This is no a an extensive dictionary of mathematics terms, just a quick reference for several of the terms typically used in this website. An ext detailed glossaries deserve to be uncovered at http://www.cut-the-knot.org/glossary/atop.shtml and http://thesaurus.maths.org/mmkb/alphabetical.html (among others).

A B C D E F G H i J K together M N O p Q R S T U V W X Y Z

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abstract algebra: the area of contemporary mathematics that considers algebraic structures to it is in sets with operations identified on them, and extends algebraic ideas usually associated with the real number device to other more general systems, such as groups, rings, fields, modules and also vector spaces

**algebra:** a branch of math that offers symbols or letters to stand for variables, values or numbers, which can then be offered to refer operations and relationships and also to settle equations

**algebraic expression:** a mix of numbers and letters tantamount to a expression in language, e.g. X2 + 3x – 4

**algebraic equation:** a combination of numbers and letters tantamount to a sentence in language, e.g. Y = x2 + 3x – 4

**algorithm:** a step by action procedure through which an operation have the right to be carried out

**amicable numbers:** pairs of numbers because that which the sum of the divisors that one number amounts to the various other number, e.g. 220 and also 284, 1184 and 1210

**analytic (Cartesian) geometry:** the research of geometry utilizing a name: coordinates system and also the principles of algebra and analysis, thus defining geometrical forms in a numerical means and extracting numerical details from the representation

**analysis (mathematical analysis):** base in the rigorous formulation of calculus, evaluation is the branch the pure mathematics came to with the id of a border (whether that a sequence or the a function)

**arithmetic:** the component of math that research studies quantity, especially as the an outcome of combining number (as protest to variables) using the traditional operations that addition, subtraction, multiplication and department (the an ext advanced manipulation of number is usually well-known as number theory)

**associative property:** building (which applies both come multiplication and addition) by which numbers can be included or multiplied in any order and still yield the very same value, e.g. (a + b) + c = a + (b + c) or (ab)c = a(bc)

**asymptote:** a line the the curve of a role tends towards as the independent variable of the curve ideologies some border (usually infinity) i.e. The distance in between the curve and also the line philosophies zero

**axiom:** a proposition the is not actually verified or demonstrated, but is taken into consideration to be self-evident and also universally welcomed as a starting point because that deducing and inferring other truths and theorems, without any need that proof

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base n: the variety of unique digits (including zero) the a positional numeral mechanism uses to represent numbers, e.g. Base 10 (decimal) supplies 0, 1, 2, 3, 4, 5, 6, 7, 8 and also 9 in each place value position; base 2 (binary) uses just 0 and also 1; base 60 (sexagesimal, as supplied in ancient Mesopotamia) provides all the numbers from 0 to 59; etc

**Bayesian probability:** a famous interpretation of probability which evaluate the probability the a hypothesis by specifying part prior probability, and then update in the light of brand-new relevant data

**bell curve:** the form of the graph that suggests a normal circulation in probability and statistics

**bijection:** a one-to-one to compare or correspondence of the members of 2 sets, so that there room no unmapped aspects in either set, which are therefore of the exact same size and cardinality

**binomial:** a polynomial algebraic expression or equation with just two terms, e.g. 2x3 – 3y = 7; x2 + 4x; etc

**binomial coefficients:** the coefficients that the polynomial expansion of a binomial power of the kind (x + y) n, which can be arranged geometrically according to the binomioal theorem as a symmetry triangle the numbers known as Pascal’s Triangle, e.g. (x + y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4 the coefficients space 1, 4, 6, 4, 1

**Boolean algebra or logic:** a kind of algebra which deserve to be applied to the systems of logical problems and mathematical functions, in i m sorry the variables room logical fairly than numerical, and also in which the just operators space AND, OR and NOT

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calculus (infinitesimal calculus): a branch the mathematics including derivatives and also integrals, used to study movement and an altering values

**calculus the variations:** an extension of calculus provided to find for a role which minimizes a specific functional (a useful is a duty of a function)

**cardinal numbers:** numbers provided to measure up the cardinality or dimension (but no the order) of to adjust – the cardinality that a finite collection is simply a organic number denote the variety of elements in the set; the sizes of unlimited sets are explained by transfinite cardinal numbers,

**Cartesian coordinates:** a pair that numerical works with which clues the place of a point on a plane based top top its distance from the the two fixed perpendicular axes (which, with their optimistic and an unfavorable values, break-up the airplane up into four quadrants)

**coefficients:** the factors of the state (i.e. The numbers in prior of the letters) in a mathematics expression or equation, e.g. In the expression 4x + 5y2 + 3z, the coefficients because that x, y2 and z are 4, 5 and also 3 respectively

**combinatorics:** the research of different combinations and also groupings of numbers, frequently used in probability and also statistics, as well as in scheduling problems and also Sudoku puzzles

**complex dynamics:** the examine of math models and also dynamical systems characterized by iteration of attributes on complicated number spaces

**complex number:** a number expressed as an bespeak pair making up a genuine number and also an imaginary number, created in the form a + bi, wherein a and also b are real numbers, and also i is the imaginary unit (equal to the square root of -1)

**composite number:** a number with at least one other factor besides itself and one, i.e. Not a prime number

**congruence:** two geometrical numbers are congruent come one another if they have the exact same size and also shape, and also so one can be transformed into the other by a combination of translation, rotation and reflection

**conic section:** the section or curve formed by the intersection of a airplane and a cone (or conical surface), depending on the edge of the airplane it could be an ellipse, a hyperbola or a parabola

**continued fraction:** a portion whose denominator consists of a fraction, who denominator in turn consists of a fraction, etc, etc

**coordinate:** the ordered pair that offers the place or position of a allude on a coordinate plane, determined by the point’s street from the x and also y axes, e.g. (2, 3.7) or (-5, 4)

**coordinate plane:** a aircraft with 2 scaled perpendicular currently that crossing at the origin, normally designated x (horizontal axis) and also y (vertical axis)

**correlation:** a measure up of relationship in between two variables or to adjust of data, a positive correlation coefficient indicating the one variable tends to increase or decrease as the various other does, and also a an adverse correlation coefficient indicating that one variable has tendency to rise as the various other decreases and also vice versa

**cubic equation:** a polynomial having a degree of 3 (i.e. The highest power is 3), of the type ax3 + bx2 + cx + d = 0, which can be solved by factorization or formula to discover its three roots

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decimal number: a genuine number which expresses fountain on the base 10 standard numbering system using place value, e.g. 37⁄100 = 0.37

**deductive reasoning or logic:** a kind of thinking where the fact of a conclusion necessarily complies with from, or is a logical repercussion of, the fact of the basic (as protest to inductive reasoning)

**derivative:** a measure of exactly how a duty or curve changes as its intake changes, i.e. The best linear approximation that the function at a specific input value, as represented by the steep of the tangent line to the graph that the function at the point, found by the procedure of differentiation

**descriptive geometry:** a an approach of representing three-dimensional objects by projections ~ above the two-dimensional airplane using a specific collection of procedures

**differential equation:** an equation the expresses a relationship in between a duty and that derivative, the equipment of i beg your pardon is not a solitary value however a function (has plenty of applications in engineering, physics economics, etc)

**differential geometry:** a ar of math that offers the techniques of differential and integral calculus (as well together linear and also multilinear algebra) to examine the geometry the curves and surfaces

**differentiation:** the procedure in calculus (inverse come the procedure of integration) of detect the derivative the a duty or equation

**Diophantine equation:** a polynomial equation with integer coefficients the also allows the variables and solutions to be integers only

**distributive property:** property through which summing 2 numbers and also then multiplying by another number yields the very same value together multiplying both values by the various other value and also then including them together, e.g. A(b + c) = abdominal + ac

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element: a member of, or an item in, a set

**ellipse:** a airplane curve result from the intersection the a cone by a plane, the looks prefer a contempt flattened one (a circle is a special instance of one ellipse)

**elliptic geometry:** a non-Euclidean geometry based (at that is simplest) top top a spherical plane, in which there space no parallel lines and the angles of a triangle sum to more than 180°

**empty (null) set:** a collection that has actually no members, and therefore has actually zero size, usually stood for by or ø

**Euclidean geometry:** “normal” geometry based upon a flat plane, in i beg your pardon there are parallel lines and also the angles of a triangle amount to 180°

**expected value:** the quantity predicted to be gained, making use of the calculation for median expected payoff, which have the right to be calculated together the integral the a random variable through respect come its probability measure up (the meant value may not actually be the most probable value and also may not also exist, e.g. 2.5 children)

**exponentiation:** the mathematical procedure where a number (the base) is multiplied by chin a specified number of times (the exponent), commonly written together a superscript an, where a is the base and n is the exponent, e.g. 43 = 4 x 4 x 4

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factor: a number that will divide into another number exactly, e.g. The determinants of 10 are 1, 2 and 5

**factorial:** the product of all the continuous integers as much as a offered number (used to give the variety of permutations the a set of objects), denoted by n!, e.g. 5! = 1 x 2 x 3 x 4 x 5 = 120

**Fermat primes:** prime numbers that are one an ext than a power of 2 (and where the exponent is chin a power of 2), e.g. 3 (21 + 1), 5 (22 + 1), 17 (24 + 1), 257 (28 + 1), 65,537 (216 + 1), etc

**Fibonacci numbers (series):** a set of numbers developed by adding the last two numbers to obtain the following in the series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

**finite differences:** a technique of approximating the derivative or slope of a duty using around equivalent difference quotients (the function difference split by the point difference) for small differences

**formula:** a dominance or equation explicate the connection of 2 or more variables or quantities, e.g. A = πr2

**Fourier series:** one approximation the more facility periodic features (such as square or saw-tooth functions) by including together various straightforward trigonometric attributes (e.g. Sine, cosine, tangent, etc)

**fraction:** a method of composing rational number (numbers that are not totality numbers), also used to represent ratios or division, in the kind of a numerator over a denominator, e.g. 3⁄5 (a unit portion is a fraction whose numerator is 1)

**fractal:** a self-similar geometric shape (one the appears similar at every levels of magnification) produced by an equation that undergoes repeated iterative actions or recursion

**function:** a relation or correspondence in between two set in i m sorry one element of the second (codomain or range) set ƒ(x) is assigned to each element of the an initial (domain) collection x, e.g. ƒ(x) = x2 or y = x2 assigns a worth to ƒ(x) or y based upon the square of each worth of x

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game theory: a branch of mathematics that attempts to mathematically record behaviour in strategy situations, in i beg your pardon an individual’s success in making selections depends on the choices of others, with applications in the locations of economics, politics, biology, engineering, etc

**Gaussian curvature:** an intrinsic measure up of the curvature that a suggest on a surface, dependent just on how ranges are measured on the surface and also not ~ above the method it is embedded in space

**geometry:** the component of mathematics concerned with the size, shape and relative position of figures, or the research of lines, angles, shapes and also their properties

**golden ratio (golden mean, divine proportion):** the ratio of two quantities (equivalent to around 1 : 1.6180339887) where the ratio of the sum of the quantities to the bigger quantity equates to the ratio of the larger quantity to the smaller one, normally denoted through the Greek letter phi φ (phi)

**graph theory:** a branch that mathematics concentrating on the nature of a variety of graphs (meaning visual depictions of data and also their relationships, as opposed to graphs of functions on a Cartesian plane)

**group:** a mathematical structure consisting the a set together with an operation that combines any two that its aspects to kind a third element, e.g. The set of integers and also the enhancement operation type a group

**group theory:** the mathematical field that researches the algebraic structures and also properties the groups and also the mappings in between them

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Hilbert problems: an influential list that 23 open (unsolved) difficulties in mathematics described by David Hilbert in 1900

**hyperbola:** a smooth symmetry curve v two branches created by the section of a conical surface

**hyperbolic geometry:** a non-Euclidean geometry based on a saddle-shaped plane, in which there room no parallel lines and also the angles of a triangle amount to less than 180°

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identity: an equality that remains true nevertheless of the worths of any variables that show up within it, e.g. For multiplication, the identification is one; for addition, the identity is zero

**imaginary numbers:** numbers in the form bi, whereby b is a genuine number and i is the “imaginary unit”, equal to √-1 (i.e. I2 = -1)

**inductive thinking or logic:** a type of reasoning that involves moving indigenous a set of certain facts come a general conclusion, denote some degree of support for the conclusion without in reality ensuring that is truth

**infinite series:** the amount of an infinite sequence of numbers (which room usually produced according to a specific rule, formula or algorithm)

**infinitesimal:** quantities or objects so tiny that over there is no way to see them or to measure up them, so the for all handy purposes they approach zero together a limit (an idea provided in the developement the infinitesimal calculus)

**infinity:** a quantity or collection of numbers there is no bound, border or end, even if it is countably boundless like the collection of integers, or uncountably unlimited like the collection of actual numbers (represented by the prize ∞)

**integers:** whole numbers, both optimistic (natural numbers) and negative, consisting of zero

**integral:** the area bounded by a graph or curve that a role and the x axis, in between two provided values of x (definite integral), found by the procedure of integration

**integration:** the procedure in calculus (inverse to the procedure of differentiation) of recognize the integral that a function or equation

**irrational numbers:** number that deserve to not be stood for as decimals (because they would contain an infinite number of non-repeating digits) or as fractions of one integer end another, e.g. π, √2, e

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Julia set: the collection of points because that a function of the form z2 + c (where c is a complicated parameter), such the a little perturbation can cause drastic transforms in the succession of iterated duty values and iterations will either approach zero, approach infinity or gain trapped in loop

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knot theory: an area the topology that studies mathematical knots (a knot is a close up door curve in space formed through interlacing a piece of “string” and joining the ends)

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least squares method: a method of regression evaluation used in probability theory and statistics to fit a curve-of-best-fit to it was observed data by minimizing the sum of the squares that the differences in between the observed values and also the values provided by the model

**limit:** the suggest towards which a collection or role converges, e.g. Together x i do not care closer and closer to zero, (sin x)⁄x i do not care closer and closer to the limit of 1

**line:** in geometry, a one-dimensional number following a consistent straight path joining two or more points, whether boundless in both direction or simply a line segment bounded by two distinctive end points

**linear equation:** an algebraic equation in which every term is either a consistent or the product that a consistent and the very first power of a single variable, and whose graph is as such a directly line, e.g. Y = 4, y = 5x + 3

**linear regression:** a technique in statistics and probability theory for modelling scattered data by assuming an approximate straight relationship between the dependent and also independent variables

**logarithm:** the inverse procedure to exponentiation, the exponent the a strength to which a base (usually 10 or e for organic logarithms) have to be raised to develop a given number, e.g. Because 1,000 = 103, the log10 100 = 3

**logic:** the study of the formal legislations of thinking (mathematical logic the applications of the approaches of formal reasonable to mathematics and mathematical reasoning, and also vice versa)

**logicism:** the concept that mathematics is simply an expansion of logic, and that because of this some or all mathematics is reducible come logic

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magic square: a square variety of numbers wherein each row, column and diagonal included up come the very same total, known as the magic sum or constant (a semi-magic square is a square numbers where simply the rows and columns, however not both diagonals, sum to a constant)

**Mandelbrot set:** a collection of clues in the facility plane, the boundary of which develops a fractal, based upon all the feasible c points and also Julia sets of a role of the form z2 + c (where c is a complex parameter)

**manifold:** a topological space or surface which, top top a little enough scale, resembles the Euclidean an are of a specific dimension (called the dimension of the manifold), e.g. A line and a circle space one-dimensional manifolds; a plane and the surface of a sphere are two-dimensional manifolds; etc

**matrix:** a rectangular variety of numbers, which can be added, subtracted and multiplied, and also used come represent direct transformations and also vectors, deal with equations, etc

**Mersenne number:** numbers that are one less than 2 to the strength of a element number, e.g. 3 (22 – 1); 7 (23 – 1); 31 (25 – 1); 127 (27 – 1); 8,191 (213 – 1); etc

**Mersenne primes:** element numbers that room one much less than a power of 2, e.g. 3 (22 – 1); 7 (23 – 1); 31 (25 – 1); 127 (27 – 1); 8,191 (213 – 1); etc – many, but not all, Mersenne numbers are primes, e.g. 2,047 = 211 – 1 = 23 x 89, so 2,047 is a Mersenne number but not a Mersenne prime

**method the exhaustion:** a method of finding the area the a form by inscribing within it a sequence of polygon whose areas converge to the area that the containing form (a precursor to the methods of calculus)

**modular arithmetic:** a system of arithmetic because that integers, where numbers “wrap around” ~ they reach a certain value (the modulus), e.g. ~ above a 12-hour clock, 15 o’clock is in reality 3 o’clock (15 = 3 mod 12)

**modulus:** a number by which two offered numbers deserve to be divided by integer division, and also produce the very same remainder, e.g. 38 ÷ 12 = 3 remainder 2, and 26 ÷ 12 = 2 remainder 2, because of this 38 and 26 space congruent modulo 12, or (38 ≡ 26) mode 12

**monomial:** one algebraic expression consists of a solitary term (although the term could be one exponent), e.g. Y = 7x, y = 2x3

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natural numbers: the set of positive integers (regular whole counting numbers), sometimes including zero

**negative numbers:** any kind of integer, ration or actual number which is much less than 0, e.g. -743, -1.4, -√5 (but not √-1, i beg your pardon is an imaginary or facility number)

**non-commutative algebra:** one algebra in which a x b does not constantly equal b x a, such as that used by quaternions

**non-Euclidean geometry:** geometry based on a curved plane, even if it is elliptic (spherical) or hyperbolic (saddle-shaped), in i m sorry there space no parallel lines and also the angles of a triangle do not amount to 180°

**normal (Gaussian) distribution:** a constant probability distribution in probability theory and also statistics that defines data which clusters approximately the average in a curved “bell curve”, highest in the middle and quickly tapering off to every side

**number line:** a line on which all points exchange mail to real numbers (a simple number line might only mark integers, but in concept all actual numbers to +/- infinity can be displayed on a number line)

**number theory:** the branch the pure mathematics concerned with the nature of number in general, and also integers in particular

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ordinal numbers: an extension of the herbal numbers (different native integers and also from cardinal numbers) used to define the order form of to adjust i.e. The bespeak of facets within a set or series

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parabola: a kind of conic section curve, any suggest of which is equally remote from a resolved focus point and a fixed straight line

**paradox:** a explain that appears to contradict itself, saying a solution which is in reality impossible

**partial differential equation:** a relation entailing an unknown duty with numerous independent variables and also its partial derivatives v respect to those variables

**Pascal’s Triangle:** a geometrical arrangement of the coefficients that the polynomial growth of a binomial strength of the kind (x + y)n together a symmetrical triangle of numbers

**perfect number:** a number that is the sum of the divisors (excluding the number itself), e.g. 28 = 1 + 2 + 4 + 7 + 14

**periodic function:** a role that repeats its worths in constant intervals or periods, such together the trigonometric features of sine, cosine, tangent, etc

**permutation:** a certain ordering of a collection of objects, e.g. Provided the collection 1, 2, 3, over there are 6 permutations: 1, 2, 3, 1, 3, 2, 2, 1, 3, 2, 3, 1, 3, 1, 2, and 3, 2, 1

**pi (π):** the ratio of a circumference of a circle to its diameter, one irrational (and transcendental) number around equal come 3.141593…

**place value:** positional notation because that numbers, permitting the usage of the same symbols for various orders of magnitude, e.g. The “one’s place”, “ten’s place”, “hundred’s place”, etc

**Platonic solids:** the five consistent convex polyhedra (symmetrical 3-dimensional shapes): the tetrahedron (made up of 4 regular triangles), the octahedron (made up of 8 triangles), the icosahedron (made increase of 20 triangles), the cube (made increase of 6 squares) and the dodecahedron (made increase of 12 pentagons)

**polar coordinates:** a two-dimensional coordinate device in which each allude on a aircraft is figured out by its distance r from a fixed allude (e.g. The origin) and its angle θ (theta) indigenous a fixed direction (e.g the x axis)

**polynomial:** one algebraic expression or equation with an ext than one term, built from variables and also constants using just the to work of addition, subtraction, multiplication and also non-negative whole-number exponents, e.g. 5x2 – 4x + 4y + 7

**prime numbers:** integers better than 1 which are just divisible by themselves and also 1

**projective geometry:** a sort of non-Euclidean geometry i beg your pardon considers what happens to shapes once they space projected on come a non-parallel plane, e.g. A circle may be projected into an ellipse or a hyperbola

**plane:** a flat two-dimensional surface (physical or theoretical) with limitless width and also length, zero thickness and zero curvature

**probability theory:** the branch the mathematics concerned with evaluation of random variables and also events, and also with the translate of probabilities (the likelihood of an occasion happening)

**Pythagoras’ (Pythagorean) theorem:** the square the the hypotenuse of a best angled triangle is equal to the amount of the squares the the two sides (a2 + b2 = c2)

**Pythagorean triples:** groups of three positive integers a, b and c such that the a2 + b2 = c2 equation of Pythagoras’ theorem, e.g. ( 3, 4, 5), ( 5, 12, 13), ( 7, 24, 25), ( 8, 15, 17), etc

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quadratic equation: a polynomial equation through a level of 2 (i.e. The greatest power is 2), the the form ax2 + bx + c = 0, which deserve to be fixed by assorted methods consisting of factoring, completing the square, graphing, Newton’s method and the quadratic formula

**quadrature:** the action of squaring, or detect a square same in area come a provided figure, or recognize the area the a geometrical figure or the area under a curve (such together by a process of numerical integration)

**quartic equation:** a polynomial having a level of 4 (i.e. The highest possible power is 4), of the form ax4 + bx3 + cx2 + dx + e = 0, the highest order polynomial equation that can be resolved by factorization right into radicals through a basic formula

**quaternions:** a number system that extends facility numbers to 4 dimensions (so that an item is defined by a actual number and three complex numbers, every mutually perpendicular to each other), which have the right to be supplied to represent a three-dimensional rotation by just an angle and also a vector

**quintic equation:** a polynomial having actually a level of 5 (i.e. The greatest power is 5), that the form ax5 + bx4 + cx3 + dx2 + ex + f = 0, not solvable by factorization right into radicals for all rational numbers

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rational numbers: number that deserve to be expressed together a fraction (or ratio) a⁄b of two integers (the integers are therefore a subset that the rationals), or alternatively a decimal i beg your pardon terminates after a finite variety of digits or starts to repeat a sequence

**real numbers:** every numbers (including herbal numbers, integers, decimals, reasonable numbers and also irrational numbers) which carry out not indicate imaginary number (multiples the the imaginary unit i, or the square root of -1), may be believed of as all point out on an infinitely long number line

**reciprocal:** a number which, when multiplied through x yields the multiplicative identification 1, and can therefore be thought of as the station of multiplication, e.g. The reciprocal of x is 1⁄x, the reciprocal of 3⁄5 is 5⁄3

**Riemannian geometry:** a non-Euclidean geometry that studies curved surfaces and also differentiable manifolds in higher dimensional spaces

**right triangle:** a triangle (three sided polygon) include an edge of 90°

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self-similarity: object is exactly or approximately similar to a component of chin (in fractals, the shapes of present at different iterations look favor smaller versions of previously shapes)

**sequence:** an ordered collection whose facets are typically determined based upon some role of the counting numbers, e.g. A geometric sequence is a collection where each aspect is a lot of of the vault element; one arithmetic sequence is a set where each facet is the previous element plus or minus a number

**set:** a arsenal of distinctive objects or numbers, there is no regard to their order, considered as an item in its very own right

**significant digits:** the variety of digits to take into consideration when making use of measuring numbers, those digits that carry definition contributing come its precision (i.e. Ignoring leading and trailing zeros)

**simultaneous equations:** a collection or device of equations containing many variables which has actually a equipment that at the same time satisfies every one of the equations (e.g. The set of simultaneous straight equations 2x + y = 8 and also x + y = 6, has actually a equipment x = 2 and also y = 4)

**slope:** the steepness or incline of a line, determined by recommendation to 2 points on the line, e.g. The slope of the heat y = mx + b is m, and represents the price at i beg your pardon y is transforming per unit of adjust in x

**spherical geometry:** a form of non-Euclidean (elliptic) geometry utilizing the two-dimensional surface of a sphere, wherein a bent geodesic (not a directly line) is the shortest paths in between points

**spherical trigonometry:** a branch of spherical geometry which faces polygons (especially triangles) ~ above the sphere, and the relationships between their sides and also angles

**subset:** a subsidiary arsenal of objects that all belonging to, or is consisted of in, one original given set, e.g. Subsets the a, b could include: a, b, a, b and

**surd:** the n-th source a number, such as √5, the cube root of 7, etc

**symmetry:** the correspondence in size, type or arrangement of parts on a plane or heat (line the contrary is where each point on one side of a line has a corresponding allude on the opposite side, e.g. A snapshot a butterfly with wings that are similar on either side; plane symmetry ad to comparable figures being repeated at different however regular places on the plane)

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tensor: a collection of number at every point in space which describe how much the an are is curved, e.g. In 4 spatial dimensions, a collection of ten number is needed at each point to define the nature of the mathematical room or manifold, no matter how distorted it might be

**term:** in one algebraic expression or equation, either a solitary number or variable, or the product of number of numbers and also variables separated from another term by a + or – sign, e.g. In the expression 3 + 4x + 5yzw, the 3, the 4x and the 5yzw room all different terms

**theorem:** a mathematical declare or theory which has actually been confirmed on the communication of previously developed theorems and also previously accepted axioms, successfully the evidence of the reality of a statement or expression

**topology:** the ar of mathematics concerned with spatial properties the are maintained under consistent deformations of objects (such together stretching, bending and morphing, yet not tearing or gluing)

**transcendental number:** an irrational number the is “not algebraic”, i.e. No limited sequence of algebraic to work on integers (such together powers, roots, sums, etc.) deserve to be same to that value, examples being π and also e. For example, √2 is irrational yet not transcendental due to the fact that it is the systems to the polynomial x2 = 2.

**transfinite numbers:** cardinal numbers or ordinal numbers that are bigger than every finite numbers, yet not necessarily absolutely infinite

**triangular number:** a number which have the right to be represented as an it is intended triangle of dots, and is the amount of all the continually numbers up to its biggest prime aspect – it can likewise be calculated together n(n + 1)⁄2, e.g.

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15 = 1 + 2 + 3 + 4 + 5 = 5(5 + 1)⁄2

**trigonometry:** the branch of mathematics that studies the relationships between the sides and also the angle of appropriate triangles, and deals with and with the trigonometric functions (sine, cosine, tangent and also their reciprocals)

**trinomial:** one algebraic equation v 3 terms, e.g. 3x + 5y + 8z; 3x3 + 2x2 + x; etc

**type theory:** an alternate to naive collection theory in which all mathematical entities space assigned come a kind within a pecking order of types, so the objects of a given form are built exclusively from objects that preceding varieties lower in the hierarchy, thus staying clear of loops and paradoxes

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vector: a physical quantity having magnitude and direction, represented by a directed arrowhead indicating that is orientation in space

**vector space:** a three-dimensional area where vectors have the right to be plotted, or a mathematics structure created by a collection of vectors

**Venn diagram:** a diagram whereby sets are represented as basic geometric figures (often circles), and also overlapping and comparable sets are stood for by intersections and also unions of the figures

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Zermelo-Fraenkel collection theory: the standard type of set theory and also the many common foundation of contemporary mathematics, based on a perform of nine axioms (usually modification by a tenth, the axiom that choice) around what type of set exist, frequently abbreviated together as ZFC

**Zeta function:** A function based on an infinite series of reciprocals of exponents (Riemann’s zeta function is the expansion of Euler’s simple zeta duty into the domain of facility numbers)