Mathematics. Dictionary

The first of the two terms by which a point is referred to, in a system of fixed rectilinear coordinate (Cartesian coordinate) axes.

For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, \sqrt{a^2+b^2}. Denoted by vertical bars | \, |.

An angle greater than 0 degrees and less than 90 degrees.

A triangle all of the angles of which are acute.

The arithmetic operation of adding.

Either of a pair of angles that share a common side

Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.

A collection of ordered steps that solve a mathematical problem. A precise step-by-step plan for a computational procedure that possibly begins with an input value and yields an output value in a finite number of steps.

The line perpendicularly connecting a figure’s vertex, especially a triangle’s apex, to the side opposite to the vertex.

A figure formed by two rays which start from a common point (a plane angle) or by three planes that intersect (a solid angle).

A ray that divides an angle into two equal parts.

Rotation opposite to the direction of the hands of a clock; counterclockwise.

An imprecise solution or result that is adequate for a defined purpose.

A continuous part of the circumference of a circle (circular arc) or of another curve.

A measure of the extent of a surface; it is measured in square units.

A series of propositions organized so that the final proposition is a conclusion which is intended to follow logically from the preceding propositions, which function as premises.

Of, relating to, or using arithmetic; arithmetical.

The measure of central tendency of a set of values computed by dividing the sum of the values by their number.

A sequence in which each term except the first is obtained from the previous by adding a constant value, known as the common difference of the arithmetic progression.

A straight line which a curve approaches arbitrarily closely as it goes to infinity. The limit of the curve; its tangent "at infinity".

Any measure of central tendency, especially any mean, the median or the mode.

A fixed one-dimensional figure, such as a line or arc, with an origin and orientation and such that its points are in one-to-one correspondence with a set of numbers; an axis forms part of the basis of a space or is used to position and locate data in a graph (a coordinate axis)

The lowest side of a triangle or other polygon, or the lowest face of a cone, pyramid or other polyhedron laid flat.

Billion is a word (in several languages) for a large number with two distinct definitions: 1,000,000,000, i.e. one thousand million, or 109 (ten to the ninth power), as defined on the short scale (also known as a milliard on the long scale). This is now the most common sense of the word in all varieties of English; it has long been established in American English and has since become common in Britain and other English-speaking countries as well. 1,000,000,000,000, i.e.…

A line or curve that bisects or divides a line segment, angle, or other figure into two equal parts.

A rectangular object in any number of dimensions.

The degree Celsius is the unit of temperature on the Celsius temperature scale (originally known as the centigrade scale in English), one of two temperature scales used in the International System of Units (SI), the other being the closely related Kelvin scale. The degree Celsius (symbol: °C) can refer to a specific point on the Celsius temperature scale or to a difference or range between two temperatures. It is named after the Swedish astronomer Anders Celsius (1701–1744), who proposed the first version of it in 1742.…

The point in the interior of any figure of any number of dimensions that has as its coordinates the arithmetic mean of the coordinates of all points on the perimeter of the figure (or of all points in the interior for a center of volume).

A line segment between two points of a curve.

A two-dimensional geometric figure, a line, consisting of the set of all those points in a plane that are equally distant from a given point (center).

The line that bounds a circle or other two-dimensional figure.

Rotation in the same direction as the hands of a clock.

A constant by which an algebraic term is multiplied.

Any integer that is a common multiple of the denominators of two or more fractions.

A number that can divide two different numbers, without leaving a remainder.

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it (for example, "3 − 5 ≠ 5 − 3"); such operations are not commutative, and so are referred to as noncommutative operations.…

A drafting instrument with two hinged legs, used for drawing circles and arcs and for measuring distances.

An angle which, together with a given angle, makes a right angle.

A (nonzero) natural number that is expressible as the product of two (or more) natural numbers other than itself and 1.

Interest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest.

A solid of revolution formed by rotating a triangle around one of its altitudes.

Having a difference divisible by a modulus.

A sequence of notes or chords that results from repeated shifts in pitch of the same interval.

A quantity that remains at a fixed value throughout a given discussion or operation.

A number representing the position of a point along a line, arc, or similar one-dimensional figure.

In a right triangle, the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse. Symbol: cos

In a right triangle, the reciprocal of the tangent of an angle. Symbols: cot, ctg or ctn

The third power of a number, value, term or expression.

Of a number or expression, a number or expression the cube of which is equal to the given number or expression.

Relating to polynomials of the form ax^3 + bx^2 + cx + d .

A surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.

A polygon with ten sides and ten angles.

Concerning numbers expressed in decimal or mathematical calculations performed using decimal.

A dot separating the whole part of a decimal number from its fractional part.

A reduction in the number of stitches, usually accomplished by suspending the stitch to be decreased from another existing stitch or by knitting it together with another stitch. See .

A unit of measurement of angle equal to of a circle's circumference.

The number or expression written below the line in a fraction (such as 2 in ½).

In an equation, the variable whose value depends on one or more variables in the equation.

A line joining non-adjacent vertices of a polygon.

Any straight line between two points on the circumference of a circle that passes through the center of the circle; a chord that passes through the center of the circle.

The quality or attribute which is added to those of the genus to constitute a species; a differentia.

A position in a sequence of numerals representing a place value in a positional number system.

A reduction from the regular price.

The length of the shortest path between two points.

In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality x ⋅ ( y + z ) = x ⋅ y + x ⋅ z {\displaystyle x\cdot (y+z)=x\cdot y+x\cdot z} is always true in elementary algebra. For example, in elementary arithmetic, one has 2 ⋅ ( 1 + 3 ) = ( 2 ⋅ 1 ) + ( 2 ⋅ 3 ) . {\displaystyle 2\cdot (1+3)=(2\cdot 1)+(2\cdot 3).} Therefore, one would say that multiplication distributes over addition.…

A number or expression that is to be divided by another.

The process of dividing a number by another.

In an expression involving division, the number by which another number is being divided.

A polyhedron with twelve faces; the regular dodecahedron has regular pentagons as faces and is one of the Platonic solids.

The set of input (argument) values for which a function is defined.

Twice as large; a number multiplied by two.

A one-dimensional face of a polytope. In particular, the joining line between two vertices of a polygon; the place where two faces of a polyhedron meet.

A closed curve, the locus of a point such that the sum of the distances from that point to two other fixed points (called the foci of the ellipse) is constant; equivalently, the conic section that is the intersection of a cone with a plane that does not intersect the base of the cone.

Either of the two nodes of a graph of degree 1.

Exactly identical, having the same value.

An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; in mathematical problems, equations describe various essential aspects of the problem, each of which contributes to the resolution of the problem in part.

A triangle having all three sides equal.

A rough calculation or assessment of the value, size, or cost of something.

An integer that is divisible by two.

The number by which a value (called the base) is said to be raised to a power in exponentiation: for example, the 3 in 2^3=8.

Any function that has an exponent as an independent variable.

An arrangement of symbols denoting values, operations performed on them, and grouping symbols.

An angle formed between one side of a polygon and an extension of an adjacent side.

Any of the flat bounding surfaces of a polyhedron; more generally, any of the bounding pieces of a polytope of any dimension.

Any of various objects multiplied together to form some whole.

The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.

The process of creating a list of factors.

The Fahrenheit scale () is a temperature scale based on one proposed in 1724 by the physicist Daniel Gabriel Fahrenheit (1686–1736). It uses the degree Fahrenheit (symbol: °F) as the unit. Several accounts of how he originally defined his scale exist, but the original paper suggests the lower defining point, 0 °F, was established as the freezing temperature of a solution of brine made from a mixture of water, ice, and ammonium chloride (a salt).…

The form of a syllogism with respect to the relative position of the middle term.

Any mathematical rule expressed symbolically.

A ratio of two numbers (numerator and denominator), usually written one above the other and separated by a horizontal bar called the vinculum or, alternatively, in sequence on the same line and separated by a solidus (diagonal bar).

A relation in which each element of the domain is associated with exactly one element of the codomain.

A measure of central tendency of a set of n values computed by extracting the nth root of the product of the values.

A sequence in which each term except the first is obtained from the previous by multiplying it by a constant value, known as the common ratio of the geometric progression.

The branch of mathematics dealing with spatial relationships.

A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field φ: ∇&phi

A data chart (graphical representation of data) intended to illustrate the relationship between a set (or sets) of numbers (quantities, measurements or indicative numbers) and a reference set, whose elements are indexed to those of the former set(s) and may or may not be numbers.

The relation >, indicating that one value is larger than another.

Any half-sphere, formed by a plane intersecting the center of a sphere. .

A polygon with seven sides and seven angles.

A polygon with six sides and six angles.

The number 100; ten tens.

One of a hundred equal parts of a whole.

The side of a right triangle opposite the right angle.

A regular icosahedron: one of the Platonic solids, all of whose faces are regular (equilateral) triangles

An equation which always holds true regardless of the choice of input variables.

A vulgar fraction of which the numerator has a greater magnitude than the denominator, such as 3/2.

In an equation, any variable whose value is not dependent on any other in the equation.

A statement that of two quantities one is specifically less than (or greater than) another. Symbol: or \leq or > or \geq or \ne, as appropriate.

Greater than any positive quantity or magnitude; limitless.

A number that has an infinite numerical value that cannot be counted.

A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.

A point where a graph crosses an axis.

The price paid for obtaining, or price received for providing, money or goods in a credit transaction, calculated as a fraction of the amount or value of what was borrowed.

The inner angle between two sides of a polygon.

Of two sets, to have at least one element in common.

The result of a circle inversion; the set of all such points; the curve described by such a set.

Any real number that cannot be expressed as a ratio of two integers.

A triangle having at least two sides equal.

The relation <, indicating that one value is smaller than another.

algebraic expressions whose literal coefficients represent the same value regardless of the numbers assigned to them.

A value to which a sequence converges. Equivalently, the common value of the upper limit and the lower limit of a sequence: if the upper and lower limits are different, then the sequence has no limit (i.e., does not converge).

An infinitely extending one-dimensional figure that has no curvature; one that has length but not breadth or thickness.

A part of a straight line bounded by two points.

A polynomial equation of the first degree (such as x = 2y - 7)

Any function whose graph is a straight line: f(x)=ax+b

The set of all points whose coordinates satisfy a given equation or condition.

For a number x, the exponent by which a given base number must be raised in order to obtain the power x. Written \log_b x. For example, \log_{10} 1000 = 3 because 10^3 = 1000 and \log_2 16 = 4 because 2^4 = 16.

A measure of the inertia of a mass of matter, one of four fundamental properties of matter. SI unit of mass: kilogram.

The greatest value of a set or other mathematical structure, especially the global maximum or a local maximum of a function.

Any function of multiple variables that satisfies certain properties and yields a number representative of its arguments; or, the number so yielded; a measure of central tendency.

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect at the triangle's centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length. The concept of a median extends to tetrahedra.

The base unit of length in the metric system, equal to 100 centimeters.

A point which divides a line segment into two lines of equal length.

The smallest member of a batch or sample or the lower bound of a probability distribution.

A minor arc may refer to: An arc that is smaller than a semicircle A term that arises in connection with the Hardy–Littlewood circle method

The sign −, indicating subtraction or a negative number.

A number consisting of a whole number and a fraction, such as 11½.

A state of a system that is represented by an eigenfunction of that system.

The absolute value of a complex number.

A whole number that is obtained by multiplying a specific whole number by another whole number.

The process of computing the sum of an addition with one and the same number a specified number of times (i.e. 4 times 5 = [0 +] 5 + 5 + 5 + 5 = 20) or any other analogous binary operation that combines other mathematical objects.

A positive integer {1, 2, 3, ...}.

In mathematics, a negative number is the opposite of a positive real number. Equivalently, a negative number is a real number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset. If a quantity, such as the charge on an electron, may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative.…

Any set of polygons joined edge to edge that, when folded along the edges between adjoining polygons so that the outer edges touch, form a given polyhedron.

The number or expression written above the line in a fraction (such as 1 in ½).

An angle that is greater than 90 degrees and less than 180 degrees.

A triangle one of whose angles is obtuse.

A polygon with eight sides and eight angles.

Any integer that produces a noninteger when divided by two.

The sequence in which the various operations in a mathematical expression are to be evaluated.

Of a figure: having all its sides and angles equal.

The point at which the axes of a coordinate system intersect.

Lines or planes that never meet, staying the same distance apart at all points.

A convex quadrilateral in which each pair of opposite edges are parallel and of equal length.

A polygon with five sides and five angles.

The sum of the distance of all the lengths of the sides of an object.

At or forming a right angle (to something).

A line that divides a line segment into two equal parts while also being perpendicular to said line segment.

An irrational and transcendental constant representing the ratio of the circumference of a Euclidean circle to its diameter; approximately 3.14159265.

The value of a digit of numbers. For example, ones, tens, hundreds in the decimal counting; ones, sixes, thirty-sixes in the senary counting.

A flat surface extending infinitely in all directions (e.g. horizontal or vertical plane); a bounded portion thereof.

The sign +, indicating addition or a positive number.

A decimal point (now especially when reading decimal fractions aloud).

A plane figure bounded by edges that are all straight lines.

A solid figure with many flat faces and straight edges.

An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as a_n x^n + a_{n-1}x^{n-1} + ... + a_0 x^0.

The probability that a statistical test will reject the null hypothesis when the alternative hypothesis is true.

The factorization of a positive integer into its constituent prime numbers.

Any natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

Chosen or assumed among a branch of possible values of a multi-valued function so that the function is single-valued.

A polyhedron with parallel ends of the same polygonal shape and size, the other faces being parallelogram-shaped sides.

A number, between 0 and 1, expressing the precise likelihood of an event happening.

A quantity obtained by multiplication of two or more numbers.

A sequence of statements consisting of axioms, assumptions, statements already demonstrated in another proof, and statements that logically follow from previous statements in the sequence, and which concludes with a statement that is the object of the proof.

A vulgar fraction in which the magnitude of the numerator is less than or equal to that of the denominator, such as 2/3.

A statement of equality between two ratios.

An instrument for measuring angles, usually a marked semicircle.

A solid with triangular lateral faces and a polygonal (often square or rectangular) base.

In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation: a 2 + b 2 = c 2 .…

One fourth of a circle or disc; a sector with an angle of 90°.

A quadratic polynomial, function or equation.

A polynomial equation of the second degree; an equation that can be rearranged in standard form as ax^2 + bx + c = 0, where x is an unknown value, a, b and c are known numbers, and where a does not equal zero.

A polygon with four sides.

The number (either a fraction or an integer) resulting from the division of one number by another.

A line segment between any point of a circle or sphere and its center.

In descriptive statistics, the range of a set of data is the size or width of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). It is expressed in the same units as the data. The range provides an indication of statistical dispersion. Robust measures of range include the interdecile range and the interquartile range.

A ratio comparing two quantities expressed in different units.

The relative magnitudes of two quantities (usually expressed as a quotient).

A number that can be expressed as the ratio of two integers.

A line extending indefinitely in one direction from a point.

The limit of a convergent sequence of rational numbers, whether the limit is a rational number such as 2, -5, or 2/7 or whether the limit is an irrational number such as the square root of two or the circumference of the circle whose radius is one.

The number obtained by dividing 1 by another given number; the result of exchanging the numerator and the denominator of a fraction.

Any quadrilateral having opposing sides parallel and four right angles.

An angle greater than 180 degrees but less than 360 degrees.

The number left over after a simple subtraction

A parallelogram having all sides of equal length.

Half of the angle formed by a single straight line, equivalent to 90 degrees.

A triangle having a right angle as one of its interior angles.

Of a number or expression, a number which, when raised to a specified power, yields the specified number or expression.

A (usually rigid), flat, rectangular measuring or drawing device with graduations in units of measurement; a straightedge with markings.

An ordered, usually numerical sequence used for measurement; means of assigning a magnitude.

A triangle having each of its three sides of different lengths.

a method of writing, or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10

A unit of time equal to 1/60 of a minute; also a unit of angular measure.

Part of a circle, extending to the center; circular sector.

The part of a circle between its circumference and a chord (usually other than the diameter).

Half of a circle, bounded by a diameter and half the circumference.

A collection of zero or more objects, possibly infinite in size, and disregarding any order or repetition of the objects which may be contained within it.

Having the same shape, in particular, having corresponding angles equal and corresponding line segments proportional.

In a right triangle, the ratio of the length of the side opposite an angle to the length of the hypotenuse.

The distance from any point on the circle of a right circular cone to its apex.

The ratio of the vertical and horizontal distances between two points lying on the line.

A three-dimensional figure (as opposed to a surface, an area, or a curve).

A value that satisfies an equation.

The set of all points in three-dimensional Euclidean space (or n-dimensional space, in topology) that are a fixed distance from a fixed point .

A polygon with four straight sides of equal length and four right angles; an equilateral rectangle; a regular quadrilateral.

Any integer which is the product of some integer times itself: any integer whose square root is also an integer.

The number which, when squared, yields the original number.

An angle that is equal to 180° (pi radians or two right angles).

Replacing a variable with a value or another expression.

The process of subtracting a number from another.

An arithmetic computation, especially one posed to a student as an exercise (not necessarily limited to addition).

The total area on the surface of an object.

a set of equations required to be satisfied simultaneously or considered as a whole

One of ten equal parts of a whole.

Any value (variable or constant) or expression separated from another term by a space or an appropriate character, in an overall expression or table.

A polyhedron with four faces; the regular tetrahedron, the faces of which are equal equilateral triangles, is one of the Platonic solids.

A mathematical statement of some importance that has been proven to be true. Minor theorems are often called propositions. Theorems which are not very interesting in themselves but are an essential part of a bigger theorem's proof are called lemmas.

The replacement of the variables in an algebraic expression by their values in terms of another set of variables; a mapping of one space onto another or onto itself; a function that changes the position or direction of the axes of a coordinate system.

A relation between two mathematical figures such as a straight line where the coordinates of each point in one figure is a constant added to the coordinates of a corresponding point in the other figure.

A line intersecting a pair of parallel lines.

A (convex) quadrilateral with two (non-adjacent) parallel sides.

A polygon with three sides and three angles.

The inequality that states that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors.

The branch of mathematics that deals with the relationships between the sides and angles of (in particular) right-angled triangles, as represented by the trigonometric functions, and with calculations based on said relationships.

The number 1,000,000,000,000; a thousand billions.

A sequence of three elements or 3-tuple.

Oneness, singularity, seen as a component of a whole number; a magnitude of one.

A fraction whose numerator is 1 and whose denominator is a positive integer; for example, \frac12 or \frac17.

A variable (usually x, y or z) whose value is to be found.

A quantity that may assume any one of a set of values.

Any member of a (generalized) vector space.

An angular point of a polygon, polyhedron or higher order polytope.

The sum of the degrees of a set of vertices.

The measurement of the extent of something from side to side.

The axis on a graph that is usually drawn left to right and usually shows the range of values of an independent variable.

The axis on a graph that is usually drawn from bottom to top and usually shows the range of values of variable dependent on one other variable, or the second of two independent variables.

A value of the independent variables of a function, for which the function is equal to zero.