# MATH GLOSSARY

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Title Description
AAS Congruence Angle-angle-side congruence between two (or more) triangles. Congruent triangles have sides and angles of identical measure.
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 distance on the real number line between an value and zero. It applies best to things for which negative values have no meaning, such as mass or length.
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 less than 90 degrees.
Acute Triangle A triangle whose interior angles are each acute, that is, less than 90 degrees (or π/2 radians).
Additive Inverse for Arithmetic The opposite of a given number. Change the sign of a number to have its additive inverse. The sum of a number and its additive inverse is always zero.
Additive Inverse for Matrices Mr. X takes the mystery out of Additive Inverse for Matrices, a matrix when added to another equals the Zero Matrix. Subscribe to my youtube channel for more instructional math videos.
Additive Property of Equality This property allows us to add equals to equals to stay equal. Given two equal values, we may add the same quantity to both values and retain an equality.
Adjacent Next to each other. The idea is especially important in geometry, as with adjacent angles that share a common ray.
Adjacent Angles Next to each other. Adjacent angles share a common ray and subsequently have a common vertex.
Algebra The branch of mathematics that allows manipulation of symbols and values to determine quantities that are not always fixed. Variables are essential to algebra.
Algorithm A sequence of steps to accomplish a familiar task; a recipe.
Alpha The first letter of the Greek alphabet.
Alternate Exterior Angles Given two parallel lines cut by a transversal, angles exterior to the parallel lines and on opposite (alternate) sides of the transversal are congruent.
Alternate Interior Angles Given two parallel lines cut by a transversal, angles interior to (between) the parallel lines and on opposite (alternate) sides of the transversal are congruent.
Alternating Series A series in which successive terms have opposite signs. Every other term is positive; every other term is negative.
Altitude Height. The perpendicular or orthogonal distance above a fixed reference, as height above mean sea level. In geometry, the shortest distance from the base of an object to its apex (or top).
Altitude of a Cone The shortest line segment from the apex (tip) of a cone to the plane of its base.
Altitude of a Cylinder The distance between the planes containing the bases of a cylinder.
Altitude of a Parellelogram The distance between opposite sides of a parallelogram
Altitude of a Prism The length of the shortest line segment between the planes containing the bases of a prism.
Altitude of a Trapezoid The distance between bases of a trapezoid.
Altitude of a Triangle The shortest line segment between the vertex of a triangle and line containing the opposide of the triangle. The three altitudes of a triangle are concurrent at the orthocenter.
Amplitude Periodic functions have an amplitude that is half the range between the highest and lowest values. The height a sinewave climbs from zero (if zero is its mean values) is its amplitude.
Analytic Geometry Effectively coordinate geometry. It is the use of coordinates (in two or more dimensions) to determine geometric relationships.
Angle The separation of two rays measured as the rotation of one of the rays. Usually measured in either degrees or radians, other systems of measuring rotation are also used to assign values to angles.
Angle Bisector A ray (or line) that divides an angle into two congruent halves. The three angle bisectors of a triangle are concurrent at the incenter.
Angle of Depression The angle below a horizontal reference. Typically it is the angle between a line-of-sight ray referenced to a horizontal line (or plane).
Angle of Elevation The angle above a horizontal reference. Typically it is the angle between a line-of-sight ray referenced to a horizontal line (or plane).
Annulus The area, or region, between two concentric circles of different radii.
Antiderivative Given a function with a derivative, the antiderivative of that derivative function returns the original function.
Apex The top. Most generally a singular situation as a point. The vertex of a cone or pyramid is an apex.
Apothem The apothem applies to a regular polygon; it is either the distance from the center to a midpoint of a side, or the radius of an inscribed circle in the polygon.
Arc A section of circumference. An arc is measured either by its own length or with a central angle.
Arc Length A curved length; it can be the distance around a portion of a circle, or around a different shape of curved figure.
Arccos The inverse cosine. Given the number that represents the cosine of an angle, the arccosine of the number returns the angle whose cosine is the given number.
Arccot The inverse cotangent. Given the number that represents the cotangent of an angle, the arccotangent of the number returns the angle whose cotangent is the given number.
Arccsc The inverse cosecant. Given the number that represents the cosecant of an angle, the arccosecant of the number returns the angle whose cosecant is the given number.
Arcsec The inverse secant. Given the number that represents the secant of an angle, the arcsecant of the number returns the angle whose secant is the given number.
Arcsin The inverse sine. Given the number that represents the sine of an angle, the arcsine of the number returns the angle whose sine is the given number.
Arctan The inverse tangent. Given the number that represents the tangent of an angle, the arctangent of the number returns the angle whose tangent is the given number.
Area The measure of a plane region defined to be within some boundary.
Area of a Circle The extent of surface contained within the circle; π times the square of the radius.
Area of a Kite Half the product of the diagonals.
Area of a Parallelogram Akin to the area of a rectangle, the area of a parallelogram can be expressed as the product of length times width.
Area of a Rectangle The extent of surface contained within the rectangle; length times width.
Area of a Regular Polygon One-half the product of perimeter times the apothem. Remember that regular means equilateral and equiangular.
Area of a Rhombus If s is the length of a side and h is the height, s-squared times the sine of the big interior angle; s-squared times the sine of the smaller interior angle; half the product of the diagonals.
Area of a Sector of a Circle It is the surface area of a slice of pie. We like arc length s=rΘ. So area of a sector is r-squared times theta all over two (Θ in radians).
Area of a Segment of a Circle Given central angle theta, area of the segment is one-half the square of the radius times the quantity (Θ minus sine Θ), provided Θ is in radians.
Area of a Trapezoid One-half the (sum of the bases) times the height. Or, the product of (median) and (altitude).
Area of a Triangle One-half times the base times the height. Also, given perimeter a+b+c, and semiperimeter s=half that sum, then area = the square root of [s times (s-a) times (s-b) times (s-c)]. (Heron).
Area of an Ellipse If 2a and 2b are the lengths of the major and minor axes of the ellipse, then the area of the ellipse is simply πab.
Area of an Equilateral Triangle Given side of length s, the area of an equilateral triangle is s-squared times the-square-root-of-three over four.
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.
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 A branch of mathematics built upon the basic operations of addition, subtraction, division, and multiplication. Powers, roots, and logarithms are often considered arithmetic in nature.
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 Progression Also Arithmetic Sequence. A series of terms where successive terms are obtained by addition of a constant.
Arithmetic Sequence Also 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.
ASA Congruence Angle-side-angle congruence between two (or more) triangles. Congruent triangles have sides and angles of identical measure.
Associative Law of Addition Provides that addition of groups of terms or values is indifferent to the order of grouping. We may add terms in any order, or group them in any order.
Associative Law of Multiplication Provides that multiplication of groups of terms or factors is indifferent to the order of grouping. We may multiply factors in any order, or group them in any order.
ASTC Mnemonic device for remembering which trig functions are positive in the four Cartesian quadrants.
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.
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 Most simply, the plural of axis. More generally, the horizontal x-axis and the vertical y-axis that comprise the skeleton of Cartesian Coordinates.
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.
Axis of Rotation A line about which a body rotates.
Axis of Symmetry A line about which a graph or body is symmetrical, that is, a mirror image on one side of the axis from the body or graph on the other side.
Base, Exponential The value being raised by powers as exponents; the number being raised to the power.
Base, Geometric For a polygon, the line segment on the bottom. For a solid, the area of the "floor."
Bearing The direction of a vector can be a heading or a bearing. Heading implies movement along a compass direction. Bearing implies a static compass direction.
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.
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.
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.
Bisect Infinite lengths are not bisected. We bisect, or divide into equal halves, angles or line segments. Rays and lines are not bisected.
Bisector A bisector cuts a geometric entity into two equal halves. It may divide an angle or a line segment, depending on the specific circumstance. A perpendicular bisector divides a line segment at a right angle.
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-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.
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).
Cardinal Number The number of objects or elements within a set is the Cardinal Number of the set.
Cardioid A heart-shaped curve formed by rotating a circle and graphing the movement of that point as the "outside" circle traces around the inside circle.
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.
Catenary Curve The curve formed by hanging a rope or chain between two posts is a Catenary Curve. Its math function is that of the hyperbolic cosine function.
Center of Mass The Center of Mass of an object is the point at which forces acting on the object may be considered to be balanced or concentrated. In a triangle it is at the centroid, the point of concurrence where the medians of the triangle meet.
Center of Rotation A point around which the rest of a body or object rotates is termed the Center of Rotation.
Center of Rotation 2 The point around which an object revolves or rotates is called the Center of Rotation.
Central Angle A Central Angle is formed at the center of a circle. Think of the angle formed by cutting a slice of pie or cake from the center of a round baked good.
Centroid The Center of Mass of a triangle (made from some flat material) is its Centroid. It is the point at which the medians of the triangles intersect, also called the point of concurrence.
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 A line (line segment) across a circle that does not pass through the center of the circle is termed a Chord.
Circular Cone A Circular Cone need not have its apex directly above the center of its base.
Circular Cylinder A Circular Cylinder does not have to have sides perpendicular to its base; its side may be oblique.
Circular Functions Circular Functions are based on the properties of circles, which are plane figures where every point on the circle is equidistant from a center point.
Circumcenter The center of a circumscribed circle is called its Circumcenter. All regular polygons have a circumcenter, but most polygons do not. All triangles have a circumcenter.
Circumcircle Also called the Circumscribed Circle, the Circumcircle encompasses a polygon and all vertices of the polygon are on the circle.
Circumference The distance around a circle is its Circumference. It is the product of pi times the diameter, or twice the product of pi and the radius of the circle.
Circumscribed Circle A circle around a polygon that contains all the vertices of that polygon is termed a Circumscribed Circle, also called a Circumcircle.
Clockwise Rotation in the same direction as the hands of a traditional clock.
Closed Interval A segment of the real number line including the endpoints.
Coefficient A number that indicates the multiple of an algebraic term.
Coefficient Matrix A matrix comprised of coefficients which can be used to solve a system of equations.
Cofactor Typically the result of taking a determinant, it is a number associated with an element in a matrix.
Cofunctions Each of the six basic trigonometric functions have a cofunction. Their names tell the story: sine and cosine, tangent and cotangent, secant and cosecant are each pairs of cofunctions.
Collinear Lined up perfectly; exactly aligned. In the same line are collinear points.
Column, Matrix Strictly speaking, a Column Matrix is often a single column. More generally, a column is a vertical array of elements within a matrix.
Combinations Combinations are calculated to be the number of ways that a number of objects may be selected from a group of objects.
Combinatorics The branch of math that provides calculations for the selection of a number of elements from a set is called Combinatorics.
Common Logarithm The base-ten logarithm is often called the Common Logarithm.
Common Ratio In a geometric progression, subsequent terms are obtained by multiplication of terms by a constant called the Common Ratio.
Commutative Law of Addition When adding terms the order in which we add them matters not at all.
Commutative Law of Multiplication The order in which we multiply any number of factors (to obtain the product of those factors) matters not at all.
Complement of an Angle Complementary Angles sum to 90 degrees or pi/2 radians. So the complement of an angle with measure x is (90 - x) degrees or (pi/2 - x) radians.
Complement of an Event The complement of an event pertains to probability. If the probability of an event is x, then the probability of the complement of that event is 100 percent minus x.
Complementary Angles Complementary Angles sum to 90 degrees or pi/2 radians.
Complex Conjugate The Complex Conjugate of (a + bi) is (a - bi). The Complex Conjugate of (c - di) is (c + di).
Complex Number All numbers, as it turns out, are complex. When the "imaginary part" has a zero coefficient, the number is purely real.
Complex Plane The complex number plane is required to map or plot complex numbers because the complex numbers themselves have two components.
Composite Number Composite Numbers relate to positive integers that are not prime. If a positive integer has factors other than itself and one, it is a Composite Number.
Compound Interest When the Time Value of Money generates interest and that interest is added to the principal to increase the amount of money to which subsequent interest is added, this is Compound Interest.
Computation Computation is the act of taking values and logical mathematical steps to make a calculation.
Concave Bending inward or with an indentation. The opposite of convex, Concave applies to physical objects such as lenses or mirrors, as well as to polygons or solids.
Concave Polygon A Concave Polygon has an "indentation." In moving around the perimeter of the polygon, at least one interior angle will be greater than 180 degrees.
Concenric Circles Circles having the same centers but different radii are termed Concentric Circles.
Concentric Literally having the same center point; centered at the same point.
Conclusion When mathematical conclusions are valid the laws of math and science have been adhered to, and a logical approach has been taken. Sometimes conclusions are invalid because scientific or mathematic rigor has not been adhered to. Reason and judgment are often important to reaching sound or valid conclusions.
Concurrent At the same point. Concurrent geometric entities occupy the same place, the same space.
Cone A Cone is a geometric shape where a simple closed curve is connected to an apex (a point) with smooth lateral sides.
Congruence Test There are various tests for congruence, which is the state of having identical size and shape.
Conic Section Any of the various geometric entities that are formed by slicing a cone (or double cone) are termed Conic Sections. The list includes: circles, ellipses, parabolas, and hyperbolas.
Conjugates Conjugates multiply to simpler entities based on changing the operator between terms of each conjugate from positive to negative, or vice versa.
Consecutive Interior Angles When two parallel lines are cut by a transversal, the two angles formed on one side of the transversal between the parallel lines are termed Consecutive Interior Angles; they are supplementary.
Consistent System of Equations When a system of equations has at least one solution (and most often a unique solution) the equations are said to be Consistent.
Constant A mathematical value that never changes is said to be constant. Real numbers are constants because their value never changes. In a polynomial, a term with a variable (or variables) raised to the zero power is constant.
Continuous A function is considered Continuous if its graph has no gaps, no holes, no steps, and no cusps or discontinuities.
Continuous Compounding When an entity experiences Continuous Compounding it grows unceasingly and constantly, that is, the addition of some portion of its size to its size happens all of the time. Bacterial growth and population growth are often considered to be functions of Continuous Compounding.
Continuous Function When the graph of a function has no holes, no gaps, no steps, or no discontinuities, then it is considered Continuous. It may have cusps.
Continuously Differentiable When a function is Continuously Differentiable it is both continuous and smooth.
Contraction Contraction is the process by which some object or entity is shrunk or diminished in size or extent. It may be diminished in one dimension, or reduced proportionally if it is a two- or three-dimensional object. A Contraction can also be the result of such a process.
Contrapositive Given a conditional statement, its Contrapositive is logically equivalent and is obtained by negating the original hypothesis and conclusion as well as reversing their order.
Convergence To approach a limit is to experience Convergence. Mathematical series experience convergence when the sum of their expanded terms reaches a boundary or limit.
Convergent Series A series is said to be Convergent when its sum approaches a limit.
Converse Given a conditional statement, as "If A, then B," the Converse results from switching the order of the hypothesis and conclusion: "If B, then A." The Converse may or may not be true given a true original statement.
Convex When a geometric or physical entity has no indentations. Or, when a polygon has the property where no line segment across it leaves the interior of the polygon, the polygon is said to be Convex.
Coordinate A value associated with the location of a point is a Coordinate. In one dimension a Coordinate is a single value. In two dimensions, a point is defined by two Coordinates as an ordered pair.
Coordinate Geometry This branch of mathematics is a combination of algebra and geometry; it is analytic geometry.
Coordinate Plane Two-dimensional entities are graphed or plotted in a plane, such as the rectangular plane or Cartesian Plane. Two-dimensional polar coordinates are also plotted in a plane. It requires an ordered pair to specify a location in a plane.
Coplanar In the same plane; of the same plane. Most generally, points within the same plane are said to be Coplanar.
Corollary A Corollary is like a baby theorem.
Correlation When two variables have a strong linear relationship, either increasing proportionally or one variable decreasing as the other increases, we say there is (strong) Correlation between the variables.
Correlation Coefficient We typically use "r" for the Correlation Coefficient. When two variables are strongly correlated, that is, have a strong linear relationship, r will have a value that approaches either 1 or -1, depending on whether the variables increase with respect to each other.
Corresponding Angles Sometimes Corresponding Angles refer to the "same" angle in two similar (or congruent) polygons. Or, when parallel lines are cut by a transversal, Corresponding Angles are "on the same corner of the intersections."
Cosecant One of the six basic trig functions, the Cosecant function is the reciprocal of the sine function, and the cofunction of the secant. The Cosecant of theta can be expressed as (r/y) for an angle in standard position, or the ratio of hypotenuse over opposite side in a right triangle.
Cosine One of the six basic trig functions, the Cosine is the cofunction of the sine function and the reciprocal of the secant function. In standard position the Cosine of theta is (x/r). In a right triangle the cosine of an angle is the ratio of the adjacent side to the hypotenuse.
Cotangent One of the six basic trig function, Cotangent is both the reciprocal function and the cofunction of the tangent function. For a right triangle, the Cotangent of an angle is the ratio of adjacent side to the opposite. In standard position for angle theta, the Cotangent can be expressed as (x/y).
Coterminal When one angle is in the same position as another, as adding or subtracting 360 degrees or 2 pi radians puts a rotating angle in the same position as the previous angle, we say the angles are Coterminal.
Countable In common language, countable just means reasonably enumerated or countable, as in there are not too many objects to physically count. In human terms, the grains of sand in the Sahara Desert are not countable. But mathematically they actually are. So Countable means something a little different to the mathematicians.
Counterclockwise For angles in standard position, we use a Counterclockwise rotation for positive measurement of the angle's rotation. This is the direction opposite the traditional movement of analog clock hands.
Counting Numbers The set of Counting Numbers is (usually) identical to the set of Natural Numbers, the positive integers that we begin to count with when we're little kids. Watch out, however: some people include zero in this set.
CPCTC In geometry class we use this shorthand for "Corresponding Parts of Congruent Triangles are Congruent."
Cramer's Rule Cramer's Rule provides a matrix manipulation to solve simultaneous equations.
Critical Number While there are many ways to define Critical Numbers, depending on the circumstances, most generally we're interested in places where a function generates either an extreme value or a discontinuity.
Cross Product A product of vectors that generates another vector is often a Cross Product.
Cube A six-sided orthogonal box with square faces; a right square parallelepiped. The result of raising a real value to its third power. The process of multiplying a number times itself and times itself again.
Cube Root The Cube Root of a real value is the number that when raised to the third power equates to the original real value.
Cubic A Cubic is a third-order polynomial.
Curve Beware that mathematicians consider straight lines to be Curves!
Cusp When the graph of a function comes to a sharp point, we say that point on the graph is a Cusp.
Cycloid The path that a point on the outside of a rolling wheel makes is termed a Cycloid.
Cylinder A Cylinder may or may not have circular bases. The lateral sides are connected with congruent, parallel bases that may be the shape of any closed curve.
Cylindrical Shell A method for volumetric calculations especially for rotated bodies around an axis. The small thickness of the shell is typically the differential "dx" (or dy or whatever differential represents the incremental thickness of the cylinder).
Decagon A 10-sided polygon is called a decagon.
Decreasing Decreasing means to lessen in extent or scope, to be reduced. A function is considered to be Decreasing if the values in the range decrease as the values from the domain increase.
Deductive Logic Deductive Logic is employed before events have transpired, before the fact.
Definite Integral An integral evaluated between limits of integration is termed a Definite Integral.
Degree, Angle One 360th of a full rotation is an angle of one degree.
Degree, Polynomial The Degree of a polynomial is the order, or highest power (term) of the polynomial.
Delta Delta is the fourth letter of the Greek alphabet. Upper-case Delta looks like a triangle and is used to mean "the change in..."
DeMoivre's Theorem This theorem allows quick calculations of powers and roots of complex numbers expressed in trigonometric form.
Denominator The Denominator of a fraction is the number on the bottom; it is the divisor of the numerator.
Dependent Variable If y = f(x), then y is a function of x and y is the Dependent Variable. Think of it this way: whatever we get for output "y" depends on the input "x" we grab from the domain of the function.
Derivative A first Derivative is the slope of the line tangent to a function. A Derivative provides an instantaneous rate of change between variables.
Determinant A Determinant is a number associated with a square matrix. It may also be a cofactor, a number associated with a square array from a larger matrix.
Diagonal Convex polygons have Diagonals from each vertex to each non-adjoining vertex.
Diagonal Matrix A square matrix with zero values everywhere except on the main diagonal (upper left to lower right) is termed a Diagonal Matrix.
Difference The result of subtraction is often considered a Difference.
Differentiable If a function is smooth and continuous it is differentiable.
Differential Equation A Differential Equation employs derivatives and algebra to solve for variables that represent functions.
Digit Each of the numerals 0 through 9 is a Digit. The term also refers to place value, as the "tens digit" or the "hundredths digit."
Dilation To grow in size is to dilate, or to undergo Dilation. Most often it means to increase proportionally in all dimensions, but not strictly. Sometimes Dilation is expansion in one dimension only.
Dimension A line has one Dimension. A plane has two Dimensions. A three-dimensional object occupies space.
Dimension, Matrix The Dimension of a matrix is its order, or size. We label the order of a matrix by its number of rows then its number of columns. A 4x3 matrix is read as "a four by three matrix" and has four rows and three columns.
Direct Proportion When variables are in Direct Proportion to one another they have the relation that as one variable grows the other either increases or decreases by a constant multiplication factor. When y = kx, we say the variables are in Direct Proportion.
Direct Variation Also direct proportion, Direct Variation describes the relation y = kx.
Directrix A line specific to conic sections hyperbolas, parabolas, and ellipses, known as a Directrix, serves to describe along with the location of the focus (or foci) the loci (points) on the graph of the function.
Discontinuity When a function is literally not continuous because of a gap, a step, a hole, or any kind of "break" it is considered discontinuous.
Discrete Function When the inputs from the domain of the function are not smooth and continuous but rather incremental, the function is considered to be a Discrete Function.
Discriminant In the Quadratic Formula, the radicand (the business inside the square-root sign) is the Discriminant. In general, a Discriminant provides algebraic information about the roots of polynomials.
Disjoint Disjoint sets have no common elements.
Disk A Disk is most often a circular object with a relatively thin measure in the direction orthogonal to the plane of the circular bases.
Distance A length from one point to another is considered a Distance. Any measurement in one dimension confers a length, which is Distance.
Distance Formula The familiar Distance Formula in Cartesian (rectangular) coordinates is a version of the Pythagorean Theorem, where the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
Distributive Property The familiar Distance Formula in Cartesian (rectangular) coordinates is a version of the Pythagorean Theorem, where the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
Divergent Geometric Progression An infinite geometric progression (or a significant portion of one) is termed Divergent when its common ratio has an absolute value less than or equal to -1, or greater than or equal to 1.
Dividend When we divide, we typically "begin" with a dividend. We divide the dividend by the divisor and we get the resulting quotient. In a fraction, which is always top-divided-by-bottom (numerator divided by denominator), the top of the fraction is the dividend, the bottom is the divisor, and the value of the resulting fraction is the quotient.
Divisor The number we "take into" the dividend when we divide is termed the Divisor. In fractions, which are always top-divided-by-bottom (numerator divided by denominator) we divide the top (the dividend) by the bottom (the divisor) and the value of the resulting fraction is the quotient.
Dodecagon A 12-sided polygon is a Decagon.
Dodecahedron A 12-faced polyhedron is called a Dodecahedron.
Domain The values that are "legal" and "legitimate" to put into a function are the elements of the Domain of that function. When y = f(x), the legitimate values of x are the Domain of the function.
Dot Product A product of vector multiplication, the Dot Product is a scalar, which means it has magnitude only and not an associated direction. The Dot Product does not result in another vector.
Double Twice the value of a real number is Double the value. To Double is to multiply by two, so to Double a half results in a whole.
Doubling Time The time it takes an exponential or geometric growth to double in size (grow by 100 percent of the original value) is its doubling time.
e, Base of Natural Logarithm A very important number, e is approximately 2.718281828459045.
Eccentricity A parameter of conic sections. Eccentricity is itself rather eccentric, or out of the ordinary.
Element Element has a lot of meanings. Each entry in a matrix is an Element. Each object in a set can be termed an Element. A constituent or piece of something bigger is also called an Element.
Ellipse One of the conic sections, an Ellipse is a plane figure with well-defined properties that often include vertices and a major axis and a minor axis.
Ellipsoid Think of a blimp (a zeppelin) or a football (American football).
Empty Set The Empty Set is also called the Null Set. It is the set with nothing in it, and there is but one Null Set (or Empty Set).
Epsilon The fifth letter of the Greek alphabet is Epsilon.
Equal In the United States all men are created Equal, endowed by their Creator with certain unalienable rights that include life, liberty, and the pursuit of happiness.
Equality A statement where two or more values are deemed to have an equal or identical value is a statement of Equality.
Equation A statement of equality, or equal value, is termed an Equation. When we solve an Equation we solve for some entity or value that makes the statement true.
Equiangular Having all angles of equal measure is to be Equiangular. Equilateral polygons are most often (but not necessarily) also equiangular; they are termed Regular Polygons.
Equidistant Literally of the same distance to some reference point is the essence of Equidistant.
Equilateral Polygons with all sides congruent are said to be Equilateral. Most Equilateral polygons are also equiangular (but not necessarily). Polygons that are both equilateral and equiangular are termed Regular Polygons.
Equivalence When we establish Equivalence we set forth two or more equivalent or equal entities.
Eta Eta is the seventh letter of the Greek alphabet.
Euclidean Geometry The plane geometry we all study in school is a form of Euclidean Geometry, spiced with a few three-dimensional figures for flavor.
Euler's Formula (Complex) Euler's Formula for complex numbers expresses a complex number in trigonometric form.
Euler's Formula (Polyhedra) V - E + F = 2. For any polyhedron, the number of vertices minus the number of edges plus the number of faces equals two.
Evaluate When we Evaluate an expression we determine its value or the value of some entity within it to (typically) make the statement true.
Even (integer) Even integers end with one of the following five digits: 0, 2, 4, 6, or 8. These digits are considered Even and the integers that end with them are also considered Even. When Even integers are divided by two the quotient is an integer.
Even Function Even Functions are symmetrical about the y-axis, provided they are expressed as y = f(x). Even Functions adhere to the following: f(-x) = f(x).
Exact When a value is an Exact value it is either precise or equal to a given value or standard value.
Exclusion Exclusion means to leave out or to not include some value, either from a set or for consideration into a set of values.
Expansion By Cofactors Expansion By Cofactors is a process to evaluate matrix values such as determinants by taking a sum of values generated by the sum of cofactor products.
Expected Value The Expected Value is, statistically, the real number or value that is most likely to occur for some event when examined as an average value. The Expected Value may not actually be an obtainable value; it is an average value.
Explicit Ideas or notions directly expressed or understandable are considered Explicit.
Exponent Usually written as a superscript, an Exponent is a number or entity to which some other value is raised, as a power.
Exponential Decay When an established quantity loses value and decreases by some constant percentage over some constant period of time it is considered to experience Exponential Decay.
Exponential Function An Exponential Function employs the independent variable as an exponent on a constant. If expressed as y = f(x), the Exponential Function will pass through (0,1). Such a function is the inverse to a logarithmic function.
Exponential Growth When an established quantity gains value and increases by some constant percentage over some constant period of time it is considered to experience Exponential Growth.
Expression A mathematical statement of almost any kind is considered an Expression.
Exterior Angle An Exterior Angle is most commonly the angle formed between the extension of a side of a polygon and the adjoining side.
Extraneous Solution Sometimes we perform mathematical manipulations and obtain solutions that do not make sense but nevertheless are obtained by following the rules of, say, algebra. Such solutions are termed Extraneous. Often they do not strictly satisfy the original conditions of the problem that was solved.
Extreme Value Theorem On any continuous function graphed on a closed interval from a domain, we are guaranteed to have a maximum and a minimum value if the range of the function is not constant.
Extremum The highest and lowest values for the output of a function are called Extremum, the singular form of plural extrema.
Face, Geometry Solids, in geometry, are considered to have faces when lateral sides are flat, that is, planar.
Factor (Noun) The noun Factor is a value that is multiplied with another Factor (or factors) to result in a product. That product of two or more factors is the result of the operation of multiplication.
Factor (Verb) The verb Factor is the act of dividing some entity into components or pieces that, when multiplied together, produce the given entity. We "break apart" some real value or quantity into its multiplicative factors when we Factor.
Factor Tree A Factor Tree is a written mechanism to see the factors or prime factors of some value (usually an integer, but not necessarily).
Factorial A Factorial results from the multiplication of successive positive integers. The term Factorial is either a function or a number, depending on its specific use.
Fibonacci Numbers This set of numbers itself grows without bound, but the ratio of successive terms in the series converges to the golden ratio.
Finite The common meaning of Finite and its meaning to mathematicians are not quite the same. In everyday language, Finite means countable within a reasonable time. To math people, Finite means not infinite; it means, simply, having a bound.
First Derivative The First Derivative of a typical function, say, y = f(x), is the slope of the line tangent to a point on the graph of the original function f(x).
First Order Differential Equation This type of equation includes first derivatives and employs algebra to treat those derivative functions as variables.
First Order Polynomial This type of equation has no variables raised to integer powers greater than one.
First Quartile In certain sets of data it is appropriate to divide the values into fourths by frequency of occurrence. The First Quartile is the 25th percentile, or the high-end value of the low-end quarter of data values.
First Quintile In certain sets of data it is appropriate to divide the values into fifths by frequency of occurrence. The First Quintile is the 20th percentile, or the high-end value of the lowest 20 percent (fifth) of data values.
Fixed Fixed terms or values are constant, never changing value.
Foci Certain points in conic sections (and other geometric entities) are termed Foci, the plural of focus. They are important to the mathematical mechanics of the functions.
Focus A specific point in a conic section (or other geometric entity) is termed a Focus, the singular form of the word foci. They are important to the mathematical mechanics of the functions.
Foil (Fiol) A mnemonic for remembering "first-outside-inside-last" for multiplication of two binomials. It is equivalent the FIOL, as we take the sum of products.
Formula A recipe or algorithm for calculation, evaluation, simplification, or just about anything we do in mathematics can be called a Formula.
Fourth Quintile When data is appropriately characterized by percentiles, the Fourth Quintile is the 80th percentile, with only 20 percent of the data values greater than this; it is the bottom of the highest fifth.
Fractal Certain shapes maintain their shape through all permutations of multiplication, growth, dilation, division, contraction, or shrinkage. Such shapes are Fractals.
Fraction Fractions are many, many things. But always, without fail, fractions are the result of dividing the top value (numerator) by the bottom value (denominator).
Fractional Exponents Real values can be raised to powers that are integers or fractions. Fractional Exponents can be thought of as having a denominator that is the root of the value being raised to the power, with a numerator akin to an integer power.
Frequency How often (or frequently) does something occur? That is its Frequency. The Frequency of a waveform is inversely proportional to its wavelength.
Frustum Slice a pyramid (or cone) parallel to its base, remove the top. What remains under the "missing top" is the Frustum.
Function Function takes on several meanings in the language of mathematics. A typical connotation is a relation between variables where for any input (an independent variable or element from the domain) we have a unique output (element in the range, or dependent variable result).
Fundamental Theorem of Algebra Single-variable polynomials with complex coefficients have at least one complex root. The field of complex numbers is closed.
Fundamental Theorem of Arithmetic A theorem that all integers can be written as the product of prime numbers is often called the Fundamental Theorem of Arithmetic.
Gamma Gamma is the third letter of the Greek alphabet.
Gauss-Jordan Elimination Gauss Jordan Elimination is a traditional matrix row manipulation used to find inverse matrices.
General Form for Equation of a Line Such a form has integer coefficients for both x and y when describing a line in Cartesian (rectangular) coordinates.
Geometric Mean The Geometric Mean of two real values is the square root of the product of the two values. More generally, the Geometric Mean of n values is the nth root of the product of the n values.
Geometric Progression This term is used for geometric series, geometric sums, or geometric sequences when subsequent terms result from multiplication by a constant that is most often called the common ratio.
Geometric Series A Geometric Series is a form of geometric progression.
Googol Ten raised to the power of one hundred equals one Googol.
Googolplex Ten raised to the power of a googol is a Googolplex; it is a huge number.
Great Circle Basically, any circle that resides on a sphere is a Great Circle.
Greatest Common Factor The GCF of two integers (usually) is the largest integer that divides evenly into both integers. We sometimes use GCF for non-integral values.
Greek Anyone interested in learning mathematics should embrace the Greek alphabet with 24 letters from alpha to omega.
Half-Life When some entity experiences exponential decay (reduction or diminution) the times it takes to lose half of its size (or strength) is its Half-Life.
Harmonic A small integral multiple (or divisor) of a waveform is a harmonic.
Heading Quite similar to bearing, Heading is a dynamic direction that implies motion.
Height Altitude. How tall something is, measured in some perpendicular fashion to the "bottom" is its height.
Helix A straight line wrapped around a circular cylinder at some angle not perpendicular to the base of the cylinder results in a Helix.
Heptagon A seven-sided polygon is a Heptagon; also called a septagon.
Heron's Formula A wonderful little recipe (algorithm) for finding the area of a triangle when sides are known and the altitude is not known, the formula is best expressed with a semiperimeter.
Hexahedron A six-faced polyhedron is termed a Hexahedron.
High Quartile The 75th percentile. Also upper quartile.
High Quintile The 80th percentile; upper quintile.
Hole A missing element (typically a point) from an otherwise continuous function is called a Hole.
Homogeneous Equations Homogeneous Equations have terms of like power or order.
Horizontal Horizontal comes from orientation like the horizon; parallel to the "flat" surface of the earth; perpendicular to vertical.
Hyperbola A conic section of specific mathematical relation to foci; its shape is the intersection of a double cone with a plane. The difference between distances from a locus on the Hyperbola to the two foci is a constant.
Hyperbolic Geometry Hyperbolic Geometry is non-Euclidean geometry; within it the Parallel Postulate does not hold.
Hypotenuse The longest side of a right triangle is the Hypotenuse; it is always opposite the 90-degree angle (or right vertex).
Hypothesis In a biconditional statement the hypothesis is followed by a conclusion. In the scientific method, the hypothesis is the conjecture to be proved or disproved.
i, Square Root of -1 The small-case i is reserved for the square-root of a negative one; the square of i is -1.
Identity As opposed to a conditional statement that is sometimes true, an Identity will always be true. The multiplicative identity is 1; the additive identity is zero.
Identity Matrix The Identity Matrix is a square matrix with zeros everywhere except on the main diagonal, which has all elements equal to one. It is the product of a matrix and its inverse.
Identity Property of Addition The Identity Property of Addition says that adding zero to (or subtracting zero from) any real value will not change the value.
Identity Property of Multiplication The Identity Property of Multiplication says that multiplication of a real value by one (or division by one) will not change the value.
If-and-Only-If (Iff) A statement that shows a condition both necessary and sufficient for the assertion.
If-Then Statement The classic biconditional statement is often phrased as an If-Then proposition.
Imaginary Number Imaginary Numbers exist, but we do not call them "real."
Implicit Implied as opposed to absolutely expressed, Implicit functions typically have two (or more) variables on one side of the equation.
Impossibility Despite what some "possibility thinkers" espouse, some things are mathematically impossible. For example, an exact real number cannot be simultaneously irrational and rational.
Incenter The center of a circle inscribed within a polygon. For a triangle, it is the point of concurrence of the angle bisectors.
Incircle A circle inscribed within a regular polygon (or any triangle) is an Incircle. In a regular polygon, the radius of the Incircle is the apothem.
Inconsistent Inconsistent equations have no simultaneous solution.
Increasing If the values in the range of a function increase as the values of the domain increase, the function is said to be Increasing.
Indefinite Integral An integral with no limits of integration, an Indefinite Integral, can be thought of an an antiderivative.
Independent Variable The set of values from the domain of a function comprise the values for the Independent Variable, the input variable into the function.
Indeterminate Often a resultant fraction like 0/0 is an Indeterminate form that requires more analysis to determine its true nature, depending on the functions involved.
Inductive Logic Inductive Logic is the logic of after-the-fact, or a posteriori. It results from observation of transpired events.
Inequality Generally of one of the following four forms: less than, less-than-or-equal-to, greater than, or greater-than-or-equal-to.
Infinite In common language, not countable in any practical manner. In math, having no bounds or boundary.
Infinite Geometric Progression When a geometric progression has a common ratio less than one (technically, a common ratio whose absolute value is less than one), then the Infinite Geometric Progression will converge to a limit.
Infinite Series Any series of terms whose progression has an unlimited (limitless) number of terms is an Infinite Series.
Infinitesimal Infinitely small is Infinitesimal, so tiny that it occupies no space. While in human terms anything really small (a molecule) is Infinitesimal, in math the term means approaching zero in size.
Infinity That without bound; limitless.
Inflection On the graph of a function, a point of Inflection is where the curve begins to "bend the other way."
Initial Side of an Angle In standard position, the Initial Side of an Angle is the ray along the positive x-axis, from the origin.
Inner Product With vectors, the dot product is considered an Inner Product.
Inscribed Angle An angle inside a circle with its vertex on the circle is an Inscribed Angle.
Inscribed Circle This term is the same as Incircle, a circle inscribed within a polygon.
Instantaneous Rate of Change The value of the first derivative of a standard function of the form y = f(x).
Instantaneous Velocity The reading at any instant on a speedometer gives an Instantaneous Velocity. To be precise, the speedometer gives an instant snapshot of speed (only) with no direction; physical velocity has both magnitude and direction, as a vector.
Integer An Integer is a whole number or its negative. When expressed as a decimal, an Integer has nothing to the right of the decimal point (in American style).
Integral A specific function in calculus. Or, simply related to integers. Integral might also mean "important" in common language.
Integrand The function that undergoes integration is the Integrand.
Integration A process, or function, in calculus to sum an infinite number of infinitesimal increments.
Interest Given the time-value-of-money, Interest is generated on a sum of capital as time passes.
Interior Interior means within or "in-between."
Interior Angle Any angle inside a geometric entity, or between geometric lines, is considered an Interior Angle.
Intermediate Value Theorem The IVT basically says that between two different values is an intermediate value somewhere between the extremes.
Interquartile Range The Interquartile Range is the half of overall data between the 25th and 75th percentiles.
Intersection Where geometric entities cross, or where sets have common elements, is termed an Intersection.
Interval The space or region between two defined values is an Interval.
Interval Notation With brackets or parentheses, depending on whether endpoints are included in the set, Interval Notation expresses the solution set for an inequality.
Invariant Constant. Not changing. Static. That which does not vary.
Inverse Inverse carries a lot of meanings within the language of mathematics.
Inverse Cosecant Given a number, this function returns the angle whose cosecant is the given number.
Inverse Cosine Given a number, this function returns the angle whose cosine is the given number.
Inverse Cotangent Given a number, this function returns the angle whose cotangent is the given number.
Inverse Function For most functions in Cartesian coordinates, the inverse function is the mirror image around the x=y line.
Inverse Secant Given a number, this function returns the angle whose secant is the given number.
Inverse Sine Given a number, this function returns the angle whose sine is the given number.
Inverse Tangent Given a number, this function returns the angle whose tangent is the given number.
Inverse Trigonometric Function Given a number, this function returns the angle whose trig function is the given number.
Inverse Variation Variables or factors that multiply to a constant value are said to be in a relation of Inverse Variation.
Inverse, Conditional Given an initial if-then statement, the negative of both the hypothesis and conclusion provides the Inverse to the original statement.
Inverse, Matrix When two matrices multiply to produce the identity matrix, each is said to be the Inverse Matrix of the other.
Inversely Proportional When the product of two variables is a constant the variables are said to be Inversely Proportional to one another.
Iota The ninth letter of the Greek alphabet, Iota means a very small amount.
Irrational Number An Irrational Number cannot be expressed exactly as the ratio of two integers. Irrational Numbers, when expressed as decimals, never repeat or terminate.
Isosceles Trapezoid A trapezoid (quadrilateral with one pair of parallel sides) whose non-parallel sides are congruent is termed an Isosceles Trapezoid.
Isosceles Triangle A triangle with two congruent sides.
Iteration A procedure that repeats, typically by adding some value to a variable in the process with each new calculation is called an iterative process, and each cycle of the calculation is an Iteration. A computational procedure in which a cycle of operations is repeated, often to approximate the solution to a problem.
Joint Variation Joint Variation is identical to direct variation; as one variable increases so, too, does the other variable increase proportionally.
Jump A step within a function is sometimes termed a Jump.
Kappa The tenth letter of the Greek alphabet is Kappa, popular on college campuses with sororities and fraternities.
Kite A quadrilateral with two pairs of congruent sides, and unlike, say, a parallelogram, the congruent sides of a kite are adjacent. Its diagonals meet at right angles.
Lambda Lambda is the eleventh letter of the Greek alphabet and is used for wavelength in physics.
Lateral The flat sides of a geometric solid are generally termed the Lateral sides or Lateral surface area.
Lateral Surface Area The Lateral Surface Area of a geometric solid is the expanse of the flat sides (or smooth sides). Be careful, some solids have faces that are termed bases and not lateral surfaces.
Law of Cosines The familiar Pythagorean Theorem is a special case of the Law of Cosines.
Law of Sines The ratio of the sine of any angle within any specific triangle and the length of the opposite side is a constant.
Leading Coefficient Most typically we write polynomials with the first term having the highest order, or power. The coefficient of this leading term is literally the Leading Coefficient.
Leading Term The first term in a polynomial, most typically the highest-order term, is the Leading Term of the polynomial.
Least Common Denominator When two or more fractions are being summed we want the LCD to facilitate the operation of addition.
Least Common Multiple The LCM is most typically applied to integers. It is the smallest value evenly divisible by each number for which we seek the LCM.
Least Upper Bound As the name implies, a function often has a highest value or a limit beyond which it may not realize.
Leg, Trapezoid The Leg of a Trapezoid is one of the non-parallel sides.
Leg, Triangle Most generally the legs of a triangle refer to the perpendicular sides of a right triangle only.
Lemma A little, inconsequential theorem is sometimes called a Lemma.
Like Terms Like Terms have the same variables raised to identical powers.
Limit Some functions have a Limit, a bound beyond which they may not realize.
Line A collection of points that comprise the shortest path between two points in Euclidean geometry is a Line; all points in a Line are collinear and, of course, coplanar.
Line Segment A section of a line, with endpoints on both ends, is a Line Segment.
Linear As the first four letters imply, Linear means "of a line" or "lined up" in a collinear fashion.
Linear Pair Two adjacent supplementary angles form a Linear Pair.
Local Maximum A Local Maximum is a high spot on the graph of a function. Also termed a relative maximum, it is the greatest value within a defined neighborhood.
Local Minimum A Local Minimum is a low spot on the graph of a function. Also termed a relative minimum, it is the least value within a defined neighborhood.
Loci The points that comprise a function (or graph thereof) are its Loci.
Locus A single point on a function or on its graph is a Locus.
Logarithm A Logarithm is a number associated with a power and a base; the function is the inverse of an exponential function.
Logic Logic takes many forms and is instrumental in understanding the language of mathematics.
Long Division Adolph Hitler actually had two middle names: Long Division. Just kidding. And we should not kid about an evil, pestiferous maniac like Hitler.
Lower Bound As the name suggests, some functions are limited on the low side.
Lower Quartile Also first quartile, it is the 25th percentile, where 75 percent of the data is greater than this value.
Lower Quintile The 20th percentile; also first quintile.
Magnitude, Powers of Ten Often when we compare the multiplication by various powers of ten we speak of the magnitude of the effect of the multiplication.
Magnitude, Vectors The Magnitude of a vector is the length of the vector. We may apply a Pythagorean relation to the perpendicular components of the vector to find the length.
Major Axis Certain conic sections have a Major Axis, a line (segment) between vertices.
Matrix A rectangular array of numbers is often called a Matrix.
Matrix Addition Matrix Addition applies to matrices of like order, the same size.
Matrix Element One of the numbers or terms within the rectangular array of terms in a matrix is an Element of the Matrix.
Matrix Multiplication To multiply two matrices: the number of columns in the first matrix must match the number of rows in the second matrix.
Maxima The plural of maximum. Maxima are "high spots" on the graph of a function.
Maximize A process to establish the greatest extent, value, or size possible.
Maximum A highest value. A local Maximum is the highest value of a function within some defined neighborhood.
Mean Value Theorem Essentially, between any two extremes is an average value.
Measure A noun or verb, Measure implies comparison to an established standard.
Measurement The result from comparison to an established standard, Measurement may be exact only to an agreed-to precision.
Median, Data The Median of a set of data is the value in the middle of an ordered or sorted list, with just as many values higher than the Median as lower than the Median.
Median, Trapezoid The average of the lengths of the bases of a trapezoid. The Median is a line segment parallel to and equidistant from the bases.
Median, Triangle A triangle has three Medians, each a line segment from a vertex to the midpoint of the opposite side of the triangle. Medians are concurrent at the centroid.
Midpoint Every line segment (or side of a polygon) contains a point equidistant from the endpoints (or vertices), the Midpoint.
Midpoint Formula A simple recipe for finding the Midpoint of a line segment in Cartesian or rectangular coordinates. Add the x-coordinates of the endpoints of the line segment and divide by two for the x-coordinate of the midpoint. The y-value follows similarly.
Minima The plural of minimum. Minima are low points on the graph of a function.
Minimize A process to establish the least extent, value, or size possible.
Minimum A low point or least value in the neighborhood of the graph of a function is a Minimum, the singular of minima.
Minor Axis A line or line segment specific to certain conic sections.
Minute, Angle For angles, one Minute is one-sixtieth of a degree. One Minute is equivalent to 1/21600 of a circular rotation.
Minute, Time One-sixtieth of an hour comprises one Minute of time.
Mixed Number We may write an "improper" fraction as a whole number followed immediately with a "proper" fraction. Such a form is termed a Mixed Fraction.
Mode While Mode can take on several meanings in mathematics, it generally is used for the value of data with the greatest frequency of occurrence in a list of values.
Modulo N Often written as "mod n," it is the remainder after division, and it makes sense in the realm of integers (only).
Modulus Most typically it is the length of a vector.
Modus Ponens We have "If A, then B." Modus Ponens is a piece of logic that goes like this: if we know A to be true, then we know that B must be true, too.
Modus Tollens Begin with "If A, then B." That's a given. We (somehow) know that B is false. We then may infer (but not conclude) that A is false. Modus Tollens is not particularly robust; it is not entirely dependable.
Moment Moment takes on many meanings in statistics and physics.
Moment of Inertia Each shape or body has an associated Moment of Inertia related to mass distribution and the choice of the axis around which the body is rotated.
Monomial A single term.
Mu The twelfth letter of the Greek alphabet, Mu is used for both the mean and median in a normal distribution.
Multiplication You know, times. The operation to simplify addition of identical values. You should learn your Times Tables, the basic facts of Multiplication.
Multiplicative Inverse Another name for Multiplicative Inverse is reciprocal. Reciprocals multiply to one.
Multiplicative Inverse, Matrix The Multiplicative Inverse of a Matrix is the matrix for whom the operation of matrix multiplication on another matrix produces the identity matrix. More commonly it is termed simply the Inverse Matrix.
Multivariable Having more than one variable. Also multivariate.
Multivariate Having more than one variable. Also multivariable.
N-gon When a polynomial has so many sides that we cannot easily remember its name, we just take the number of sides (n) and add "gon" to our characterization, as a 16-sided polygon would be called a "16-gon."
Natural The set of Natural Numbers is also the set of counting numbers, the same numbers we learn to count when we're little kids: 1, 2, 3, 4.... Precisely in the language of math these are the positive integers.
Natural Logarithm The base of the Natural Logarithms is e, approximately 2.718. At 100 percent annual interest with continuous compounding over a year, the multiplication factor of principal is precisely e.
Natural Numbers The set of Natural Numbers is also the set of counting numbers, the same numbers we learn to count when we're little kids: 1, 2, 3, 4.... More precisely in the language of math these are the positive integers.
Negative Real values less than zero are Negative. We also consider the Negative of a real value to have the opposite sign, as the opposite (or Negative) of a Negative value is positive.
Negative Number A real value less than zero is a Negative Number.
Negative Reciprocal The product of two Negative Reciprocals is -1. When lines in Cartesian or rectangular coordinates meet at right angles they have Negative Reciprocal slopes, unless they are precisely horizontal and vertical.
Newton's Method An iterative method for finding roots of polynomials.
Non-collinear Not linear, not aligned, not part of the same line. Not collinear.
Non-Euclidean A geometry in which the Parallel Postulate does not hold may be termed a Non-Euclidean geometry. In such a geometry, the shortest distance between two points may not be a straight line.
Nonagon A nine-sided polygon.
Noninvertible Chiefly a term for matrices, literally unable to be inverted.
Nonnegative We have occasions to refer to all positive values as well as to zero. These are all the real values that are Nonnegative. Literally, not negative.
Nonzero Literally, not zero. Typically used to mean either positive or negative values.
Norm The heavy-set guy from the Boston tavern Cheers. Actually, its either a kind of average or a length.
Normal Usually meaning orthogonal (as to a plane), Normal sometimes means also merely perpendicular.
Normalize We might Normalize data by culling errors. Or we might Normalize a vector by assigning a unit vector in its direction.
Nth Degree Simply raised to the degree of integer (usually) n, or N. In common, everyday language, to pursue something excessively, as parents giving the suitor of their teenage daughter an interrogation "to the nth degree."
Nth Root Given some integer N and a real value, the Nth Root of the real value is the number that when raised to the N power returns the real value.
Nu Nu is the 13th letter of the Greek alphabet.
Null Set The Null Set is the empty set. Mathematically there is but one empty set, the unique Null Set, the set with nothing in it.
Number Line The real Number Line is a depiction of the set of all real numbers from negative infinity to positive infinity. All real numbers lie on the Real Number Line.
Numerator The top number in a fraction, above the fraction bar, is the Numerator. It is the dividend to be divided by the divisor, which is the denominator.
Oblique In one sense, at an angle or not perfectly horizontal or vertical. An Oblique triangle is any triangle that is not a right triangle.
Obtuse In common language Obtuse means obscure and confusing, obfuscatory. An Obtuse angle measures more than 90 degrees (and less than 180 degrees).
Octagon An eight-sided polygon.
Octant As we have four quadrants in the rectangular plane, we have eight Octants in rectangular space. In three dimensions the three axes divide space into eight sections, each termed an Octant.
Odd In common language: strange or unusual. For integers, numbers ending with any of these digits: 1, 3, 5, 7, or 9.
Odd Function An Odd Function adheres to this property: f(-x) = -f(x). The standard sine function is an odd function.
Odds The likelihood or probability of an event or specific outcome is termed the Odds of the event occurring. Odds, or probabilities, are always represented with values between 0 and 1, or between zero and 100 percent (inclusively).
Omega The last, or 24th, letter of the Greek alphabet is Omega. Upper-case Omega is used for ohms, a unit of electrical resistance. Lower-case Omega is used for angular velocity, a speed of rotation.
Omicron The 15th letter of the Greek alphabet. We don't use it in math because it looks just like an "o" or a zero.
One-Dimensional Linear, or along one line of direction. Informally, constrained to stay along a narrow line.
Open Interval A section of a line whose set does not include the endpoints is considered an Open Interval.
Operation The processes of addition, subtraction, multiplication, and division are each termed an Operation. So, too, is raising a value to a exponent.
Opposite Many meanings are found for Opposite, including having direction 180 degrees from an original direction, or having the negative sign of a previous sign. Opposite real values have identical absolute values.
Order of Operations We have a hierarchy of Order to Operations in the language of mathematics. We do multiplication before we do addition, and we also work left-to-right. We work first inside of expressions within parentheses, then outward.
Order, Matrix The Order of a Matrix is its size, expressed as "rows by columns."
Order, Polynomial The Order of a Polynomial relates to the highest power of variables in a term, typically the Order of the leading term of the Polynomial.
Ordered Pair Two coordinates are required to label a point in a plane, typically (x, y).
Ordered Triple Three coordinates are required to label a point in space, typically (x, y, z).
Ordinal Number Ordinal Numbers are ordinary numbers, or the sequential references of order as first, second, third, and so on.
Ordinary Differential Equation A Differential Equation with no partial derivatives is considered an Ordinary Differential Equation.
Ordinate In Cartesian or rectangular coordinates, the y-axis, or the coordinate from the y-axis; the second coordinate in an ordered pair.
Origin In one dimension: (0). In two dimensions: (0,0). In three dimensions: (0, 0, 0).
Orthocenter The Orthocenter of a triangle is the point of concurrence of the altitudes of the triangle.
Orthogonal Most generally Orthogonal means perpendicular to a plane.
Outcome A specific event is often termed an Outcome.
Outlier When plotting data points, as in a scatterplot, if a single data point is far removed from the neighborhood of the other data points, such a far-removed data point is called an Outlier.
Oval In common language, any elliptical shape or not-quite round "circular" shape is called an Oval. Mathematically, an ellipse is not an Oval.
Parabola The graph of a quadratic function is a Parabola, a conic section.
Parallel Lines Coplanar Lines that never meet or cross are Parallel. If lines simply never cross, they may be skew (non-coplanar).
Parallel Planes Two distinct planes, collections of flat expansion of points, that never meet are considered Parallel Planes.
Parallel Postulate Given a line and a specific point not on the line, there is only one line through the specific point parallel to the given line.
Parallelepiped A shoebox is a Parallelepiped. Any geometric body with six faces that are each parallelograms that are in planes parallel to the opposite face.
Parallelogram A quadrilateral with two pairs of parallel sides is a Parallelogram; it has many dependable properties.
Parametric Equation In a general sense, we have a Parametric Equation when we define something in specific terms of something else.
Parentheses Symbols ( ) serve to isolate or group written entities.
Partial Derivative The derivative with respect to a single variable is a Partial Derivative.
Partial Differential Equation A Differential Equation with a Partial derivative.
Partial Fraction A Fraction built from the decomposition of other terms.
Partial Sum A Partial Sum occurs when we sum only a finite number of terms from a larger or infinite series of terms.
Pascal's Triangle Pascal's Triangle is an important device for understanding binomial expansion and combinatorics.
Pentagon A five-sided polygon.
Percent Literally, per hundred.
Percentage Any reference to percent is a Percentage; the fraction of 100 a value represents.
Percentile Certain types of data lend themselves to description by what percent of the values exceed (or fall below) a specific data value. A Percentile states what percent of the data is less than the specific data value.
Perfect Square Most generally a Perfect Square is an integer that is the product of another integer times itself.
Perimeter The distance around the outside of a planar object or a plane figure is its perimeter.
Period Measured in time, or angle, or even sometimes distance, the Period of a repetitive function is the time (or angle or distance) it takes to complete a cycle.
Periodic Functions that repeat a cycle over and over again are considered Periodic.
Permutation A specific order to the grouping of objects in a combination is termed a Permutation.
Perpendicular At right angles.
Perpendicular Bisector A line segment (or side of a polygon) has a unique line through its midpoint perpendicular to the line segment (or side).
Phase Shift This applies to sinusoids moved left or right by a change to the argument (the angle).
Phi The twenty-first letter of the Greek alphabet.
Pi The constant ratio of circumference to diameter is represented by the 16th letter of the Greek alphabet; it is approximately 3.14159.
Piecewise Literally taken in sections or pieces.
Piecewise Continuous Function When a function is defined over an interval of the domain by different relations to the dependent variable we call it a Piecewise Continuous Function.
Plane An infinite expanse of points in two dimensions.
Plane Geometry Basic geometry is Plane Geometry. We hold to the parallel postulate and Euclidean principles.
Plus A symbol for addition, or the operation itself.
Point A location of infinitesimal size, that is, no size. A mathematical idea.
Point-
Polar Complex Number We may express complex numbers in trigonometric form.
Polar Coordinates In labeling a point in a plane we need two coordinates. In Polar Coordinates we use a radius and an angle, as (r, theta).
Polar-Rectangular Conversion An algorithm for changing (r, theta) to (x, y).
Polygon A closed plane figure with straight sides.
Polyhedron A geometric solid with faces that are polygons.
Polynomial A series of terms (or a single term, a monomial), usually with at least one variable; terms are separated by plus signs or minus signs.
Population Statistically when we sample a Population we generally seek a representative sample. A Population is the group from which we take a sample.
Positive Real values are Positive when they are greater than zero.
Postulate A far-reaching conjecture or sense of reasoning for which an obvious and substantive base appears most reasonable.
Power Power most often means the value of an exponent.
Power Rule A simple device in calculus to determine the derivative of a monomial.
Precision The quality of finer measurement or estimation is termed Precision.
Prime Factorization The process of finding the prime factors of a composite number is called Prime Factorization.
Prime Number A positive integer evenly divisible by itself and one but no other integers is considered a Prime Number.
Principal An amount, typically money, upon which the time value of money (accumulation of an added percentage over a defined time) generates interest is termed Principal.
Prism A Prism is a geometric solid with two congruent polygons within parallel bases connected by faces that are parallelograms.
Probability The likelihood of an event or particular outcome is its Probability. All Probabilities are between 0 and 1 (between zero percent and 100 percent).
Product The result of the operation of multiplication is called a Product.
Product Rule An algorithm within the calculus to find the derivative of the Product of two functions.
Projectile Motion Projectile Motion is a parabolic arc caused by gravity.
Proof An ingredient in pudding.
Proper Subset A set that is a subset of a given set and not identical to the given set is a Proper Subset of the given set.
Proportional In a (constant) ratio.
Psi The 23rd letter (next-to-last) of the Greek alphabet.
Pure Imaginary Number Given a complex number of the form a + bi, when a = 0 we say that the number is a Pure (or purely) Imaginary Number.
Pyramid A geometric solid with a base of a polygon and planar lateral sides that meet at a point called an apex is termed a Pyramid.
Pythagorean Identities sin²x + cos²x = 1; 1 + tan²x = sec²x; 1 + cot²x = csc²x
Pythagorean Triple A series of three integers for whom the Pythagorean relation holds, as 3-4-5 or 5-12-13, because 3² + 4² = 5² and 5² + 12² = 13².
Quadrant One of the four areas of the rectangular or Cartesian plane that is divided into fourths by the two axes.
Quadratic A second-order polynomial of the form ax² + bx = c = 0 is considered a Quadratic; it graphs to a parabola.
Quadratic Equation Any second-order polynomial in one variable set equal to a constant is termed a Quadratic Equation.
Quadruple A verb or noun; to multiply by four or the fourth integral multiple, respectively.
Quartiles Most generally, the 25th and 75th percentiles are termed the Low Quartile and High Quartile, respectively.
Quintiles Most generally, the 20th and 80th percentiles are termed the Low Quintile and High Quintile, respectively.
Quintuple A verb or noun; to multiply by five or the fifth integral multiple, respectively.
Quotient The result of the operation of division, the Quotient results from dividing a dividend by a divisor; also the value of a fraction that is always numerator divided by denominator.
Radian A Radian is an angle (measure) that subtends an arc length (on a circle) equal to the radius of the circle. Radians are just as good as degrees for measuring angles, and sometimes better.
Radian Measure Radian Measure is just as good as degree measure for angles, and sometimes better. Pi radians are equivalent to 180 degrees.
Radical A root symbol or the root itself is sometimes termed a Radical.
Radicand A number taken to a root is a Radicand; the number under a root sign.
Radius One-half the diameter of a circle is the Radius. It is the distance from the center of a circle to any point on the circle.
Range We may speak of a Range of values as simply the difference between high and low values of a data set. More specifically, the values generated by the input of domain values into a function map into the Range of values of the function.
Ratio Sometimes Ratio is meant to state a constant proportion. More generally, the Ratio of two real values is the quotient of one number divided by the other.
Rational A Rational number can be expressed as the ratio of two integers. When expressed as a decimal, a Rational number will either repeat or terminate (with repeating zeros).
Rational Expression Mathematical statements written as fractions with a numerator and a denominator are often termed Rational Expressions.
Ray A set of collinear points, a Ray has an endpoint and proceeds infinitely far in a single direction.
Real Number Depicted on the Real Number line, such a value is either less than, equal to, or greater than every other real value.
Reciprocal Every nonzero real value has a Reciprocal. A number and its Reciprocal multiply to one. We may find a Reciprocal of a number by dividing it into 1.
Rectangle A quadrilateral with many special properties, including all those of a parallelogram, and then some.
Rectangular Coordinates The familiar x-y coordinate plane; Cartesian Coordinates.
Rectangular-Polar Conversion A simple algorithm to change (x, y) into (r, theta).
Recursive A Recursive formula or series has successive terms defined by operations or permutations on the term.
Reference Angle In standard position, any angle in quadrants II, III, or IV has a Reference Angle equal to the acute angle made with the x-axis.
Reflexive Literally "in relation to itself." When we say A = A, we employ a Reflexive property.
Regression A statistical method of evaluating least-squares to find a best-fit line or curve to data.
Regression Line To find a best-fit linear relation with scatterplot data, we use Linear Regression to find a Regression Line.
Regular Polygon A Regular Polygon is both equilateral (all sides congruent) and equiangular (all angles congruent).
Regular Polyhedron A geometric solid with all faces regular polygons.
Regular Prism A Prism with bases of Regular polygons.
Regular Pyramid A Pyramid with a base of a Regular polygon.
Regular Right Prism A Prism with bases of Regular polygons and lateral faces perpendicular to those bases.
Regular Right Pyramid A Pyramid with a Regular polygon for a base and an apex directly above the center of the base.
Relative Maximum Also a local Maximum, a high spot on the graph of a function. It is the greatest value within a defined neighborhood.
Relative Minimum Also a local Minimum, a low spot on the graph of a function. It is the least value within a defined neighborhood.
Relatively Prime Two integers with no common factors other than one are said to be Relatively Prime.
Remainder When a divisor does not divide evenly into the dividend, we have a Remainder.
Revolutions Per Minute Abbreviated "rpm" it conveys the number of complete circular rotations that occur every 60 seconds at some constant rate of revolution.
Rho Lower-case Rho, the 17th letter of the Greek alphabet, is often used for density (mass per unit volume) in physics.
Rhombus A quadrilateral with four congruent sides. Its diagonals are perpendicular.
Riemann Sum Effectively the definite integral in calculus.
Right Angle An angle of 90 degrees or pi/2 radians. Perpendicular lines meet at Right Angles.
Right Circular Cone A cone with a circular base and an apex directly above the center of the base.
Right Circular Cylinder A circular cylinder with sides orthogonal to parallel bases.
Right Cone Any Cone, circular or otherwise, with its apex directly above the center of the base.
Right Cylinder Any Cylinder, circular or otherwise, with lateral sides orthogonal to the bases.
Right Prism A Prism with lateral sides orthogonal to the bases.
Right Pyramid A Pyramid with its apex directly above the center of the base.
Right Regular Prism A Prism with bases of Regular polygons and lateral faces perpendicular to the bases.
Right Regular Pyramid A Pyramid with a Regular polygon for a base and an apex directly above the center of the base.
Right Square Parallelepiped Cube.
Right Square Prism A cube, or a shoebox if the ends of the shoebox are square.
Right Triangle A triangle with a right angle.
Rolle's Theorem A principle from first-semester calculus that asserts a first derivative of zero exists on a smooth, continuous, differentiable function between constant range values.
Root Mean Square Abbreviated RMS it is the square root of the arithmetic mean of the squares of some real values, as from a data set.
Root, Number The Root of a given Number is the value that raised to the power of the root returns the given number.
Rotation Movement in a circulation or circular fashion, often around a point or an axis, is termed Rotation.
Rounding Not exactly truncating, rounding involves reduction in the precision of a value to approximate that value to some exact value with less precision.
Row Operations Arithmetic Operations on the Rows of a matrix to solve simultaneous equations.
Row-Echelon Matrix A Matrix upon which Row operations have been performed.
SAA Congruence Side-Angle-Angle Congruence establishes two congruent triangles.
Sample When we Sample a population we typically seek a representative Sample.
Sample Space We often use Sample Space to designate all the possibilities of potential outcomes for an event or process.
SAS Congruence Side-Angle-Side Congruence establishes Congruence between two triangles.
SAS Similarity Side-Angle-Side Similarity employs a fixed ratio between pairs of sides of triangles.
Scalar A value with unit of size (magnitude) and no direction is termed a Scalar. Contrast with a vector that has both magnitude and direction; a Scalar has magnitude but no direction.
Scalar Product A Product of vector multiplication, such as a dot product, that results in a value that is Scalar with size (magnitude) but no associated direction.
Scalene A triangle is considered Scalene if no two sides have the same length.
Scatterplot A planar plot of points from two variables with each point representative of a datum from both variables, most often with some relation or correlation.
Scientific Notation Scientific Notation is a way to easily represent values far from zero, in terms of powers of ten, either very large numbers or very small numbers; they are usually representative of physical quantities or values.
Secant The term applies to either a line containing the chord of a circle (or some other line segment between points on a function), or one of the six basic functions in trigonometry, the cofunction of the cosecant and the reciprocal of the cosine.
Second Derivative A Derivative taken of a first Derivative is termed a Second Derivative.
Second, Degree While "second degree" applies to a polynomial, a single Second with respect to Degree measure is one-sixtieth of one minute, or one sixtieth of one sixtieth of one degree, or 1/1,296,000 of a revolution.
Second, Time One sixtieth of a minute, or 1/3600 of an hour, is one Second of Time.
Second-order Differential Equation An ordinary Differential Equation in which the highest derivative is a second derivative is called a Second-Order Differential Equation.
Second-Order Polynomial A polynomial in which the highest-order term is of order two.
Sector A piece of a circle bounded by a central angle.
Segment, Circle A portion of a circle bounded by a chord and the circle itself.
Segment, Line A Line Segment is a set of collinear points bounded on both ends with, literally, endpoints.
Semicircle Half a circle; the portion of a circle on one side of a diameter.
Sequence Informally, any series is a Sequence. More formally, any series of terms that adheres or conforms to a pattern.
Series Most often a sequence of terms to be summed. Informally, any sequence of terms may be a Series.
Set Any collection of objects or values is considered a Set, whose cardinal number is the number of objects in the Set.
Set Intersection The Intersection of two (or more) Sets is the subset common to both (or all) Sets. Logically, the Intersection of two Sets A and B is literally the Set of "A and B."
Set Union The Union of two (or more) Sets is the Set that contains both (or all) Sets. Logically, the Union of two Sets A and B is the Set of elements contained in either Set A or B, literally "A or B."
Shell Method A method in calculus to calculate volumetric values from functions having been rotated about an axis.
Sigma The 18th letter of the Greek alphabet, upper-case sigma is used for summation notation, lower-case Sigma often denotes a standard deviation in statistics.
Sigma Notation Literally summation Notation, Sigma Notation employs an iterative mechanism around an upper-case Sigma to express the sum of a series or sequence of terms.
Significant Digits Informally, Digits that are not zero. Slightly more formally, nonzero Digits as well as zeros between nonzero Digits. Strictly, the number of Digits required to express a calculated value to within the reasonable tolerance or uncertainty of calculation.
Similar Geometrically, figures of like shape and proportions are said to be Similar.
Similarity Literally the quality of being Similar, which is to have the same shape and proportions, but not necessarily of the same size.
Simple Closed Curve A planar figure that neither crosses itself or contains a gap is a Simple Closed Curve; note that a curve can be "straight" according to the mathematicians.
Simple Harmonic Motion Periodic Motion with constant length of cycle time (a fixed period) is termed Simple Harmonic Motion.
Simplify When we Simplify mathematical expressions we restate them (or rewrite them) in more concise terms.
Simpson's Rule In calculus we may use three points of a parabola to approximate the function's range of values to determine the area of each partition of the integral.
Simultaneous Equations Equations with common solutions are Simultaneous Equations. Also, equivalent equalities (statements with equal signs) may be termed Simultaneous Equations.
Sine One of the six basic trig functions, in a right triangle the Sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.
Singular Matrix A square Matrix with no inverse is termed a Singular Matrix.
Sinusoid A sine wave is called a Sinusoid; a cosine graph is also a Sinusoid.
Skew Lines neither intersecting nor parallel (non-coplanar lines) are termed Skew lines.
Slope A number associated with a line graphed in a plane, Slope is the ratio of rise over run, an indication of the steepness of the line. We may write a line as y = mx + b and use the value of m for Slope.
Slope-Intercept Equation of a Line The familiar y = mx + b, where m represents Slope and b is the y-Intercept.
SOHCAHTOA A mnemonic device for remembering: sine-opposite-hypotenuse; cosine-adjacent-hypotenuse; tangent-opposite-adjacent. Also stands for "some old hippie caught another hippie tripping on acid."
Solid A three-dimensional geometric figure or body that includes the interior region.
Solid of Revolution When a function is rotated around an axis (of Revolution) it generates a Solid of Revolution.
Solution Too often in math class, "the answer." More directly, a Solution is a value (or set of values) that makes a mathematical statement true.
Solution Set Strictly, any Solution is a Solution Set, the value(s) that make a mathematical statement true.
Speed A (typically fixed) ratio of length or distance to a unit of time; Speed is a scalar value, as in miles per hour (mph) or feet per second (fps).
Sphere A three-dimensional figure comprised of points equidistant from a center point; a Sphere has a fixed radius.
Spherical Geometry Unlike plane Geometry, Spherical Geometry is not based on the parallel postulate. Many of our accepted geometric theorems, principles, and tenets (from plane Geometry) simply do not hold in Spherical Geometry.
Spherical Trigonometry Unlike plane Trigonometry, elementary Spherical Trigonometry is three dimensional. If based in spherical geometry, the math of Spherical Trig gets downright grisly.
Spheroid An oblate sphere. Sometimes, an ellipsoid.
Spiral Sometimes Spiral is used to describe a helix. A genuine Spiral is a plane figure of changing radius from a (usually fixed) origin.
Square One noun: the regular quadrilateral, equilateral and equiangular. Another noun: the result of multiplying a number times itself. Or, the verb: the operation of multiplying a number times itself, equivalently raising it to power two.
Square Matrix A Square Matrix has the same number of rows as columns.
Square Root Given a real value, the number that times itself (squared) produces the given value is its Square Root
SSA Ambiguity Side-Side-Angle congruence is not enough to establish congruence between two triangles; it is the Ambiguous case.
SSS Congruence Two triangles whose corresponding sides are congruent are themselves congruent.
SSS Similarity When corresponding sides of two triangles are in a fixed ratio the triangles are similar.
Standard Equation of a Line When expressing the Equation of a Line with integral coefficients we may have the Standard Equation of a Line.
Standard Position An angle in Standard Position has been rotated counterclockwise (for positive rotation) from an initial ray on the positive x-axis.
Stem-and-Leaf Plot A graphical device to group statistical data, typically by leading digits.
Step Function A discontinuous Function where the range jumps in increments (usually fixed) may be a Step Function.
Straight Angle An angle of 180 degrees or pi radians.
Strict Inequality A Strict Inequality does not include an "or equal to..."
Subset Every set is a Subset of itself. A Subset has elements all contained in a "parent" set.
Subtraction The operation we begin thinking of as "take away" or "minus" is a way to find the difference between values.
Supplementary Supplementary angles sum to 180 degrees, or pi radians.
Symmetry Having a like but reversed profile or image (a mirror image) about a line is having the quality of Symmetry about the axis (of Symmetry).
Synthetic Division Synthetic Division is a technique to simplify the long division of polynomials.
System of Equations Most generally simultaneous Equations, or a set of Equations with identical variables.
Tangent A line that touches a function curve at a single point is said to be Tangent to the function. Tangent is also one of the six basic trigonometric functions; it is the ratio of the opposite side (from a specified angle) of a right triangle to the adjacent side.
Tangent Line A Line is said to be Tangent to a function when it touches the graph of the function at a single point.
Tau Tau is the 19th letter of the Greek alphabet.
Taylor Series Many common functions can be written as an expansion of the function about a point in a form known as a Taylor Series.
Term In most mathematical expressions a single Term is isolated from other Terms by plus or minus signs. A monomial is a Term.
Terminal Side of an Angle When in standard position, an Angle has an initial side, a ray on the positive x-axis, and a Terminal Side where the rotation of the angle stops, at an angle of specific measure (in degrees or radians).
Tessellate A planar pattern of repeating geometric shapes is a Tessellation; to produce these shapes is to Tessellate.
Tetrahedron A polyhedron with four faces.
Theorem A mathematical principle typically proved with some rigor is often a Theorem.
Theta The eighth letter of the Greek alphabet is Theta, a common variable for an angle.
Third Quartile For certain types of data, it is the 75th percentile. Also high quartile or upper quartile.
Three Dimensions The Dimensions of space or volume are Three Dimensions, typically labeled with rectangular, spherical, or cylindrical coordinates.
Three-Dimensional Coordinates Three-Dimensional Coordinates require an ordered triple to label a point in space.
Transcendental Number A Transcendental Number will not be the root of a polynomial with integer coefficients; it is an irrational number.
Transitive Property The Transitive Property is exhibited when three values are related in the following manner: If A = B and B = C, then A = C. The relation need not be equality.
Transpose (Matrix) When we interchange the rows and columns of a matrix we Transpose the Matrix.
Transversal A line that crosses two or more parallel lines is often termed a Transversal.
Trapezium In the United States, a quadrilateral with no parallel sides; in other English-speaking countries, what Americans term a trapezoid, a quadrilateral with one pair of parallel sides.
Trapezoid A quadrilateral with one pair of parallel sides (U.S.); the same figure is a trapezium in some other English-speaking countries.
Trapezoidal Rule When approximating an integral in calculus we may treat each partition as a Trapezoid to determine the area under the curve.
Triangle A three-sided polygon. Triangles are either acute, right, or obtuse.
Triangulation We may conduct geographic surveys or determine the altitude of various objects by a process termed Triangulation.
Trigonometric Identities The various statements in Trigonometry that are universally true, typically for any angle in the statement, are called Trigonometric Identities. For example, sin²x + cos²x = 1 for any angle x.
Trigonometry One of the more beautiful and elegant branches of mathematics, Trigonometry provides innumerable relationships built from similar (right) triangles.
Trinomial A polynomial with three terms.
Triple As a verb, Triple means to multiply by three. As a noun, the result from multiplication by three.
Triple Product (Scalar) Effectively, a Scalar Triple Product is akin to the determinant of a 3x3 matrix.
Truncation Replace the lesser digits of some number with zeros with no regard for rounding; this is Truncation.
Two Dimensions A plane has Two Dimensions. Planar figures are Two Dimensional.
Uncountable In human terms, Uncountable means too many to practically count or enumerate. In math, an infinite function without a one-to-one correspondence to natural numbers.
Uniform Constant and unchanging; fixed.
Union The Union of two or more sets is the set of elements from all the sets. The Union of sets A and B is literally the set "A and B."
Unit Circle A Circle of radius one centered at the origin is termed the Unit Circle.
Unit Vector A vector of length one directed along one of the coordinate axes.
Upper Bound The greatest permissible value of a function may be termed its Upper Bound.
Upper Quartile Also the high quartile, the 75th percentile.
Upper Quintile Also high quintile, the 80th percentile.
Upsilon Upsilon is the 20th letter of the Greek alphabet.
Variable A Variable is a symbol, most often a letter, to represent a quantity that may change value, that is literally to vary in its value.
Vector Often represented with an arrow, a Vector is a quantity with both magnitude (size) and direction.
Vector Calculus A piece of multivariable (or multivariate) Calculus, Vector Calculus concerns itself with Vector fields, their derivatives and integrals, most often in three-dimensional space.
Velocity Formally a vector in physics, Velocity has both magnitude (speed) and direction.
Venn Diagram Most often graphics of overlapping circles and ovals, a Venn Diagram depicts sets, subsets, and their intersections and unions.
Verify To confirm is to Verify. When we Verify, we prove or establish some assertion to a dependable conclusion independent from bias. There is wisdom in these words: "Trust, but Verify."
Vertex A "corner" of a polygon is a Vertex; an extremum of a conic section is a Vertex; the endpoint(s) of rays that form an angle is a Vertex.
Vertical Straight up, perpendicular to horizontal, is Vertical. Vertical lines have an indeterminate or infinite slope.
Vertical Angles When two lines cross (intersect) they form two pairs of Vertical Angles; the Angles within each pair of Vertical Angles are congruent.
Vertical Line Test Given a relation between x and y expressed as y = f(x), the relation is a function if the graph passes the Vertical Line Test; no vertical line may cross the graph more than once. No single element from the domain of x may generate more than a single value of y mapped into the range, to be considered a function.
Volume The extent to which an object fills units of three-dimensional space is its Volume.
Washer Essentially the same as a cylinder, the Washer method for integrating a volume of revolution in calculus employs a thin, hollow disk as the partition of integration.
Wavelength The length of a wave, literally, is its Wavelength. Typically symbolized with Greek letter lambda, a Wavelength can be measured by actual length, or by the period, which may be the angle traversed through one complete cycle, or the time required to complete a cycle.
Weighted Average When several factors comprise a score or calculation and the factors have different amounts of importance to the overall result, a Weighted Average may be calculated by assigning more importance (or "weight") to one factor over another.
Whole Numbers Most often, the set of positive integers and zero.
Work Equivalent to energy, Work is the product of force and distance.
x-Intercept Where a graph crosses (intersects) the x-axis in rectangular or Cartesian coordinates is termed an X-Intercept.
x-y Plane The familiar coordinate plane. The x-axis is almost universally horizontal; the y-axis is subsequently vertical. Or, the Plane of X-Y in three-dimensional space with ordered triples (x, y, z).
x-z Plane In three dimensions, the plane orthogonal to the y-axis.
Xi The 14th letter of the Greek alphabet.
y-Intercept The point where a function graph crosses (intersects) the y-axis is termed the Y-Intercept. In the familiar linear equation form (Slope-Intercept form) of y = mx + b, the value of b is the Y-Intercept.
y-z Plane In three dimensions, the plane orthogonal to the x-axis.
Zero The only real value that is neither negative nor positive. It is an integer value.
Zero Slope When the calculation of Slope is Zero there is a rise of Zero over any value of run. Most generally, a horizontal line has Zero Slope.
Zero Vector A Vector of length Zero.
Zero, Function The Zero of a Function is the x value for which the output, y, of the function is zero; provided, of course, that y = f(x).
Zero, Matrix Technically an identity Matrix for Matrix addition, the Zero Matrix is a Matrix with all elements equal to zero.
Zeta The sixth letter of the Greek alphabet.

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