MOL Math Glossary
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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
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
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 -
| 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 =
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 -
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 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.
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.
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.
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: 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.
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-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.