase "never odd or even".

**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.

**paradox:** A statement that appears to contradict itself,
for example, suggesting a solution which is actually impossible.

**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.

**pattern:** Characteristic(s) observed in one item that may
be repeated in similar or identical manners in other items.

**pentagon:** a five sided polygon.

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

**perfect number:** a number that is the sum of all its
factors except itself. For example, 6.

**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 degrees.

**pi**: the ratio of the circumference of a circle to
its diameter.

**pie graph:** A diagram showing a system of connections or
interrelations between two or more things by using a circle divided into
segments that look like pieces of pie.

**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:
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.

**prisoners:** values for c in the Julia Set or Mandelbrot
set where at each iteration the resulting value becomes smaller and smaller,
approaching zero.

**probability:** The measure of how likely it is for an event
to occur. The probability of an event is always a number between zero and
100%. The meaning (interpretation) of probability is the subject of theories
of probability. However, any rule for assigning probabilities to events
has to satisfy the axioms of probability.

**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.

**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**: 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.

**random number generators:** A device used to produce a selection
of numbers in a fair manner, in no particular order and with no favor being
given to any numbers. Examples include dice, spinners, coins, and computer
programs designed to randomly pick number.

**range:** The range of a set of numbers is the largest value
in the set minus the smallest value in the set. Note that the range is
a single number, not many numbers.

**range of the function f:** The set of all the numbers f(x)
for x in the domain of f.

**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.

**recursion:** Given some starting information and a rule for
how to use it to get new information, the rule is then repeated using the
new information.

**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.

**relative frequency:** Relative frequency is the number of
items of a certain type divided by the number of all the numbers being
considered.

**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.

**remainders:** After dividing one number by another, if any
amount is left that does not divide evenly, that amount is called the remainder.
For example, when 8 is divided by 3, three goes in to eight twice (making
6), and the remainder is 2. When dividing 9 by 3, there is no remainder,
because 3 goes in to 9 exactly 3 times, with nothing left over.

**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.

**rule of probabilities multiplication for simultaneous independent
events:** When finding the probability of two independent events
(two things happening where the outcomes are not affected by each other),
multiply the probabilities of each event happening to get the probability
of both events happening. For example, to find the probability of getting
"heads" and then "tails" when flipping a coin twice, multiply the probability
of getting heads once by the probability of getting tails once.

**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.

**self-similarity:** Two or more objects having the same characteristics.
In fractals, the shapes of lines at different iterations look like smaller
versions of the earlier shape.

**sequence:** A set whose elements are determined based on
some constant being applied.

**series:** the sum of a sequence.

**set:** a well defined group of objects.

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

**simultaneous 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.

**standard deviation:** Standard deviation tells how spread
out numbers are from the average, calculated by taking the square root
of the arithmetic average of the squares of the deviations from the mean
in a frequency distribution.

**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.

**superscript:** In mathematics, superscripts are numbers or
letters written above and to the right of other numbers or letters or symbols
indicating how many times the latter is to be used as a factor. When typing,
one can represent a superscript by using the ^ symbol to indicate raising
the number. For example, x3 is the same as x^3, which equals x * x * x.

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

**surface area:** A measure of the number of square units needed
to cover the outside of a figure.

**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.

**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).

**tessellation:** A tessellation is a repeated geometric design
that covers a plane without gaps or overlaps.

**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.

**theoretical probability:** The chances of events happening
as determined by calculating results that would occur under ideal circumstances.
For example, the theoretical probability of rolling a 4 on a four-sided
die is 1/4 or 25%, because there is one chance in four to roll a 4, and
under ideal circumstances one out of every four rolls would be a 4.

**theories of probability:** A theory of probability is a way
of understanding probability statements. That is, a theory of probability
connects the mathematics of probability, which is the set of consequences
of the axioms of probability, with the real world of observation and experiment.
There are several common theories of probability. According to the frequency
theory of probability, the probability of an event is the limit of the
percentage of times that the event occurs in repeated, independent trials
under essentially the same circumstances. According to the subjective theory
of probability, probability is a number that measures how strongly we believe
an event will occur. The number is on a scale of 0% to 100% (or 0 to 1),
with 0% indicating that we are completely sure it won't occur, and 100%
indicating that we are completely sure that it will occur.

**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.

**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.

**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.

**variable:**a symbol used to represent a value.

**vector:** a quantity that has both magnitude and direction.

**vector space:** A vector is a quantity having magnitude and
direction, represented by a directed arrow indicating its orientation in
space. Vector space is the three dimensional area where vectors can be
plotted.

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

**Venn Diagram:** A diagram where sets are represented as simple
geometric figures, with overlapping and similarity of sets represented
by intersections and unions of the figures.

**vertical angles:** Angles that share only one point. They
are on opposite sides of the transversal.

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

**volume:** measurement of space.

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

**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-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.

**zero:** the additive identity. The number
that when you add it to a number, n, you will get n as a result.