Dictionary

The operation, or process, of calculating the sum of two numbers or quantities

Two angles that share a ray, thereby being directly next to each other

Step-by-step procedure by which an operation can be carried out

Angles located inside a set of parallel lines and on opposite sides of the transversal

The number of square units needed to cover a surface

This property applies both to multiplication and addition and states that you can group several numbers that are being added or multiplied (not both) in any way and yield the same value. In mathematical terms, for all real numbers a, b, and c, (a+b)+c=a+(b+c) or (ab)c=a(bc)

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

the triangular end of the prism.

Having two modes, which are the most frequently occurring numbers in a list

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

The numbers in front of the letters in a mathematical expression, for example, in: 4d + 5t² + 3s, the 4, 5, and 3 are coefficients for the d, t², and s

This property of both multiplication and addition states that you can rearrange the order of the numbers being added or reorder numbers being multiplied without changing the value of the expression. In mathematical terms, for all real numbers a and b, a+b=b+a and ab=ba

Considering probabilites in decimal form, the sum of two probabilites equal to one. As a percent, the two probabilites are considered complementary if they sum to 100%.

Two or more events that happen simultaneously

circles that have the same center and varying radii.

Two figures are congruent to one another if they have the same size and shape

In math, things that do not change are called constants. The things that do change are called variables.

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

A statistical measure referring to the relationship between two random variables. It is a positive correlation when each variable tends to increase or decrease as the other does, and a negative or inverse correlation if one tends to increase as the other decreases.

Two angles in the same relative position on two lines when those lines are cut by a transversal

A prism with six square faces

A fraction where the denominator is a power of ten and is therefore expressed using a decimal point. For example: 0.37 is the decimal equivalent of 37/100

In a rational number, the number below the fraction bar that indicates how many parts the whole is divided into.

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

The inverse operation of multiplication

The empty set, Ø, is the set that has no members

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

The best guess arrived at after considering all the information given in a problem

In probability, an event is a set of outcomes from a given experiment.

The chances of something happening, based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested. 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

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

The number of items occurring in a given category

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

A set where each element is a multiple of the previous element. See also sequence

The set of all the points on the coordinate plane of the form (x, f(x)) with x in the domain of f

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

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)

A line-segment or figure that begins as the beginning geometric shape for a fractal. The initiator is then replaced by the generator for the fractal

Any positive or negative number (including zero) that does not include a fraction or decimal

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.

A triangle that has at least two congruent sides

Repeating a set of rules or steps over and over. One step is called an iterate

The set of all the points for a function of the form Z²+C. The iterations will either approach zero, approach infinity, or get trapped

The target value that terms in a sequence of numbers are getting closer to. This limit is not necessarily ever reached; the numbers in the sequence eventually get arbitrarily close to the limit

A diagram showing a system of connections or interrelations between two or more things by using lines

A piece of a line with endpoints at both ends

An equation or graph is linear if the graph of the equation is a straight line

An attempt to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered as the independent variable, and the other is considered as the dependent variable.

"Middle value" of a list. The smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two. The median can be estimated from a histogram by finding the smallest number such that the area under the histogram to the left of that number is 50%

For lists, the mode is the most common (frequent) value. A list can have more than one mode. For histograms, a mode is a relative maximum ("bump"). A data set has no mode when all the numbers appear in the data with the same frequency. A data set has multiple modes when two or more values appear with the same frequency.

A unit of measure. For example, when measuring days, a modulus could be 24 for the number of hours in a day. 75 hours would be divided by 24 to give 3 remainder 3, or 3 days and 3 hours. See also modular arithmetic

The product of multiplying a number by a whole number. For example, multiples of 5 are 10, 15, 20, or any number that can be evenly divided by 5

The probability that events A and B both occur, is equal to the conditional probability that A occurs given that B occurs, times the unconditional probability that B occurs: P(A and B)=P(A/B)*P(B)

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

In the Cartesian coordinate plane, the origin is the point at which the horizontal and vertical axes intersect, at zero (0,0)

The outcome space is the set of all possible outcomes of a given experiment. Also called sample space

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

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

A quadrilateral that contains two pairs of parallel sides

A ratio that compares a number to one hundred. The symbol for percent is %

A a particular ordering of a set of objects. For example, given the set {1, 2, 3}, there are six permutations: {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}

See Rose Curve

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

in the polar coordinate system, a fixed point, analogous to the origin in the Cartesian coordinate system. The distance from this point to a point of interest gives the value of r in the coordinate pair (r, θ) used in the polar coordinate system.

Any solid figure with an outer surface composed of polygon faces

A complex number is a prisoner in a Julia Set if its orbit, a sequence of complex numbers generated by successive iterations of a given function, is bounded.

A relationship between two ratios is proportional if the two ratios are equal in value.

Used to find side lengths of right triangles, the Pythagorean Theorem states that the square of the hypotenuse is equal to the squares of the two sides, or A² + B² = C², where C is the hypotenuse

A function of the form f(x) = ax² + bx + c where a is not equal to zero (in which case the function turns into a linear function)

When performing division, the number of times one value can be multiplied to reach the other value represents the quotient. For example, when dividing 7 by 3, 3 can be multiplied twice, making 6, and the remainder is 1, so the quotient is 2

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

A rational number of the form a/b where a is called the numerator and b is called the denominator

Real numbers can be thought of as all the points falling along the number line in the coordinate plane

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

In the plane, a reflection is a rigid motion that keeps all the points on some line fixed, and flips the rest of the points to the opposite side of that line. In space, a reflection is a rigid motion that keeps all the points on one plane fixed, and flips all points to the opposite side of that plane. Note that if you perform any reflection twice, all points end up back where they started. When you reflect an object, you are creating a "mirror image" of that object, with the fixed line or plane being the mirror.

A polygon whose side lengths are all the same and whose interior angle measures are all the same

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

A parallelogram with four congruent sides

A triangle containing an angle of 90 degrees

The graph of a function in polar coordinates of the form a*sin(b*t) or a*cos(b*t) where a ≠ 0 and b is an integer > 1

A rotation in the plane is a rigid motion keeping exactly one point fixed, called the "center" of the rotation. Since distances are unchanged, all the other points can be thought of as having moved on circles whose center is the center of the rotation. The "angle" of the rotation is how far around the circles the points travel. A rotation in three-dimensional space is a rigid motion that keeps the points on one line fixed, called the "axis" of the rotation, with the rest of the points moving some constant angle around circles centered on and perpendicular to the axis.

Angles located inside a set of parallel lines and on the same side of the transversal

A graphical representation of the distribution of two random variables as a set of points whose coordinates represent their observed paired values.

Two or more objects having the same characteristics. In fractals, the shapes of lines at different iterations look like smaller versions of the earlier shapes

A set is a collection of things, without regard to their order

The slope of the line y = mx + b is the rate at which y is changing per unit of change in x. The units of measurement of the slope are units of y per unit of x (cf. Linear Functions Discussion).

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

The operation in which the difference between two numbers or quantities is calculated. Also, the inverse of addition

A measure of the number of square units needed to cover the outside of a figure

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. See frequency view and personal view

A total is determining the overall sum of numbers or a quantity.

A translation is a rigid motion that moves each point the same distance, in the same direction

A quadrilateral with exactly one pair of parallel sides

A circle of radius 1 centered at the origin (0,0) of the Cartesian coordinate system.

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

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

A measure of the number of cubic units needed to fill the space inside an object