English dictionary of Mathematics

English dictionary of Mathematics

 English dictionary of Mathematics

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Abelian group ; commutative group
a group that satisfies the commutative law

absolute value ; numerical value
a real number regardless of its sign

academic degree ; degree
an award conferred by a college or university signifying that the recipient has satisfactorily completed a course of study; "he earned his degree at Princeton summa cum laude"

move faster; "The car accelerated"

the arithmetic operation of summing; calculating the sum of two or more numbers; "the summation of four and three gives seven"; "four plus three equals seven"

adept ; champion
someone who is dazzlingly skilled in any field

affine transformation
(mathematics) a transformation that is a combination of single transformations such as translation or rotation or reflection on an axis

aim ; object ; objective ; target
the goal intended to be attained (and which is believed to be attainable); "the sole object of her trip was to see her children"

the mathematics of generalized arithmetical operations

algebraic number
root of an algebraic equation with rational coefficients

a precise rule (or set of rules) specifying how to solve some problem

a character set that includes letters and is used to write a language

(physics) the maximum displacement of a periodic wave

analysis ; analytic thinking
the abstract separation of a whole into its constituent parts in order to study the parts and their relations

analytic geometry
the use of algebra to study geometric properties; operates on symbols defined in a coordinate system

the space between two lines or planes that intersect; the inclination of one line to another; measured in degrees or radians

Greek mathematician and physicist noted for his work in hydrostatics and mechanics and geometry (287-212 BC)

area ; country
a particular geographical region of indefinite boundary (usually serving some special purpose or distinguished by its people or culture or geography); "it was a mountainous area"; "Bible country"

area ; expanse
the extent of a 2-dimensional surface enclosed within a boundary; "the area of a rectangle"; "it was about 500 square feet in area"

argument ; debate
a discussion in which reasons are advanced for and against some proposition or proposal; "the argument over foreign aid goes on and on"

argument ; statement
a fact or assertion offered as evidence that something is true; "it was a strong argument that his hypothesis was true"

one of the greatest of the ancient Athenian philosophers; pupil of Plato; teacher of Alexander the Great (384-322 BC)

the branch of pure mathematics dealing with the theory of numerical calculations

arithmetic mean
the sum of the values of a random variable divided by the number of values

arithmetic progression
(mathematics) a progression in which a constant is added to each term in order to obtain the next term; "1-4-7-10-13- is the start of an arithmetic progression"

arithmetical ; arithmetic
relating to or involving arithmetic; "arithmetical computations"

an orderly arrangement; "an array of troops in battle order"

(mathematics) a lack of symmetry

a straight line that is the limiting value of a curve; can be considered as tangent at infinity; "the asymptote of the curve"

average ; mean
approximating the statistical norm or average or expected value; "the average income in New England is below that of the nation"; "of average height for his age"; "the mean annual rainfall"

average ; norm
a statistic describing the location of a distribution; "it set the norm for American homes"

(logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident

a straight line through a body or figure that satisfies certain conditions

axis ; axis of rotation
the center around which something rotates

azimuth ; AZ
the azimuth of a celestial body is the angle between the vertical plane containing it and the plane of the meridian

ball-shaped ; global ; globular ; spheric ; spherical
having the shape of a sphere or ball; "a spherical object"; "nearly orbicular in shape"; "little globular houses like mud-wasp nests"- Zane Grey

base ; alkali
any of various water-soluble compounds capable of turning litmus blue and reacting with an acid to form a salt and water; "bases include oxides and hydroxides of metals and ammonia"

basis ; footing ; ground
a relation that provides the foundation for something; "they were on a friendly footing"; "he worked on an interim basis"

beam ; ray ; shaft
a column of light (as from a beacon)

the 2nd letter of the Greek alphabet

of or pertaining to a number system have 2 as its base; "a binary digit"

binomial distribution ; Bernoulli distribution
a theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success

binomial theorem
a theorem giving the expansion of a binomial raised to a given power

block ; cube
a three-dimensional shape with six square or rectangular sides

Boole ; George Boole
English mathematician; creator of Boolean algebra (1815-1864)

boundary ; bound ; bounds
the line or plane indicating the limit or extent of something

bracket ; square bracket
either of two punctuation marks ([ or ]) used to enclose textual material

built-in ; inbuilt ; integral
existing as an essential constituent or characteristic; "the Ptolemaic system with its built-in concept of periodicity"; "a constitutional inability to tell the truth"

capable of being calculated or estimated; "a calculable risk"; "calculable odds"

calculate ; compute ; work out ; reckon
make a mathematical calculation or computation

calculation ; computation
the procedure of calculating; determining something by mathematical or logical methods

calculation ; computation ; figuring ; reckoning
problem solving that involves numbers or quantities

cardinal number ; cardinal
the number of elements in a mathematical set; denotes a quantity but not the order

(mathematics) the number of elements in a set or group (considered as a property of that grouping)

an epicycloid in which the rolling circle equals the fixed circle

not modified or restricted by reservations; "a categorical denial"; "a flat refusal"

a collection of things sharing a common attribute; "there are two classes of detergents"

ceaseless ; constant ; incessant ; unceasing ; unremitting
uninterrupted in time and indefinitely long continuing; "the ceaseless thunder of surf"; "in constant pain"; "night and day we live with the incessant noise of the city"; "the never-ending search for happiness"; "the perpetual struggle to maintain standards in a democracy"; "man's unceasing warfare with drought and isolation"; "unremitting demands of hunger"

center ; centre ; middle
an area that is approximately central within some larger region; "it is in the center of town"; "they ran forward into the heart of the struggle"; "they were in the eye of the storm"

center ; centre ; midpoint
a point equidistant from the ends of a line or the extremities of a figure

changeless ; constant ; invariant ; unvarying
unvarying in nature; "maintained a constant temperature"; "principles of unvarying validity"

a written symbol that is used to represent speech; "the Greek alphabet has 24 characters"

typical or distinctive; "heard my friend's characteristic laugh"; "red and gold are the characteristic colors of autumn"; "stripes characteristic of the zebra"

a digit representing the sum of the digits in an instance of digital data; used to check whether errors have occurred in transmission or storage

ellipse in which the two axes are of equal length; a plane curve generated by one point moving at a constant distance from a fixed point; "he calculated the circumference of the circle"

code ; computer code
(computer science) the symbolic arrangement of data or instructions in a computer program or the set of such instructions

a constant number that serves as a measure of some property or characteristic

a punctuation mark (:) used after a word introducing a series or an example or an explanation (or after the salutation of a business letter)

a punctuation mark (,) used to indicate the separation of elements within the grammatical structure of a sentence

complex number
(mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1

composite number
an integer that is divisible without remainder by at least one positive integer other than itself and one

computer ; calculator ; reckoner
an expert at calculation (or at operating calculating machines)

the act of linking together as in a series or chain

curving inward

concentric ; homocentric
having a common center; "concentric rings"

the quality of agreeing; being suitable and appropriate

a number representing a quantity assumed to have a fixed value in a specified mathematical context; "the velocity of light is a constant"

a continuous nonspatial whole or extent or succession in which no part or portion is distinct or distinguishable from adjacent parts

contortion ; deformation
the act of twisting or deforming the shape of something (e.g., yourself)

controversy ; contention ; contestation
a contentious speech act; a dispute where there is strong disagreement; "they were involved in a violent argument"

convention ; rule
something regarded as a normative example; "the convention of not naming the main character"; "violence is the rule not the exception"; "his formula for impressing visitors"

convergence ; convergency
the approach of an infinite series to a finite limit

convex ; bulging
curving or bulging outward

coordinate system
a system that uses coordinates to establish position

a statistic representing how closely two variables co-vary; it can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation); "what is the correlation between those two variables?"

cosine ; cos
ratio of the adjacent side to the hypotenuse of a right-angled triangle

cotangent ; cotan
ratio of the adjacent to the opposite side of a right-angled triangle

counting ; numeration ; reckoning
the act of counting; reciting numbers in ascending order; "the counting continued for several hours"

countless ; innumerable ; multitudinous ; myriad ; numberless
too numerous to be counted; "incalculable riches"; "countless hours"; "an infinite number of reasons"; "innumerable difficulties"; "the multitudinous seas"; "myriad stars"; "untold thousands"

curve ; curvature
the property possessed by the curving of a line or surface

curve ; curved shape
the trace of a point whose direction of motion changes

an interval during which a recurring sequence of events occurs; "the never-ending cycle of the seasons"

cyclic redundancy check
an error correction code that is recorded in each sector of a magnetic disk and used to catch errors in the data

a surface generated by rotating a parallel line around a fixed line

decay ; decomposition
the organic phenomenon of rotting

(chemistry) separation of a substance into two or more substances that may differ from each other and from the original substance

decomposition ; rot ; putrefaction
(biology) the process of decay caused by bacterial or fungal action

a concise explanation of the meaning of a word or phrase or symbol

a unit of temperature on a specified scale; "the game was played in spite of the 40-degree temperature"

degree ; arcdegree
a measure for arcs and angles; "there are 360 degrees in a circle"

degree ; grade ; level
a position on a scale of intensity or amount or quality; "a moderate grade of intelligence"; "a high level of care is required"; "it is all a matter of degree"

the boundary of a specific area

the divisor of a fraction

a line of reasoning that shows how a conclusion follows logically from accepted propositions

derived function ; derivative
the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx

detail ; item ; point
an isolated fact that is considered separately from the whole; "several of the details are similar"; "a point of information"

a variation that deviates from the standard or norm; "the deviation from the mean"

a drawing intended to explain how something works; a drawing showing the relation between the parts

the quality of being unlike or dissimilar; "there are many differences between jazz and rock"

(biology) the structural adaptation of some body part for a particular function; "cell differentiation in the developing embryo"

differentiation ; distinction
a discrimination between things as different and distinct; "it is necessary to make a distinction between love and infatuation"

digit ; figure
one of the elements that collectively form a system of numeration; "0 and 1 are digits"

the spatial relation between something and the course along which it points or moves; "he checked the direction and velocity of the wind"

direction ; instruction
a message describing how something is to be done; "he gave directions faster than she could follow them"

a difference between conflicting facts or claims or opinions; "a growing divergence of opinion"

discrete ; distinct
constituting a separate entity or part; "a government with three discrete divisions"; "on two distinct occasions"

the property created by the space between two objects or points

divergence ; divergency
an infinite series that has no limit

that part of the earnings of a corporation that is distributed to its shareholders; usually paid quarterly

an arithmetic operation that is the inverse of multiplication; the quotient of two numbers is computed

division ; partition ; segmentation
the act of dividing or partitioning; separation by the creation of a boundary that divides or keeps apart

the number by which a dividend is divided

divisor ; factor
one of two or more integers that can be exactly divided into another integer; "what are the 4 factors of 6?"

territory over which rule or control is exercised; "his domain extended into Europe"; "he made it the law of the land"

dot product
a real number (a scalar) that is the product of two vectors

dynamical system
(physics) a phase space together with a transformation of that space

the branch of social science that deals with the production and distribution and consumption of goods and services and their management

edge ; border
the boundary of a surface

elaborateness ; intricacy
marked by elaborately complex detail

electrical engineering ; EE
the branch of engineering science that studies the uses of electricity and the equipment for power generation and distribution and the control of machines and communication

an abstract part of something; "jealousy was a component of his character"; "two constituents of a musical composition are melody and harmony"; "the grammatical elements of a sentence"; "a key factor in her success"; "humor: an effective ingredient of a speech"

elementary geometry ; parabolic geometry ; Euclidean geometry
(mathematics) geometry based on Euclid's axioms

ellipse ; oval
a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it; "the sums of the distances from the foci to any point on an ellipse is constant"

embrace ; encompass ; comprehend
include in scope; include as part of something broader; have as one's sphere or territory; "This group encompasses a wide range of people from different backgrounds"; "this should cover everyone in the group"

encoding ; encryption
the activity of converting data or information into code

(communication theory) a numerical measure of the uncertainty of an outcome; "the signal contained thousands of bits of information"

a line generated by a point on a circle rolling around another circle

the 5th letter of the Greek alphabet

a mathematical statement that two expressions are equal

Greek geometer (3rd century BC)

Euler ; Leonhard Euler
Swiss mathematician (1707-1783)

experiment ; experimentation
the act of conducting a controlled test or investigation

exponent ; index
a mathematical notation indicating the number of times a quantity is multiplied by itself

exponential ; exponential function
a function in which an independent variable appears as an exponent

exponentiation ; involution
the process of raising a quantity to some assigned power

the communication (in speech or writing) of your beliefs or opinions; "expressions of good will"; "he helped me find verbal expression for my ideas"; "the idea was immediate but the verbalism took hours"

(mathematics) calculation of the value of a function outside the range of known values

anything that contributes causally to a result; "a number of factors determined the outcome"

factorization ; factorisation
(mathematics) the resolution of an entity into factors such that when multiplied together they give the original entity

Fermat ; Pierre de Fermat
French mathematician who founded number theory; contributed (with Pascal) to the theory of probability (1601-1665)

Fibonacci number
a number in the Fibonacci sequence

device that removes something from whatever passes through it

the process whereby fluids pass through a filter or a filtering medium

formula ; chemical formula
a representation of a substance using symbols for its constituent elements

formula ; expression
a group of symbols that make a mathematical statement

the cardinal number that is the sum of three and one

Fourier ; Charles Fourier ; Francois Marie Charles Fourier
French sociologist and reformer who hoped to achieve universal harmony by reorganizing society (1772-1837)

Fourier series
the sum of a series of trigonometric expressions; used in the analysis of periodic functions

fourth ; quarter
one of four equal parts; "a quarter of a pound"

(mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry

the quotient of two rational numbers

constituting or comprising a part or fraction of a possible whole or entirety; "a fractional share of the vote"; "a partial dose"

function ; office
the actions and activities assigned to or required or expected of a person or group; "the function of a teacher"; "the government must do its part"; "play its role"

fuzzy logic
a form of mathematical logic in which truth can assume a continuum of values between 0 and 1

game theory ; theory of games
(economics) a theory of competition stated in terms of gains and losses among opposing players

the 3rd letter of the Greek alphabet

geodesic ; geodesic line
(mathematics) the shortest line between two points on a mathematically defined surface (as a straight line on a plane or an arc of a great circle on a sphere)

geometric mean
the mean of n numbers expressed as the n-th root of their product

the pure mathematics of points and lines and curves and surfaces

a cardinal number represented as 1 followed by a googol of zeros (ten raised to the power of a googol)

gradient ; slope
the property possessed by a line or surface that departs from the horizontal; "a five-degree gradient"

greatest common divisor
the largest integer that divides without remainder into a set of integers

half ; one-half
one of two equal parts of a divisible whole; "half a loaf"; "half an hour"; "a century and one half"

of or relating to or using a general formulation that serves to guide investigation

Hilbert ; David Hilbert
German mathematician (1862-1943)

a bar chart representing a frequency distribution; heights of the bars represent observed frequencies

the quality of being similar or corresponding in position or value or structure or function

homomorphism ; homomorphy
similarity of form

an open curve formed by a plane that cuts the base of a right circular cone

hyphen ; dash
a punctuation mark (-) used between parts of a compound word or between the syllables of a word when the word is divided at the end of a line of text

the side of a right triangle opposite the right angle

a tentative insight into the natural world; a concept that is not yet verified but that if true would explain certain facts or phenomena; "a scientific hypothesis that survives experimental testing becomes a scientific theory"; "he proposed a fresh theory of alkalis that later was accepted in chemical practices"

conforming to an ultimate standard of perfection or excellence; embodying an ideal

ideal ; paragon
model of excellence or perfection of a kind; one having no equal

the distinct personality of an individual regarded as a persisting entity; "you can lose your identity when you join the army"

identity matrix ; unit matrix
a scalar matrix in which all of the diagonal elements are unity

implicit ; inexplicit
implied though not directly expressed; inherent in the nature of something; "an implicit agreement not to raise the subject"; "there was implicit criticism in his voice"; "anger was implicit in the argument"; "the oak is implicit in the acorn"

an alphabetical listing of names and topics along with page numbers where they are discussed

a device for showing the operating condition of some system

impossible of undergoing division; "an indivisible union of states"; "one nation indivisible"

lack of equality; "the growing inequality between rich and poor"

information theory
(computer science) a statistical theory dealing with the limits and efficiency of information processing

integer ; whole number
any of the natural numbers (positive or negative) or zero; "an integer is a number that is not a fraction"

the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)

interpolate ; extrapolate
estimate the value of

(mathematics) calculation of the value of a function between the values already known

a representation of common ground between theories or phenomena; "there was no overlap between their proposals"

a set containing all points (or all real numbers) between two given endpoints

inverse function
a function obtained by expressing the dependent variable of one function as the independent variable of another; f and g are inverse functions if f(x)=y and g(y)=x

isometric ; isometrical
having equal dimensions or measurements

isomorphism ; isomorphy
(biology) similarity or identity of form or shape or structure

isotropy ; symmetry
(physics) the property of being isotropic; having the same value when measured in different directions

small rapid variations in a waveform resulting from fluctuations in the voltage supply or mechanical vibrations or other sources

Klein bottle
a closed surface with only one side; formed by passing one end of a tube through the side of the tube and joining it with the other end

Kronecker delta
a function of two variables i and j that equals 1 when i=j and equals 0 otherwise

limit ; bound ; boundary
the greatest possible degree of something; "what he did was beyond the bounds of acceptable behavior"; "to the limit of his ability"

limit ; limitation
the greatest amount of something that is possible or allowed; "there are limits on the amount you can bet"; "it is growing rapidly with no limitation in sight"

limit ; restrict ; restrain ; trammel ; bound ; confine
place limits on (extent or access); "restrict the use of this parking lot"; "limit the time you can spend with your friends"

a mark that is long relative to its width; "He drew a line on the chart"

linear algebra
the part of algebra that deals with the theory of linear equations and linear transformation

linear equation
a polynomial equation of the first degree

linear programming
a mathematical technique used in economics; finds the maximum or minimum of linear functions in many variables subject to constraints

logarithm ; log
the exponent required to produce a given number

the branch of philosophy that analyzes inference

anything with a round or oval shape (formed by a curve that is closed and does not intersect itself)

lowest common multiple ; least common multiple ; lcm
the smallest multiple that is exactly divisible by every member of a set of numbers; "the least common multiple of 12 and 18 is 36"

the property of relative size or extent (whether large or small); "they tried to predict the magnitude of the explosion"; "about the magnitude of a small pea"

manifold ; multiplex
many and varied; having many features or forms; "manifold reasons"; "our manifold failings"; "manifold intelligence"; "the multiplex opportunities in high technology"

mantissa ; fixed-point part
the positive fractional part of the representation of a logarithm; in the expression log 643 = 2.808 the mantissa is .808

mathematical logic
any logical system that abstracts the form of statements away from their content in order to establish abstract criteria of consistency and validity

mathematical space ; topological space
(mathematics) any set of points that satisfy a set of postulates of some kind; "assume that the topological space is finite dimensional"

a person skilled in mathematics

mathematics ; math
a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement

(mathematics) a rectangular array of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules

mean ; mean value
an average of n numbers computed by adding some function of the numbers and dividing by some function of n

mean ; signify ; stand for
denote or connote; "`maison' means `house' in French"; "An example sentence would show what this word means"

measure ; evaluate ; valuate ; assess ; appraise ; value
evaluate or estimate the nature, quality, ability, extent, or significance of; "I will have the family jewels appraised by a professional"; "access all the factors when taking a risk"

median ; median value
the value below which 50% of the cases fall

metric space
a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality

a billion; "in England they call one thousand million a milliard"

mistake ; error ; fault
a wrong action attributable to bad judgment or ignorance or inattention; "he made a bad mistake"; "she was quick to point out my errors"; "I could understand his English in spite of his grammatical faults"

mnemonic ; mnemotechnic
of or relating to or involved the practice of aiding the memory; "mnemonic device"

monotone ; monotonic ; monotonous
sounded or spoken in a tone unvarying in pitch; "the owl's faint monotonous hooting"

Muller ; Johann Muller ; Regiomontanus
German mathematician and astronomer (1436-1476)

the product of a quantity by an integer; "36 is a multiple of 9"

having or involving or consisting of more than one part or entity or individual; "multiple birth"; "multiple ownership"; "made multiple copies of the speech"; "his multiple achievements in public life"; "her multiple personalities"; "a pineapple is a multiple fruit"

multiplication ; times
an arithmetic operation that is the inverse of division; the product of two numbers is computed; "the multiplication of four by three gives twelve"; "four times three equals twelve"

multiplier ; multiplier factor
the number by which a multiplicand is multiplied

combine by multiplication; "multiply 10 by 15"

Napier ; John Napier
Scottish mathematician who invented logarithms; introduced the use of the decimal point in writing numbers (1550-1617)

Nash equilibrium
(game theory) a stable state of a system that involves several interacting participants in which no participant can gain by a change of strategy as long as all the other participants remain unchanged

natural number
the number 1 and any other number obtained by adding 1 to it repeatedly

characterized by or displaying negation or denial or opposition or resistance; having no positive features; "a negative outlook on life"; "a colorless negative personality"; "a negative evaluation"; "a negative reaction to an advertising campaign"

net ; network ; mesh
an open fabric of string or rope or wire woven together at regular intervals

Newton ; Isaac Newton ; Sir Isaac Newton
English mathematician and physicist; remembered for developing the calculus and for his law of gravitation and his three laws of motion (1642-1727)

the number designating place in an ordered sequence

nomogram ; nomograph
a graphic representation of numerical relations

non-Euclidean geometry
(mathematics) geometry based on axioms different from Euclid's; "non-Euclidean geometries discard or replace one or more of the Euclidean axioms"

a standard or model or pattern regarded as typical; "the current middle-class norm of two children per family"

notation ; notational system
a technical system of symbols used to represent special things

a concept of quantity involving zero and units; "every number has a unique position in the sequence"

give numbers to; "You should number the pages of the thesis"

numeral ; number
a symbol used to represent a number; "he learned to write the numerals before he went to school"

numeral ; numerical ; numeric
of or relating to or denoting numbers; "a numeral adjective"

the dividend of a fraction

the study of the supposed occult influence of numbers on human affairs

object ; physical object
a tangible and visible entity; an entity that can cast a shadow; "it was full of rackets, balls and other objects"

a quantity upon which a mathematical operation is performed

(mathematics) a symbol or function representing a mathematical operation

optical illusion
an optical phenomenon that results in a false or deceptive visual impression

optimization ; optimisation
the act of rendering optimal; "the simultaneous optimization of growth and profitability"; "in an optimization problem we seek values of the variables that lead to an optimal value of the function that is to be optimized"; "to promote the optimization and diversification of agricultural products"

established customary state (especially of society); "order ruled in the streets"; "law and order"

order of magnitude ; magnitude
a number assigned to the ratio of two quantities; two quantities are of the same order of magnitude if one is less than 10 times as large as the other; the number of magnitudes that the quantities differ is specified to within a power of 10

the process of oscillating between states

outside ; exterior
the outer side or surface of something

a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve

parabolic ; parabolical
having the form of a parabola

an imaginary line around the Earth parallel to the equator

being everywhere equidistant and not intersecting; "parallel lines never converge"; "concentric circles are parallel"; "dancers in two parallel rows"

any factor that defines a system and determines (or limits) its performance

(computer science) a bit that is used in an error detection procedure in which a 0 or 1 is added to each group of bits so that it will have either an odd number of 1's or an even number of 1's; e.g., if the parity is odd then any group of bits that arrives with an even number of 1's must contain an error

Pascal ; Blaise Pascal
French mathematician and philosopher and Jansenist; invented an adding machine; contributed (with Fermat) to the theory of probability (1623-1662)

percent ; percentage
a proportion in relation to a whole (which is usually the amount per hundred)

period ; point ; full stop ; stop ; full point
a punctuation mark (.) placed at the end of a declarative sentence to indicate a full stop or after abbreviations; "in England they call a period a stop"

permanence ; permanency
the property of being able to exist for an indefinite duration

act of changing the lineal order of objects in a group

a straight line at right angles to another line

phase change ; phase transition ; state change
a change from one state (solid or liquid or gas) to another without a change in chemical composition

the ratio of the circumference to the diameter of a circle; approximately equal to 3.14159265358979323846...

picture ; image
a visual representation (of an object or scene or person or abstraction) produced on a surface; "they showed us the pictures of their wedding"; "a movie is a series of images projected so rapidly that the eye integrates them"

plane ; sheet
(mathematics) an unbounded two-dimensional shape; "we will refer to the plane of the graph as the X-Y plane"; "any line joining two points on a plane lies wholly on that plane"

a geometric element that has position but no extension; "a point is defined by its coordinates"

sharp end; "he stuck the point of the knife into a tree"; "he broke the point of his pencil"

point ; dot
a very small circular shape; "a row of points"; "draw lines between the dots"

polygon ; polygonal shape
a closed plane figure bounded by straight sides

polynomial ; multinomial
a mathematical function that is the sum of a number of terms

characterized by or displaying affirmation or acceptance or certainty etc.; "a positive attitude"; "the reviews were all positive"; "a positive benefit"; "a positive demand"

postulate ; posit
(logic) a proposition that is accepted as true in order to provide a basis for logical reasoning

prime number
an integer that has no integral factors but itself and 1

probability ; chance
a measure of how likely it is that some event will occur; a number expressing the ratio of favorable cases to the whole number of cases possible; "the probability that an unbiased coin will fall with the head up is 0.5"

the set of elements common to two or more sets; "the set of red hats is the intersection of the set of hats and the set of red things"

proof ; cogent evidence
any factual evidence that helps to establish the truth of something; "if you have any proof for what you say, now is the time to produce it"

property ; attribute
a construct whereby objects or individuals can be distinguished; "self-confidence is not an endearing property"

proportion ; dimension
magnitude or extent; "a building of vast proportions"

prototype ; paradigm ; epitome
a standard or typical example; "he is the prototype of good breeding"; "he provided America with an image of the good father"

purpose ; function
what something is used for; "the function of an auger is to bore holes"; "ballet is beautiful but what use is it?"

a particularly baffling problem that is said to have a correct solution; "he loved to solve chessmate puzzles"; "that's a real puzzler"

a game that tests your ingenuity

Greek philosopher and mathematician who proved the Pythagorean theorem; considered to be the first true mathematician (circa 580-500 BC)

quadratic equation ; quadratic
an equation in which the highest power of an unknown quantity is a square

the construction of a square having the same area as some other figure

an adequate or large amount; "he had a quantity of ammunition"

(physics) the smallest discrete quantity of some physical property that a system can possess (according to quantum theory)

(football, professional basketball) one of four divisions into which some games are divided; "both teams scored in the first quarter"

quartet ; foursome
four people considered as a unit; "he joined a barbershop quartet"; "the foursome teed off before 9 a.m."

(statistics) any of three points that divide an ordered distribution into four parts each containing one quarter of the scores

the ratio of two quantities to be divided

radian ; rad
the unit of plane angle adopted under the Systeme International d'Unites; equal to the angle at the center of a circle subtended by an arc equal in length to the radius (approximately 57.295 degrees)

lacking any definite plan or order or purpose; governed by or depending on chance; "a random choice"; "bombs fell at random"; "random movements"

random variable ; variate
a variable quantity that is random

rate ; grade
assign a rank or rating to; "how would you rank these students?"; "The restaurant is rated highly in the food guide"

rate ; value
estimate the value of; "How would you rate his chances to become President?"; "Gold was rated highly among the Romans"

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

rationale ; principle
(law) an explanation of the fundamental reasons (especially an explanation of the working of some device in terms of laws of nature); "the rationale for capital punishment"; "the principles of internal-combustion engines"

reciprocal ; mutual
concerning each of two or more persons or things; especially given or done in return; "reciprocal aid"; "reciprocal trade"; "mutual respect"; "reciprocal privileges at other clubs"

(mathematics) an expression such that each term is generated by repeating a particular mathematical operation

reduction ; simplification
the act of reducing complexity

remainder ; difference
the number that remains after subtraction; the number that when added to the subtrahend gives the minuend

rest ; remainder ; balance ; residue ; residuum
something left after other parts have been taken away; "there was no remainder"; "he threw away the rest"; "he took what he wanted and I got the balance"

result ; outcome
something that results; "he listened for the results on the radio"

revolutionary ; radical
markedly new or introducing radical change; "a revolutionary discovery"; "radical political views"

Riemann ; Bernhard Riemann ; Georg Friedrich Bernhard Riemann
pioneer of non-Euclidean geometry (1826-1866)

a toroidal shape; "a ring of ships in the harbor"; "a halo of smoke"

a number that, when multiplied by itself some number of times, equals a given number

round off ; round
express as a round number; "round off the amount"

rounding ; rounding error
(mathematics) a miscalculation that results from rounding off numbers to a convenient number of decimals; "the error in the calculation was attributable to rounding"; "taxes are rounded off to the nearest dollar but the rounding error is surprisingly small"

rule ; prescript
prescribed guide for conduct or action

rule ; principle
a basic generalization that is accepted as true and that can be used as a basis for reasoning or conduct; "their principles of composition characterized all their works"

rule ; regulation
a principle or condition that customarily governs behavior; "it was his rule to take a walk before breakfast"; "short haircuts were the regulation"

a variable quantity that cannot be resolved into components

relative magnitude; "they entertained on a grand scale"

size or measure according to a scale; "This model must be scaled down"

scale ; musical scale
(music) a series of notes differing in pitch according to a specific scheme (usually within an octave)

schema ; scheme
an internal representation of the world; an organization of concepts and actions that can be revised by new information about the world

scheme ; strategy
an elaborate and systematic plan of action

a punctuation mark (`;') used to connect independent clauses; indicates a closer relation than does a period

sequel ; subsequence
something that follows something else

serial arrangement in which things follow in logical order or a recurrent pattern; "the sequence of names was alphabetical"; "he invented a technique to determine the sequence of base pairs in DNA"

sequence ; succession
a following of one thing after another in time; "the doctor saw a sequence of patients"

(mathematics) an abstract collection of numbers or symbols; "the set of prime numbers is infinite"

set theory
the branch of pure mathematics that deals with the nature and relations of sets

a place within a region identified relative to a center or reference location; "they always sat on the right side of the church"; "he never left my side"

a character indicating a relation between quantities; "don't forget the minus sign"

sign ; mark
a perceptible indication of something not immediately apparent (as a visible clue that something has happened); "he showed signs of strain"; "they welcomed the signs of spring"

freedom from difficulty or hardship or effort; "he rose through the ranks with apparent ease"; "they put it into containers for ease of transportation"; "the very easiness of the deed held her back"

simplicity ; simpleness
the quality of being simple or uncompounded; "the simplicity of a crystal"

singular ; unique
the single one of its kind; "a singular example"; "the unique existing example of Donne's handwriting"; "a unique copy of an ancient manuscript"; "certain types of problems have unique solutions"

singularity ; uniqueness
the quality of being one of a kind; "that singularity distinguished him from all his companions"

a method for solving a problem; "the easy solution is to look it up in the handbook"

solution ; answer ; resolution
a statement that solves a problem or explains how to solve the problem; "they were trying to find a peaceful solution"; "the answers were in the back of the book"; "he computed the result to four decimal places"

an empty area (usually bounded in some way between things); "the architect left space in front of the building"; "they stopped at an open space in the jungle"; "the space between his teeth"

an ordered array of the components of an emission or wave

speculation ; conjecture
a hypothesis that has been formed by speculating or conjecturing (usually with little hard evidence); "speculations about the outcome of the election"; "he dismissed it as mere conjecture"

a rate (usually rapid) at which something happens; "the project advanced with gratifying speed"

a three-dimensional closed surface such that every point on the surface is equidistant from the center

sphere ; domain ; area ; field
a particular environment or walk of life; "his social sphere is limited"; "it was a closed area of employment"; "he's out of my orbit"

square ; foursquare
(geometry) a plane rectangle with four equal sides and four right angles; a four-sided regular polygon; "you can compute the area of a square if you know the length of its sides"

square ; second power
the product of two equal terms; "nine is the second power of three"; "gravity is inversely proportional to the square of the distance"

stability ; stableness
the quality or attribute of being firm and steadfast

a specific identifiable position in a continuum or series or especially in a process; "a remarkable degree of frankness"; "at what stage are the social sciences?"

standard ; criterion ; measure
a basis for comparison; a reference point against which other things can be evaluated; "the schools comply with federal standards"; "they set the measure for all subsequent work"

standard deviation
the square root of the variance

a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters

stochastic process
a statistical process involving a number of random variables depending on a variable parameter (which is usually time)

stripe ; streak
a narrow marking of a different color or texture from the background; "a green toad with small black stripes or bars"; "may the Stars and Stripes forever wave"

subroutine ; subprogram
a set sequence of steps, part of larger computer program

a set whose members are members of another set; a set contained within another set

the act of putting one thing or person in the place of another: "he sent Smith in for Jones but the substitution came too late to help"

subtract ; deduct
make a subtraction; "subtract this amount from my paycheck"

subtraction ; deduction
the act of subtracting (removing a part from the whole); "he complained about the subtraction of money from their paychecks"

subtraction ; minus
an arithmetic operation in which the difference between two numbers is calculated; "the subtraction of three from four leaves one"; "four minus three equals one"

succession ; sequence
the action of following in order; "he played the trumps in sequence"

suit ; fit
be agreeable or acceptable to; "This suits my needs"

the outer boundary of an artifact or a material layer constituting or resembling such a boundary; "there is a special cleaner for these surfaces"; "the cloth had a pattern of red dots on a white surface"

(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane

a straight line or plane that touches a curve or curved surface at a point but does not intersect it at that point

tangent ; tan
ratio of the opposite to the adjacent side of a right-angled triangle

of or relating to or acting along or in the direction of a tangent; "tangential forces"

the cardinal number that is the sum of nine and one; the base of the decimal system

a word or expression used for some particular thing; "he learned many medical terms"

test ; trial
the act of testing something; "in the experimental trials the amount of carbon was measured separately"; "he called each flip of the coin a new trial"

a proposition deducible from basic postulates

a diacritical mark (~) placed over the letter n in Spanish to indicate a palatal nasal sound or over a vowel in Portuguese to indicate nasalization

topology ; analysis situs
the branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions

topology ; network topology
the configuration of a communication network

tot ; tot up ; sum ; add ; tally
determine the sum of; "Add all the people in this town to those of the neighboring town"

total ; aggregate
the whole amount

total ; number ; add up
add up in number or quantity; "The bills amounted to $2,000"; "The bill came to $2,000"

total ; sum ; amount
a quantity obtained by the addition of a group of numbers

a method of surveying; the area is divided into triangles and the length of one side and its angles with the other two are measured, then the lengths of the other sides can be calculated

trigonometry ; trig
the mathematics of triangles and trigonometric functions

Turing machine
a hypothetical computer with an infinitely long memory tape

the cardinal number that is the sum of eleven and one

twelve ; dozen
denoting a quantity consisting of 12 items or units

a set containing all and only the members of two or more given sets; "let C be the union of the sets A and B"

not known; "an unknown amount"; "an unknown island"; "an unknown writer"; "an unknown source"

the quality (positive or negative) that renders something desirable or valuable; "the Shakespearean Shylock is of dubious value in the modern world"

a symbol (like x or y) that is used in mathematical or logical expressions to represent a variable quantity

liable to or capable of change; "rainfall in the tropics is notoriously variable"; "variable winds"; "variable expenses"

the second moment around the mean; the expected value of the square of the deviations of a random variable from its mean value

a repetition of a musical theme in which it is modified or embellished

a straight line segment whose length is magnitude and whose orientation in space is direction

vector product ; cross product
a vector that is the product of two other vectors

version ; variant
something a little different from others of the same type; "an experimental version of the night fighter"; "a variant of the same word"; "an emery wheel is the modern variation of a grindstone"; "the boy is a younger edition of his father"

vertex ; peak ; apex ; acme
the highest point (of something); "at the peak of the pyramid"

vertical ; perpendicular
at right angles to the plane of the horizon or a base line; "a vertical camera angle"; "the monument consists of two vertical pillars supporting a horizontal slab"; "measure the perpendicular height"

visibility ; visibleness
quality or fact or degree of being visible; perceptible by the eye or obvious to the eye; "low visibility caused by fog"

the point above the observer that is directly opposite the nadir on the imaginary sphere against which celestial bodies appear to be projected

zero ; nought
a mathematical element that when added to another number yields the same number

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