maths+dictionary

maths dictionary **A**


 * **absolute value** || **The distance a number is from zero on the number line.** ||
 * **acute angle** || **An angle whose measure is less than 90 degrees** ||
 * **addition** || **The operation, or process, of calculating the sum of two numbers or quantities** ||
 * **adjacent angles** || **Two angles that share a ray, thereby being directly next to each other** ||
 * **affine cipher** || **Affine ciphers use linear functions to scramble the letters of secret messages** ||
 * **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** ||
 * **angle bisector** || **A ray that divides an angle into two congruent angles** ||
 * **area** || **The number of square units needed to cover a surface** ||
 * **arithmetic mean** || **See mean** ||
 * **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 **


 * <span style="color: rgb(255, 0, 0);">**height of the triangular prism** || <span style="color: rgb(0, 0, 0);">**the distance between the two bases** ||
 * <span style="color: rgb(255, 0, 0);">**histogram** || **A bar graph such that the area over each class interval is proportional to the relative frequency of data within this interval** ||
 * <span style="color: rgb(255, 0, 0);">**hypotenuse** || **The side of the triangle that is opposite the right angle** ||


 * <span style="color: rgb(0, 255, 0);">I **<span style="color: rgb(0, 255, 0);">


 * **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** ||


 * <span style="color: rgb(0, 255, 0);">L **<span style="color: rgb(0, 255, 0);">


 * **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.** ||


 * <span style="color: rgb(0, 255, 0);">M **<span style="color: rgb(0, 255, 0);">


 * **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** ||


 * <span style="color: rgb(0, 255, 0);">N **<span style="color: rgb(0, 255, 0);">


 * **<span style="color: rgb(255, 0, 0);">natural numbers ** || **One of the counting numbers, i.e. 1, 2, 3, 4... In graphing, numbers to the right of zero** ||
 * **<span style="color: rgb(255, 0, 0);">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** ||
 * **<span style="color: rgb(255, 0, 0);">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** ||
 * **<span style="color: rgb(255, 0, 0);">numerator ** || **The number above the fraction bar that indicates the number of parts of the whole there are in a rational number** ||

<span style="color: rgb(0, 255, 0);">**O**


 * **<span style="color: rgb(255, 0, 0);">obtuse angle ** || **An angle whose measure is greater than 90 degrees** ||
 * **<span style="color: rgb(255, 0, 0);">optical illusion ** || **A drawing or object that appears to have an effect that it does not really have/** ||
 * **<span style="color: rgb(255, 0, 0);">origin ** || **In the Cartesian coordinate plane, the origin is the point at which the horizontal and vertical axes intersect, at zero.** ||
 * **<span style="color: rgb(255, 0, 0);">outcome ** || **Any one of the possible results of an experiment** ||
 * **<span style="color: rgb(255, 0, 0);">outcome space ** || **The outcome space is the set of all possible outcomes of a given experiment** ||
 * **<span style="color: rgb(255, 0, 0);">outlier ** || **A data point (or points) that lie far outside most of the rest of the points in the data set** ||
 * **<span style="color: rgb(255, 0, 0);">output ** || **The number or value that comes out from a process.** ||


 * <span style="color: rgb(0, 255, 0);">P **<span style="color: rgb(0, 255, 0);">


 * **<span style="color: rgb(255, 0, 0);">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"** ||
 * **<span style="color: rgb(255, 0, 0);">paradox ** || **A statement that appears to contradict itself, for example, suggesting a solution which is actually impossible** ||
 * **<span style="color: rgb(255, 0, 0);">parallel ** || **Lines that are in the same plane that do not intersect** ||
 * **<span style="color: rgb(255, 0, 0);">parallelogram ** || **A quadrilateral that contains two pairs of parallel sides** ||
 * **<span style="color: rgb(255, 0, 0);">pattern ** || **Characteristic(s) observed in one item that may be repeated in similar or identical manners in other items** ||
 * **<span style="color: rgb(255, 0, 0);">percent ** || **A ratio that compares a number to one hundred. The symbol for percent is %** ||
 * **<span style="color: rgb(255, 0, 0);">perimeter ** || **The sum of the lengths of all the sides of a polygon** ||
 * **<span style="color: rgb(255, 0, 0);">permutation ** || **A a particular ordering of a set of objects.** ||
 * **<span style="color: rgb(255, 0, 0);">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** ||
 * **<span style="color: rgb(255, 0, 0);">Pi ** || **The designated name for the ratio of the circumference of a circle to its diameter** ||
 * **<span style="color: rgb(255, 0, 0);">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** ||
 * **<span style="color: rgb(255, 0, 0);">polygon ** || **A closed plane figure formed by three or more line segments that do not cross over each other** ||
 * **<span style="color: rgb(255, 0, 0);">polyhedra ** || **Any solid figure with an outer surface composed of polygon faces** ||
 * **<span style="color: rgb(255, 0, 0);">prime number ** || **A number that has exactly two factors, 1 and the number itself** ||
 * **<span style="color: rgb(255, 0, 0);">prisoners ** || **values for c in the Julia Set or Mandelbrot set where at each iteration the resulting value becomes smaller and smaller, approaching zero** ||
 * **<span style="color: rgb(255, 0, 0);">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** ||
 * **<span style="color: rgb(255, 0, 0);">proportion ** || **A relationship between two ratios in which the first ratio is always equal to the second** ||
 * **<span style="color: rgb(255, 0, 0);">protractor ** || **An instrument for laying down and measuring angles on paper, used in drawing and plotting** ||


 * <span style="color: rgb(0, 255, 0);">Q **


 * <span style="color: rgb(255, 0, 0);">**quadrilateral** || **A polygon that has four sides** ||
 * <span style="color: rgb(255, 0, 0);">**quotient** || **When performing division, the number of times one value can be multiplied to reach the other value represents the quotient.** ||


 * <span style="color: rgb(0, 255, 0);">R **


 * <span style="color: rgb(255, 0, 0);">**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.** ||
 * <span style="color: rgb(255, 0, 0);">**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** ||
 * <span style="color: rgb(255, 0, 0);">**ratio** || **A rational number of the form a/b where a is called the numerator and b is called the denominator** ||
 * <span style="color: rgb(255, 0, 0);">**ray** || **A straight line that begins at a point and continues outward in one direction** ||
 * <span style="color: rgb(255, 0, 0);">**real numbers** || **Real numbers can be thought of as all the points falling along the number line in the coordinate plane** ||
 * <span style="color: rgb(255, 0, 0);">**rectangle** || **A parallelogram with four right angles** ||
 * <span style="color: rgb(255, 0, 0);">**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** ||
 * <span style="color: rgb(255, 0, 0);">**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** ||
 * <span style="color: rgb(255, 0, 0);">**regular polygon** || **A polygon whose side lengths are all the same and whose interior angle measures are all the same** ||
 * <span style="color: rgb(255, 0, 0);">**relative frequency** || **Relative frequency is the number of items of a certain type divided by the number of all the numbers being considered** ||
 * <span style="color: rgb(255, 0, 0);">**remainders** || **After dividing one number by another, if any amount is left that does not divide evenly, that amount is called the remainder.** ||
 * <span style="color: rgb(255, 0, 0);">**residual** || **The observed value minus the predicted value. It is the difference of the results obtained by observation, and by computation from a formula.** ||
 * <span style="color: rgb(255, 0, 0);">**rhombus** || **A parallelogram with four congruent sides** ||
 * <span style="color: rgb(255, 0, 0);">**right angle** || **An angle of 90 degrees** ||
 * <span style="color: rgb(255, 0, 0);">**right triangle** || **A triangle containing an angle of 90 degrees** ||
 * <span style="color: rgb(255, 0, 0);">**rotate** || **To rotate an object in a tessellation means to repeat the object by spinning it on a point a certain angle** ||


 * <span style="color: rgb(0, 255, 0);">S **

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** ||
 * <span style="color: rgb(255, 0, 0);">**scatter plot** || **A graphical representation of the distribution of two random variables as a set of points whose coordinates represent their observed paired values.** ||
 * <span style="color: rgb(255, 0, 0);">**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** ||
 * <span style="color: rgb(255, 0, 0);">**sequence** || **An ordered set whose elements are usually determined based on some function of the counting numbers** ||
 * <span style="color: rgb(255, 0, 0);">**set** || **A set is a collection of things, without regard to their order** ||
 * <span style="color: rgb(255, 0, 0);">**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.
 * <span style="color: rgb(255, 0, 0);">**square** || **A parallelogram with four congruent sides and four right angles** ||
 * <span style="color: rgb(255, 0, 0);">**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** ||
 * <span style="color: rgb(255, 0, 0);">**subset** || **A subset of a given set is a collection of things that belong to the original set.** ||
 * <span style="color: rgb(255, 0, 0);">**subtraction** || **The operation in which the difference between two numbers or quantities is calculated. Also, the inverse of addition** ||
 * <span style="color: rgb(255, 0, 0);">**surface area** || **A measure of the number of square units needed to cover the outside of a figur** ||


 * <span style="color: rgb(0, 255, 0);">T **


 * <span style="color: rgb(255, 0, 0);">**tessellation** || **A tessellation is a repeated geometric design that covers a plane without gaps or overlaps** ||
 * <span style="color: rgb(255, 0, 0);">**tolerance** || **Tolerance is the amount of error accepted in a given situation. See Estimator** ||
 * <span style="color: rgb(255, 0, 0);">**total** || **A total is determining the overall sum of numbers or a quantity.** ||
 * <span style="color: rgb(255, 0, 0);">**translate** || **In a tessellation, to translate an object means repeating it by sliding it over a certain distance in a certain direction** ||
 * <span style="color: rgb(255, 0, 0);">**transversal** || **A line or ray that divides other lines or rays** ||
 * <span style="color: rgb(255, 0, 0);">**trapezoid** || **A quadrilateral with exactly one pair of parallel sides** ||


 * <span style="color: rgb(0, 255, 0);">U **


 * <span style="color: rgb(255, 0, 0);">**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** ||


 * <span style="color: rgb(0, 255, 0);">V **<span style="color: rgb(0, 255, 0);">


 * <span style="color: rgb(255, 0, 0);">**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** ||
 * <span style="color: rgb(255, 0, 0);">**velocity** || **The rate of change of position over time is velocity, calculated by dividing distance by time** ||
 * <span style="color: rgb(255, 0, 0);">**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** ||
 * <span style="color: rgb(255, 0, 0);">**vertical angles** || **The two nonadjacent angles formed when two straight lines intersect** ||
 * <span style="color: rgb(255, 0, 0);">**volume** || **A measure of the number of cubic units needed to fill the space inside an object** ||


 * <span style="color: rgb(0, 255, 0);">W **


 * <span style="color: rgb(255, 0, 0);">**width of the triangular prism** || **the length of the base of the triangle** ||


 * <span style="color: rgb(0, 255, 0);">X **<span style="color: rgb(0, 255, 0);">


 * <span style="color: rgb(255, 0, 0);">**x-intercept** || **The x-coordinate of the point where the line crosses the x-axis** ||


 * <span style="color: rgb(0, 255, 0);">Y **<span style="color: rgb(0, 255, 0);">


 * <span style="color: rgb(255, 0, 0);">**y-intercept** || **The y-coordinate of the point where the line crosses the y-axis** ||