Mathematics Encyclopedia

Mathematics Encyclopedia

If you would like to prepare for school subjects or simply increase your general knowledge, then enjoy our mathematics encyclopedia. We tried to focus only on very important terms and definitions. We also kept our terminology very brief so that you absorb the concept more quickly and easily.

Mathematics Glossary (Page 1)

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3-D FIGURE: A set of points in space; examples-box, cone, cylinder, parallelpiped, prism, pyramid, regular pyramid, right cone, right cylinder, right prism, sphere,.
45-45-90 TRIANGLE: An isoscoles right triangle.
ABSCISSA: The horizontal axis, or the first coordinate in an ordered pair.
ABSOLUTE MAXIMUM: The highest point on a graph, especially over a specified domain. It is the greatest value of f(x) over a defined interval of x, provided y=f(x).
ABSOLUTE MINIMUM: The lowest point on a graph, especially over a specified domain. It is the least value of f(x) over a defined interval of x, provided y=f(x).
ABSOLUTE VALUE: The absolute value of a number is the distance the number is from the zero point on the number line. The absolute value of a number or an expression is always greater than or equal to zero (i.e. Nonnegative).
ACCURACY: The quality of approaching an exact value. Distinct from precision, accuracy means to approach correctness, to tend toward an established value.
ACUTE ANGLE: An angle whose measure is greater than 0 but less than 90 degrees.
ADDING INTEGERS: To ADD integers with the same sign, add their absolute values. Give the result the same sign as the integers. To ADD integers with different signs, SUBTRACT the lesser absolute value from the greater absolute value. Give the result the same sign as the integer with the greater absolute value.
ADDITION: A mathematical process to combine numbers and/or variables into an equivalent quantity, number or algebraic expression.
ADDITIVE INVERSE FOR MATRICES: A matrix when added to another equals the Zero Matrix.
ADJACENT ANGLES: 2 nonstraight and nonzero angles that have a common side in the interior of the angle formed by the noncommon sides.
ALGEBRA: A language that helps translate real-life situations into mathematical form so that we can analyze change and answer the question "What if?".
ALGEBRAIC EXPRESSION: An expression consisting of one or more numbers and variables along with one or more arithmetic operations.
ALGORITHM: A sequence of steps to accomplish a familiar task; a recipe.
ALPHA: The first letter of the Greek alphabet.
ALTERNATE EXTERIOR ANGLES: Exterior angles on alternate sides of the transversal (not on the same parallel line).
ALTERNATE INTERIOR ANGLES: Interior angles on alternate sides of the transversal (not on the same parallel line).
ALTERNATING SERIES: A series in which successive terms have opposite signs. Every other term is positive; every other term is negative.
ALTITUDE: Height.
ALTITUDE OF A CONIC SOLID: The length of a segment whose endpoints are the vertex and a point on the plane of the base that is perpendicular to the plane of the base.
ALTITUDE OF A CYLINDRIC SOLID: The distance between the planes of the bases.
ALTITUDE OF A TRAPEZOID: The distance between the bases of a trapeziod.
ALTITUDE OF A TRIANGLE: The perpendicular segment from a vertex to the line containing the opposite side of a triangle.
AMBIGUOUS: Not stable; changing.
ANALYTIC GEOMETRY: See coordinate geometry.
ANGLE: The union of 2 rays that have the same endpoint; measured in degrees or radians (trig.); the five types of angles are zero, acute, right, obtuse, and straight.
ANGLE BISECTOR: A ray that is in the interior of an angle and forms two equal angles with the sides of that angle.
ANGLE SIDE: One of the two rays forming an angle.
ANNULUS: A ring; the area bounded by two concentric circles.
ANTECEDENT: The 'if' part of a conditional; represented by p; aka hypothesis, given, problem; see consequent.
ANTIDERIVATIVE: Given a function with a derivative, the antiderivative of that derivative function returns the original function.
APOTHEM: In a regular polygon, the perpendicular distance from the center to a side; in a circle with a chord, the distance from the midpoint of a chord to the circle's center.
ARBELOS: A plane region bounded by three mutually tangent semicircles whose diameters are collinear.
ARBITRARY NUMBER: A number which could be any number it is defined to be but for which no specific value is chosen. It is often used in proofs since it can represent any number but does actually have the value of any number so that the proof applies to more than one situation.
ARC: A path from one node in a network to another; doesn't have to be straight & can be more than 1 line between 2 nodes; part of a circle; see minor arc, major arc.
ARC LENGTH: The distance between an arc's endpoints along the path of the circle.
AREA: The amount of space taken up in a plane by a figure.
AREA UNDER A CURVE: If we have limits of integration, it is most simply the definite integral of the function defined between those limits of integration.
AREA(F): The area of figure F.
ARGUMENT OF A FUNCTION: The term or expression upon which a function operates. In y=f(x), the argument of the function is x.
ARGUMENT OF A VECTOR: The angle at which a vector is directed.
ARITHMETIC MEAN: What we generally consider to be the average. The sum of a set of values divided by the cardinal number of the set of values.
ARITHMETIC OPERATION: A mathematical process of addition, subtraction, multiplication or division.
ARITHMETIC PROGRESSION: A series of terms where successive terms are obtained by addition of a constant.
ARITHMETIC SEQUENCE: A series of terms where successive terms are obtained by addition of a constant.
ARITHMETIC SERIES: Akin to Arithmetic Progressions and Arithmetic Sequences, the series typically reflects an addition operator between terms, as a sum.
ASYMPTOTE: A line (or curve) that a function approaches without actually reaching the line as the domain either grows unbounded or approaches a limit.
AUGMENTED MATRIX: A matrix form for a linear system of equations where the number of columns is one greater than the number of rows, the final column typically coming from the constants in the linear equations.
AUTOMATIC DRAWER: A computer program that lets you build constructions.
AVERAGE: Most commonly, average means the arithmetic mean; we sum the values and divide that sum by the number of numbers. The average between two real values is the midpoint between those values.
AVERAGE RATE OF CHANGE: The change in value divided by elapsed time.
AXES: Two perpendicular number lines that are used to locate points in a coordinate plane. By convention, the x-axis is the horizontal line and the y-axis is the vertical line.
AXIOM: Accepted without proof (unlike a theorem), an axiom is readily understood and regarded as fact.
AXIS: In physics, a line about which a body rotates. In mathematics, a line that divides a plane or space into two equal halves, typically demarcated in units.
BALL: A "solid sphere"; the interior of a sphere (open ball); a sphere and its interior (closed ball);.
BASE: The side of an isoscoles triangle whose endpoints are the vertices of the base angles.
BASE ANGLE: The angle opposite one of the equilateral sides in an isoscoles triangle.
BASE ANGLE OF A TRAPEZOID: Consecutive angles that share a base of a trapezoid.
BASE OF A CONIC SOLID: The planar region that forms the widest point of a conic solid; often labeled as the 'bottom' of the conic solid, it determines the exact shape of the conic solid.
BASE OF A CYLINDRIC SOLID: The original region and its translation image.
BASE OF A TRAPEZOID: The parallel sides of a trapezoid.
BASE, EXPONENTIAL: The value being raised by powers as exponents; the number being raised to the power.
BEST-FIT LINE: A line drawn so it is close to most or all of the data points in a graph.A best-fit line is described as strong or weak depending on how close the data points are on average.
BETA: Beta is the second letter of the Greek alphabet.
BICONDITIONAL: A biconditional statement has literally two conditions. The classic If-Then statement is the biconditional with a hypothesis and conclusion.
BILATERAL SYMMETRY: See reflection symmetry.
BINOMIAL: A binomial has two terms. Terms are usually separated by plus signs or minus signs.
BINOMIAL COEFFICIENTS: Binomial coefficients are found in Pascal's Triangle. We use these coefficients to raise binomials to successive powers as well as to determine the number of combinations or ways we can take a number of objects from a set of objects. Statistics and probability calculations make significant use of binomial coefficients.
BINOMIAL PROBABILITY: When outcomes are of a binary nature, the logic of two states (high or low, true or false, or the ones and zeroes of computer data streams) we can employ techniques of binomial probability, with coefficients from Pascal's Triangle, to determine the likelihood of potential events or outcomes.
BINOMIAL THEOREM: The Binomial Theorem affords the use of coefficients to calculate probabilities that are determined with the logic of two states. In situations where outcomes are either true or false, high or low, or the 1 or 0 of binary data streams, the Binomial Theorem gives us efficient calculations for likelihoods of events.
BISECTOR OF AN ANGLE: See angle bisector.
BISECTOR PF A SEGMENT: Any plane, point or two-dimensional figure containing the the midpoint of the segment and no other points on that segment.
BORROMEAN RINGS: A set of three rings joined in such a way that no pair is interlinked, but the three cannot be separated.
BOUNDARY: Some functions are bounded, some are not. Some regions are bounded, some are not. To be bounded means to have a limit; its extent only goes so far, and then it stops or ends.
BOUNDED FUNCTION: A bounded function approaches or reaches a limit. If a function goes toward infinity it is generally considered unbounded.
BOX: A surface made up of rectangles; a rectangular parallelpided.
BOX-AND-WHISKER PLOT: In statistical data, a box-and-whisker plot is sometimes used to graphically represent quartiles. Quartiles are the extremes of the body of data, as well as the 25th, 50th and 75 percentiles.
BRACES: Braces act just like parentheses. Always (almost) used in pairs, braces look like this: { }.
BRACKETS: Brackets act just like parentheses, coming in pairs to group data or terms.
BUNDLE: The set of planes through a point, in projective geometry.
CAGE: Regular graph that has as few vertices as possible for its girth. Formally, an (r,g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. The (r,3)-cage is a complete graph Kr+1 on r+1 vertices, and the (r,4)-cage is a complete bipartite graph Kr,r on 2r vertices. Other cages listed in Wikipedia include the Moore graphs: (3,5)-cage: Petersen graph, (3,6)-cage: Heawood graph, (3,8)-cage: Tutte Coxeter graph, (7,5)-cage: Hoffman Singleton graph.
CALCULUS: Calculus is the branch of mathematics concerned with the rates of changes between variables (derivatives) as well as areas under curves that represent functions (integrals).
CAPACITY: See volume.
CARDINAL NUMBER: The number of objects or elements within a set is the Cardinal Number of the set.
CARTESIAN COORDINATES: The familiar x-y coordinate plane is called the plane of Cartesian Coordinates; it is named for Rene Descartes.
CARTESIAN PLANE: The Cartesian Plane contains the familiar x-axis and y-axis in which we plot ordered pairs. It is the familiar Rectangular Coordinate system.
CENTER OF A CIRCLE: The point that all points in the circle are equidistant from.
CENTER OF A ROTATION: The point where the two intersecting lines of a rotation meet.
CENTER OF GRAVITY: The mean of the coordinates of points in a figure, whether one, two, or three-dimensional.
CENTRAL ANGLE OF A CIRCLE: An angle whose vertex is the center of the circle.
CEVIAN: A line segment connecting a vetex of a triangle with a point on the opposite side of the triangle. The condition for three general Cevians from the three vertices of a triangle to concur (at a cevian point) is known as Ceva's theorem.
CEVIAN POINT: The point of concurrence of three cevians.
CEVIAN TRIANGLE: Given a point P and a triangle ABC, the Cevian triangle A'B'C' is defined as the triangle composed of the endpoints of the cevians through the Cevian point P.
CHAIN RULE: The Chain Rule is a basic rule in calculus to find the derivative of a composite function.
CHANGE-OF-BASE FORMULA: There is an easy way to change the bases between logarithms. A simple formula, the Change-of-Base formula is an acquired taste.
CHI: The twenty-second letter of the Greek alphabet.
CHORD: In general, a straight line joining two points on a curve; often, chord is used to mean a straight line segment joining and included between two points on a circle;.
CHORD OF A CIRCLE: A segment whose endpoints are on a circle.
CIRCLE: The set of points on a plane at a certain distance (radius) from a certain point (center); a polygon with infinite sides.

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