Dictionary
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A (...)
The distance a number is from zero on the number line. For example -5 is 5 units away from zero. It would be written as |-5|
Angles located outside a set of parallel lines and on opposite sides of the transversal
Angles located inside a set of parallel lines and on opposite sides of the transversal
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)
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 mean, among other things
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
There are three axioms of probability: 1) The probability of an event is a real number greater than or equal to zero; 2) The sum of the probabilities of all possible outcomes of a given experiment is 1; 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.
B (...)
A diagram showing a system of connections or interrelations between two or more things by using bars
the perpendicular distance from the base of the triangle to the top of the triangle.
Also called box-and-whisker plot, this graph shows the distribution of data by dividing the data into four groups with the same number of data points in each group. The box contains the middle 50% of the data points and each of the two whiskers contain 25% of the data points.
C (...)
The resulting graph in polar coordinates of a function of the form a+b*sin(t) or a+b*cos(t) where |a| = |b|
Ciphers are codes for writing secret messages. Two simple types are shift ciphers and affine ciphers
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
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
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
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%.
One can think of them as an ordered pair of numbers. Complex numbers helped earlier mathematicians deal with the problem of taking the square root of a negative number. A complex number takes the form a + b*sqrt(-1), where a and b are real numbers
A curve is "concave up" when it is a concave shape, meaning curved like the inside of a bowl, with the two ends of the curve pointing up
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
Functions that stay the same no matter what the variable does are called constant functions
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 unique ordered pair of numbers that identifies a point on the coordinate plane. The first number in the ordered pair identifies the position with regard to the x-axis while the second number identifies the position on the y-axis
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.
A numerical value (between +1 and -1) that identifies the strength of the linear relationship between variables. A value of +1 indicates an exact positive relationship, -1 indicates an exact inverse relationship, and 0 indicates no predictable relationship between the variables.
Two angles in the same relative position on two lines when those lines are cut by a transversal
D (...)
Short for the term "decimal fraction", a decimal is another way to represent fractional numbers. The decimal uses place value to express the value of a number as opposed to a fraction that uses a numerator and denominator.
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
A circle is measured in units called degrees. The entire circle is 360 degrees, half a circle is 180 degrees, and one quarter of a circle is 90 degrees. The "L" shaped 90 degree circle forms what is called a right angle. When examining circular objects, such as spinners, the size of each segment in the circle can be described in degrees
In a rational number, the number below the fraction bar that indicates how many parts the whole is divided into.
A line in a graph that is interrupted, or has breaks in it forms a discontinuous graph
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
Summing two numbers and then multiplying by another number yields the same value as multiplying both values by the other value and then adding. In mathematical terms, for all real numbers a, b, and c, a(b+c) = ab+ac
E (...)
A period of time that has passed, usually between a given starting time and ending time
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 chosen
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
A complex number is an escapee of a Julia Set if its orbit, a sequence of complex numbers generated by successive iterations of a given function, is unbounded.
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 24 from 25, leaving 1 as the remainder
The amount that is predicted to be gained, using the calculation for average expected payoff
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
F (...)
Any of the numbers or symbols in mathematics that when multiplied together form a product. For example, 3 is a factor of 12, because 3 can be multiplied by 4 to give 12. Similarly, 5 is a factor of 20, because 5 times 4 is 20
A set of numbers formed by adding the last two numbers to get the next in the series: 0, 1, 1, 2, 3, 5, 8, 13. Named for Leonardo of Pisa, an Italian mathematician of the Middle Ages, who called himself Fibonacci, short for filius Bonacci which means "son of Bonacci". The original problem he investigated in1202 A.D. was about how fast rabbits could breed under ideal circumstances. His research led to the construction of this unique set of numbers
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
A rational number of the form a/b where a is called the numerator and b is called the denominator
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. See theories of probability
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
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The bent line-segment or figure that replaces the initiator at each iteration of a fractal
A set where each element is a multiple of the previous element. See also sequence
A visual representation of data that displays the relationship among variables, usually cast along x and y axes.
The set of all the points on the coordinate plane of the form (x, f(x)) with x in the domain of f
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A bar graph such that the area over each class interval is proportional to the relative frequency of data within this interval
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A number that when an operation is applied to a given number yields that given number. For multiplication, the identity is one and for addition the identity is zero
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)
Greater than any fixed counting number, or extending forever. No matter how large a number one thinks of, infinity is larger than it. Infinity has no limits
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
The number or value that is entered, for example, into a function machine. The number that goes into the machine is the input
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.
Complex fractals whose dimension is often difficult to determine and in some cases is unknown
J (...)
The probability of event A and event B happening at the same time is expressed as P(A & B). For independent events A and B, P(A & B)=P(A)P(B). P(A & B) is also known as the probability of intersection of events A and B, from the Venn diagram description
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
K (...) L (...)
The resulting graph in polar coordinates of a function of the form a+b*sin(t) or a+b*cos(t) where |a| ≠ |b|
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 straight line used as a best approximation of a summary of all the points in a scatter-plot. The position and slope of the line are determined by the amount of correlation between the two, paired variables involved in generating the scatter-plot. This line can be used to make predictions about the value of one of the paired variables if only the other value in the pair is known.
If a figure can be divided by a line where both divisions are mirrors of each other, the figure has line symmetry. The line that divides the figure is the line of symmetry
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
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.
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
M (...)
Discovered much later than Julia sets, it is generated by taking the set of all functions f(Z)=Z2+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
The sum of a list of numbers, divided by the total number of numbers in the list. Also called arithmetic mean
"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 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
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
A distribution with more than one mode. The histogram of a multimodal distribution has more than one "bump"
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 operation by which the product of two quantities is calculated. To multiply a number b by c is to add b to itself c times
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)
The number that when multiplied by the original number will result in a product of one
N (...)
One of the counting numbers, i.e. 1, 2, 3, 4... In graphing, numbers to the right of zero
Numbers less than zero. In graphing, numbers to the left of zero. Negative numbers are represented by placing a minus sign (-) in front of the number
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
The number above the fraction bar that indicates the number of parts of the whole there are in a rational number
O (...)
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 depth
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
A data point (or points) that lies far outside most of the rest of the points in the data set
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
P (...)
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"
A statement that appears to contradict itself, for example, suggesting a solution which is actually impossible
Characteristic(s) observed in one item that may be repeated in similar or identical manners in other items
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}
An approach taken by mathematicians and philosophers to calculate probability. Using their knowledge and reasoning skills, they think through the problem. See theories of probability
The designated name for the ratio of the circumference of a circle to its diameter, represented by the symbol π
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 ray from the pole in a fixed direction, analogous to the x-axis in the Cartesian system. The angle between this fixed ray and a ray through the pole and the point of interest gives the value of theta in the coordinate pair (r, θ) used in the polar coordinate system.
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.
A closed plane figure formed by three or more line segments that do not cross over each other
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.
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
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
Q (...)
In Cartesian Coordinate geometry, the coordinate plane is divided into four parts. Each of the four parts is called a "quadrant" and is designated by a roman numeral, I, II, III, or IV. Quadrant I contains all coordinates with positive x and positive y values; Quadrant II contains all negative x and positive y values; Quadrant III contains all negative x and negative y values; and Quadrant IV contains all positive x and negative y values.
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
R (...)
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 numbers
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
Relative frequency is the number of items of a certain type divided by the number of all the numbers being considered
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
The observed value minus the predicted value. It is the difference of the results obtained by observation, and by computation from a formula.
A rigid motion, of the plane or of space, is one that keeps the distances between all
pairs of points unchanged. Rotations, reflections and translations are examples of rigid motions.
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.
S (...)
Angles located outside a set of parallel lines and on the same side of the transversal
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.
A non-overlapping piece of an object. In the context of a spinner or a circle graph, a "sector" is one of the sections of the graph.
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
An ordered set whose elements are usually determined based on some function of the counting numbers
The number of digits to consider when using measuring numbers. There are three rules in determining the number of digits considered significant in a number.
1) All non-zeros are significant. 2) Any zeros between two non-zeros are significant. 3) Only trailing zeros behind the decimal are considered significant 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
A subset of a given set is a collection of things that belong to the original set. For example, A={a,b} could include, a, b, a and b, or the null set (neither)
The operation in which the difference between two numbers or quantities is calculated. Also, the inverse of addition
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
The correspondence in size, form, or arrangement of parts on a plane or line. In line symmetry, each point on one side of the line has a corresponding point on the opposite side of the line (picture a butterfly, with wings that are identical on either side). Plane symmetry refers to similar figures being repeated at different but regular locations on the plane
T (...)
A tessellation is a repeated geometric design that covers a plane without gaps or overlaps
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. Contrast with experimental 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. See frequency view and personal view
A translation is a rigid motion that moves each point the same distance, in the same direction
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The union of two or more sets is the set of all the objects contained by at least one of the sets. The symbol for union is U
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In math, things that can change are called variables. The things that do not change are called constants.
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
The rate of change of position over time is velocity, calculated by dividing distance by time
A diagram where sets are represented as simple geometric figures, with overlapping and similarity of sets represented by intersections and unions of the figures
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