Maths Dictionary

Maths Dictionary

A

absolute value	The distance a number is from zero on the number line.
acute angle	An angle that measures less than 90 degrees
addition	The operation, or process, of calculating the sum of two numbers or quantities/ adding
algorithm	Step-by-step procedure by which an operation can be carried out
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
area	The number of square units needed to cover a surface
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
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
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

B

bar graph	A diagram showing a system of connections or interrelations between two or more things by using bars
base depth of the triangular prism	the perpendicular distance from the base of the triangle to the top of the triangle.
base of the triangular prism	the triangular end of the prism.
bell curve	See normal distribution
bimodal	Having two modes, which are the most frequently occurring number in a list
boxplot	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

chaos	Chaos is the breakdown of predictability, or a state of disorder
cipher	Ciphers are codes for writing secret messages. Two simple types are shift ciphers and affine ciphers
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
coefficients	The numbers in front of the letters in a mathematical expression.
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	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
complementary angles	Two angles that have a sum of 90 degrees
complementary probability	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%.
compound event	Two or more events that happen simultaneously
congruent	Two figures are congruent to one another if they have the same size and shape
constant functions	Functions that stay the same no matter what the variable does are called constant functions
constants	In math, things that do not change: for example distance, volume, mass, are called constants. The things that do change are called variables
continuous graph	In a graph, a continuous line with no breaks in it forms a continuous graph
coordinate plane	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.
coordinates	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
correlation	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.
corresponding angles	Two angles in the same relative position on two lines when those lines are cut by a transversal
cube	A prism with six square faces

D

decimal	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.
decimal number	A fraction where the denominator is a power of ten and is therefore expressed using a decimal point.
degrees	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
denominator	In a rational number, the number below the fraction bar that indicates how many parts the whole is divided into. See also numerator
discontinuous graph	A line in a graph that is interrupted, or has breaks in it forms a discontinuous graph
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
division	The inverse operation of multiplication
domain of the function f	The set of numbers x for which f(x) is defined

E

element	A member of or an object in a set
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 chosen
equally likely	In probability, when there are the same chances for more than one event to happen, the events are equally likely to occur.
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.
event	In probability, an event is an occurrence or the possibility of an occurrence that is being investigated
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. 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
exponent	An expression of the number of times that a base is used as a factor

F

factor	Any of the numbers or symbols in mathematics that when multiplied together form a product.
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. See theories of 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

G

generator	The bent line-segment or figure that replaces the initiator at each iteration of a fractal
geometric sequence	A set where each element is a multiple of the previous element. See also sequence
graph	A visual representation of data that displays the relationship among variables, usually cast along x and y axes.
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

H

height of the triangular prism	the distance between the two bases
histogram	A bar graph such that the area over each class interval is proportional to the relative frequency of data within this interval
hypotenuse	The side of the triangle that is opposite the right angle

I

identity	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
indefinitely	An unspecified amount, having no exact limits
infinity	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
initiator	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
input	The number or value that is entered, for example, into a function machine. The number that goes into the machine is the input
integer	Any positive or negative number that does not include a fraction or decimal, including zero
intercept	See x-intercept or y-intercept
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 ∩ .
inverse, additive	A number when added to a given number yields zero.
inverse, multiplicative	A number when multiplied by a given number yields one.
irregular fractals	Complex fractals whose dimension is often difficult to determine and in some cases is unknown
isosceles triangle	A triangle that has at least two congruent sides
item	The things or objects that are the subject of a bar graph
iteration	Repeating a set of rules or steps over and over. One step is called an iterate

L

limit	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
line	A continuous extent of length containing two or more points
line graph	A diagram showing a system of connections or interrelations between two or more things by using lines
line of best fit	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.
line segment	A piece of a line with endpoints at both ends
line symmetry	If a figure is divided by a line and both divisions are mirrors of each other, the figure has line symmetry. The line that divides the figure is the line os symytry
linear	An equation or graph is linear if the graph of an equation is a straight line
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
linear regression	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.

M

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
mean	The sum of a list of numbers, divided by the total number of numbers in the list. Also called arithmetic mean
mixed numbers	Numbers that have both whole numbers and decimals.
mode	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.
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	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.
multimodal distribution	A distribution with more than one mode. The histogram of a multimodal distribution has more than one "bump"
multiples	The product of multiplying a number by a whole number.
multiplication	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

N

natural numbers	One of the counting numbers, i.e. 1, 2, 3, 4... In graphing, numbers to the right of zero
negative numbers	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
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 sides
numerator	The number above the fraction bar that indicates the number of parts of the whole there are in a rational number

O

obtuse angle	An angle whose measure is greater than 90 degrees
optical illusion	A drawing or object that appears to have an effect that it does not really have/
origin	In the Cartesian coordinate plane, the origin is the point at which the horizontal and vertical axes intersect, at zero.
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
outlier	A data point (or points) that lie far outside most of the rest of the points in the data set
output	The number or value that comes out from a process.

P

palindrome	Words, numbers and phrases that can be read the same backwords as forwards. Some examples are: "racecar" or the phrase "never odd or even"
paradox	A statement that appears to contradict itself, for example, suggesting a solution which is actually impossible
parallel	Lines that are in the same plane that do not intersect
parallelogram	A quadrilateral that contains two pairs of parallel sides
pattern	Characteristic(s) observed in one item that may be repeated in similar or identical manners in other items
percent	A ratio that compares a number to one hundred. The symbol for percent is %
perimeter	The sum of the lengths of all the sides of a polygon
permutation	A a particular ordering of a set of objects.
personal view	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
Pi	The designated name for 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
polygon	A closed plane figure formed by three or more line segments that do not cross over each other
polyhedra	Any solid figure with an outer surface composed of polygon faces
prime number	A number that has exactly two factors, 1 and the number itself
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
proportion	A relationship between two ratios in which the first ratio is always equal to the second
protractor	An instrument for laying down and measuring angles on paper, used in drawing and plotting

Q

quadrilateral	A polygon that has four sides
quotient	When performing division, the number of times one value can be multiplied to reach the other value represents the quotient.

R

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.
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
ratio	A rational number of the form a/b where a is called the numerator and b is called the denominator
ray	A straight line that begins at a point and continues outward in one direction
real numbers	Real numbers can be thought of as all the points falling along the number line in the coordinate plane
rectangle	A parallelogram with four right angles
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
reflect	In a tessellation, reflect means to repeat an image by flipping it across a line so it appears as it would in a mirror
regular polygon	A polygon whose side lengths are all the same and whose interior angle measures are all the same
relative frequency	Relative frequency is the number of items of a certain type divided by the number of all the numbers being considered
remainders	After dividing one number by another, if any amount is left that does not divide evenly, that amount is called the remainder.
residual	The observed value minus the predicted value. It is the difference of the results obtained by observation, and by computation from a formula.
rhombus	A parallelogram with four congruent sides
right angle	An angle of 90 degrees
right triangle	A triangle containing an angle of 90 degrees
rotate	To rotate an object in a tessellation means to repeat the object by spinning it on a point a certain angle

S

scatter plot	A graphical representation of the distribution of two random variables as a set of points whose coordinates represent their observed paired values.
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 shapes
sequence	An ordered set whose elements are usually determined based on some function of the counting numbers
set	A set is a collection of things, without regard to their order
significant digits	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
square	A parallelogram with four congruent sides and four right angles
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 subset of a given set is a collection of things that belong to the original set.
subtraction	The operation in which the difference between two numbers or quantities is calculated. Also, the inverse of addition
surface area	A measure of the number of square units needed to cover the outside of a figur

T

tessellation	A tessellation is a repeated geometric design that covers a plane without gaps or overlaps
tolerance	Tolerance is the amount of error accepted in a given situation. See Estimator
total	A total is determining the overall sum of numbers or a quantity.
translate	In a tessellation, to translate an object means repeating it by sliding it over a certain distance in a certain direction
transversal	A line or ray that divides other lines or rays
trapezoid	A quadrilateral with exactly one pair of parallel sides

U

union of sets

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

V

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 over time is velocity, calculated by dividing distance by time
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	The two nonadjacent angles formed when two straight lines intersect
volume	A measure of the number of cubic units needed to fill the space inside an object

W

width of the triangular prism

the length of the base of the triangle

X

x-intercept

The x-coordinate of the point where the line crosses the x-axis

Y

y-intercept

The y-coordinate of the point where the line crosses the y-axis