Synonyme von mathematics: Mathematical terms
acute anglean angle that is less than 90° additiona mathematical operation in which the sum of two numbers or quantities is calculated. Usually indicated by the symbol + algorithm or algorisma recursive procedure whereby an infinite sequence of terms can be generated anglethe extent to which one such line or plane diverges from another, measured in degrees or radians arca section of a curve, graph, or geometric figure areathe two-dimensional extent of the surface of a solid, or of some part thereof, esp one bounded by a closed curve averagethe result obtained by adding the numbers or quantities in a set and dividing the total by the number of members in the set axisone of two or three reference lines used in coordinate geometry to locate a point in a plane or in space basethe number of distinct single-digit numbers in a counting system, and so the number represented as 10 in a place-value system binarybinomiala mathematical expression consisting of two terms, such as 3x + 2y cardinal numbera number denoting quantity but not order in a set Cartesian coordinatesa system of representing points in space in terms of their distance from a given origin measured along a set of mutually perpendicular axes. Written (x,y,z) with reference to three axes chorda straight line connecting two points on a curve or curved surface circlea closed plane curve every point of which is equidistant from a given fixed point, the centre. Equation: (x –h)2 + (y –k)2 = r2 where r is the radius and (h, k) are the coordinates of the centre; area πr2; circumference: 2πr circumferencethe boundary of a specific area or geometric figure, esp of a circle closed seta set that includes all the values obtained by application of a given operation to its members coefficienta numerical or constant factor in an algebraic term common denominatoran integer exactly divisible by each denominator of a group of fractions: , , and have a common denominator of 12 common factora number or quantity that is a factor of each member of a group of numbers or quantities complex numberany number of the form a + ib, where a and b are real numbers and i = √–1 concentricconea geometric solid consisting of a plane base bounded by a closed curve, often a circle or an ellipse, every point of which is joined to a fixed point, the vertex, lying outside the plane of the base. A right circular cone has a vertex perpendicularly above or below the centre of a circular base. Volume of a cone: πr2h, where r is the radius of the base and h is the height of the cone constanta symbol representing an unspecified number that remains invariable throughout a particular series of operations coordinate or co-ordinateany of a set of numbers that defines the location of a point in space cosecant(of an angle) a trigonometric function that in a right-angled triangle is the ratio of the length of the hypotenuse to that of the opposite side; the reciprocal of sine cosinea trigonometric function that in a right-angled triangle is the ratio of the length of the adjacent side to that of the hypotenuse; the sine of the complement cotangent(of an angle) a trigonometric function that in a right-angled triangle is the ratio of the length of the adjacent side to that of the opposite side; the reciprocal of tangent cubea solid having six plane square faces in which the angle between two adjacent sides is a right angle cube rootthe number or quantity whose cube is a given number or quantity: 2 is the cube root of 8 (usually written 3√ 8 or 81⁄3) cuboida geometric solid whose six faces are rectangles; rectangular parallelepiped curvea system of points whose coordinates satisfy a given equation; a locus of points cuspa point at which two arcs of a curve intersect and at which the two tangents are coincident cylindera solid consisting of two parallel planes bounded by identical closed curves, usually circles, that are interconnected at every point by a set of parallel lines, usually perpendicular to the planes. Volume base area × length decagona polygon having ten sides decimala fraction that has a denominator of a power of ten, the power depending on or deciding the decimal place. It is indicated by a decimal point to the left of the numerator, the denominator being omitted. Zeros are inserted between the point and the numerator, if necessary, to obtain the correct decimal place denarydenominatorthe divisor of a fraction, as 8 in diagonalany oblique row of squares of the same colour diametera straight line connecting the centre of a geometric figure, esp a circle or sphere, with two points on the perimeter or surface digitany of the ten Arabic numerals from 0 to 9 divisiona mathematical operation, the inverse of multiplication, in which the quotient of two numbers or quantities is calculated. Usually written: a ÷ b, , a/b, dodecahedrona solid figure having twelve plane faces. A regular dodecahedron has regular pentagons as faces ellipsea closed conic section shaped like a flattened circle and formed by an inclined plane that does not cut the base of the cone. Standard equation x2/a2 + y2/b2 = 1, where 2a and 2b are the lengths of the major and minor axes. Area: πab equalsequationa mathematical statement that two expressions are equal: it is either an identity in which the variables can assume any value, or a conditional equation in which the variables have only certain values (roots) equilaterala geometric figure having all its sides of equal length evenexponentialan exponential function, etc factorone of two or more integers or polynomials whose product is a given integer or polynomial factorialthe product of all the positive integers from one up to and including a given integer. Factorial zero is assigned the value of one: factorial four is 1 × 2 × 3 × 4. Symbol: n!, where n is the given integer formulaa general relationship, principle, or rule stated, often as an equation, in the form of symbols fractiona ratio of two expressions or numbers other than zero frequencythe number of times that an event occurs within a given period; rate of recurrence functiona relation between two sets that associates a unique element (the value) of the second (the range) with each element (the argument) of the first (the domain): a many-one relation. Symbol: f(x) The value of f(x) for x = 2 is f(2) grapha drawing depicting the relation between certain sets of numbers or quantities by means of a series of dots, lines, etc, plotted with reference to a set of axes helixa curve that lies on a cylinder or cone, at a constant angle to the line segments making up the surface; spiral hemisphereone half of a sphere heptagona polygon having seven sides hexagona polygon having six sides hyperbolaa conic section formed by a plane that cuts both bases of a cone; it consists of two branches asymptotic to two intersecting fixed lines and has two foci. Standard equation: x2/a2 – y2/b2 = 1 where 2a is the distance between the two intersections with the x-axis and b = a√(e2 – 1), where e is the eccentricity hypotenusethe side in a right-angled triangle that is opposite the right angle icosahedrona solid figure having 20 faces. The faces of a regular icosahedron are equilateral triangles imaginary numberany complex number of the form ib, where i = √–1 improper fractiona fraction in which the numerator has a greater absolute value or degree than the denominator, as or (x2 + 3)/(x + 1) indexa number or variable placed as a superscript to the left of a radical sign indicating by its value the root to be extracted, as in 3√8 = 2 infinitythe concept of a value greater than any finite numerical value integerany rational number that can be expressed as the sum or difference of a finite number of units, being a member of the set …–3, –2, –1, 0, 1, 2, 3… integralthe limit of an increasingly large number of increasingly smaller quantities, related to the function that is being integrated (the integrand). The independent variables may be confined within certain limits (definite integral) or in the absence of limits (indefinite integral) intersectiona point or set of points common to two or more geometric configurations irrational numberany real number that cannot be expressed as the ratio of two integers, such as π isosceleslocusa set of points whose location satisfies or is determined by one or more specified conditions logarithm or logthe exponent indicating the power to which a fixed number, the base, must be raised to obtain a given number or variable. It is used esp to simplify multiplication and division: if ax = M, then the logarithm of M to the base a (written logaM) is x lowest common denominatorthe smallest integer or polynomial that is exactly divisible by each denominator of a set of fractions lowest common multiplethe smallest number or quantity that is exactly divisible by each member of a set of numbers or quantities Mandelbrot seta set of points in the complex plane that is self-replicating according to some predetermined rule such that the boundary of the set has fractal dimensions, used in the study of fractal geometry and in producing patterns in computer graphics matrixa substance, situation, or environment in which something has its origin, takes form, or is enclosed meanthe second and third terms of a proportion, as b and c in a/b = c/d mediana straight line joining one vertex of a triangle to the midpoint of the opposite side minusmodethat one of a range of values that has the highest frequency as determined statistically multiplicationan arithmetical operation, defined initially in terms of repeated addition, usually written a × b, a.b, or ab, by which the product of two quantities is calculated: to multiply a by positive integral b is to add a to itself b times. Multiplication by fractions can then be defined in the light of the associative and commutative properties; multiplication by 1/n is equivalent to multiplication by 1 followed by division by n: for example 0.3 × 0.7 = 0.3 × = (0.3 × 7)/10 = 2 = 0.21 natural logarithma logarithm to the base e. Usually written loge or ln natural numberany of the numbers 0,1,2,3,4,… that can be used to count the members of a set; the non-negative integers nodea point at which the amplitude of one of the two kinds of displacement in a standing wave has zero or minimum value. Generally the other kind of displacement has its maximum value at this point nonagona polygon having nine sides numbera concept of quantity that is or can be derived from a single unit, the sum of a collection of units, or zero. Every number occupies a unique position in a sequence, enabling it to be used in counting. It can be assigned to one or more sets that can be arranged in a hierarchical classification: every number is a complex number; a complex number is either an imaginary number or a real number, and the latter can be a rational number or an irrational number; a rational number is either an integer or a fraction, while an irrational number can be a transcendental number or an algebraic number numeratorthe dividend of a fraction oblongobtuse angleoctagona polygon having eight sides octahedrona solid figure having eight plane faces odda thing or person that is odd in sequence or number open seta set which is not a closed set operationany procedure, such as addition, multiplication, involution, or differentiation, in which one or more numbers or quantities are operated upon according to specific rules operatorany symbol, term, letter, etc, used to indicate or express a specific operation or process, such as Δ (the differential operator) ordinal numbera number denoting relative position in a sequence, such as first, second, third originthe point of intersection of coordinate axes or planes parabolaa conic section formed by the intersection of a cone by a plane parallel to its side. Standard equation: y2 = 4ax, where 2a is the distance between focus and directrix parallelseparated by an equal distance at every point; never touching or intersecting parallelograma quadrilateral whose opposite sides are parallel and equal in length pentagona polygon having five sides percentageperfect numberan integer, such as 28, that is equal to the sum of all its possible factors, excluding itself pia transcendental number, fundamental to mathematics, that is the ratio of the circumference of a circle to its diameter. Approximate value: 3.141 592…; symbol: π plusincreased by the addition of polygona closed plane figure bounded by three or more straight sides that meet in pairs in the same number of vertices, and do not intersect other than at these vertices. The sum of the interior angles is (n–2) × 180° for n sides; the sum of the exterior angles is 360°. A regular polygon has all its sides and angles equal. Specific polygons are named according to the number of sides, such as triangle, pentagon, etc polyhedrona solid figure consisting of four or more plane faces (all polygons), pairs of which meet along an edge, three or more edges meeting at a vertex. In a regular polyhedron all the faces are identical regular polygons making equal angles with each other. Specific polyhedrons are named according to the number of faces, such as tetrahedron, icosahedron, etc polynomiala mathematical expression consisting of a sum of terms each of which is the product of a constant and one or more variables raised to a positive or zero integral power. For one variable, x, the general form is given by: a0xn + a1xn–1 + … + an–1x + an, where a0, a1, etc, are real numbers powerthe value of a number or quantity raised to some exponent prime numberan integer that cannot be factorized into other integers but is only divisible by itself or 1, such as 2, 3, 5, 7, and 11 prisma transparent polygonal solid, often having triangular ends and rectangular sides, for dispersing light into a spectrum or for reflecting and deviating light. They are used in spectroscopes, binoculars, periscopes, etc probabilitya measure or estimate of the degree of confidence one may have in the occurrence of an event, measured on a scale from zero (impossibility) to one (certainty). It may be defined as the proportion of favourable outcomes to the total number of possibilities if these are indifferent (mathematical probability), or the proportion observed in a sample (empirical probability), or the limit of this as the sample size tends to infinity (relative frequency), or by more subjective criteria (subjective probability) productthe result of the multiplication of two or more numbers, quantities, etc proofproper fractiona fraction in which the numerator has a lower absolute value than the denominator, as or x/(3 + x2) Pythagoras' theoremthe theorem that in a right-angled triangle the square of the length of the hypotenuse equals the sum of the squares of the other two sides quadranta quarter of the circumference of a circle quadratic equationan equation containing one or more terms in which the variable is raised to the power of two, but no terms in which it is raised to a higher power quadrilaterala polygon having four sides. A complete quadrilateral consists of four lines and their six points of intersection quotientthe result of the division of one number or quantity by another radianan SI unit of plane angle; the angle between two radii of a circle that cut off on the circumference an arc equal in length to the radius. 1 radian is equivalent to 57.296 degrees and π/2 radians equals a right angle radiusa straight line joining the centre of a circle or sphere to any point on the circumference or surface ratioa quotient of two numbers or quantities rational numberany real number of the form a/b, where a and b are integers and b is not zero, as 7 or 7/3 real numbera number expressible as a limit of rational numbers reciprocala number or quantity that when multiplied by a given number or quantity gives a product of one rectanglea parallelogram having four right angles recurring decimala rational number that contains a pattern of digits repeated indefinitely after the decimal point reflex angleremainder the amount left over when one quantity cannot be exactly divided by another rhombusan oblique-angled parallelogram having four equal sides right anglethe angle between two radii of a circle that cut off on the circumference an arc equal in length to one quarter of the circumference; an angle of 90° or π/2 radians right-angled trianglea triangle one angle of which is a right angle rootany plant part, such as a rhizome or tuber, that is similar to a root in structure, function, or appearance scalaran element of a field associated with a vector space scalenesecant(of an angle) a trigonometric function that in a right-angled triangle is the ratio of the length of the hypotenuse to that of the adjacent side; the reciprocal of cosine sectoreither portion of a circle included between two radii and an arc. Area: r2θ, where r is the radius and θ is the central angle subtended by the arc (in radians) semicircleone half of a circle seta collection of numbers, objects, etc, that is treated as an entity significant figuresthe figures of a number that express a magnitude to a specified degree of accuracy, rounding up or down the final figure simultaneous equationsa set of equations that are all satisfied by the same values of the variables sinea trigonometric function that in a right-angled triangle is the ratio of the length of the opposite side to that of the hypotenuse slide rulea mechanical calculating device consisting of two strips, one sliding along a central groove in the other, each strip graduated in two or more logarithmic scales of numbers, trigonometric functions, etc. It employs the same principles as logarithm tables solida closed surface in three-dimensional space spherethe solid figure bounded by this surface or the space enclosed by it. Equation: (x–a)2 + (y–b)2 + (z–c)2 = r2, where r is the radius and (a, b, c) are the coordinates of the centre; surface area: 4πr2; volume: 4πr3/3 squarea plane geometric figure having four equal sides and four right angles square roota number or quantity that when multiplied by itself gives a given number or quantity strange attractorsubseta set within a larger set subtractiona mathematical operation in which the difference between two numbers or quantities is calculated. Usually indicated by the symbol (–) sumthe limit of a series of sums of the first n terms of a converging infinite series as n tends to infinity surdan expression containing one or more irrational roots of numbers, such as 2√3 + 3√2 + 6 tangenta geometric line, curve, plane, or curved surface that touches another curve or surface at one point but does not intersect it tetrahedrona solid figure having four plane faces. A regular tetrahedron has faces that are equilateral triangles torusa ring-shaped surface generated by rotating a circle about a coplanar line that does not intersect the circle. Area: 4π2Rr; volume: 2π2Rr2, where r is the radius of the circle and R is the distance from the line to the centre of the circle trapeziuma quadrilateral having two parallel sides of unequal length trianglea three-sided polygon that can be classified by angle, as in an acute triangle, or by side, as in an equilateral triangle. Sum of interior angles: 180°; area: base × height uniona set containing all members of two given sets. Symbol: ⋃, as in A⋃B universal setthe set of all objects or elements considered in a given problem valuea particular magnitude, number, or amount variablean expression that can be assigned any of a set of values vectora variable quantity, such as force, that has magnitude and direction and can be resolved into components that are odd functions of the coordinates. It is represented in print by a bold italic symbol: F or ̄F Venn diagrama diagram in which mathematical sets or terms of a categorial statement are represented by overlapping circles within a boundary representing the universal set, so that all possible combinations of the relevant properties are represented by the various distinct areas in the diagram volumethe magnitude of the three-dimensional space enclosed within or occupied by an object, geometric solid, etc vulgar fractionx-axisthe horizontal, or more nearly horizontal, axis in a plane Cartesian coordinate system, along which the abscissa is measured y-axisthe vertical, or more nearly vertical, axis in a plane Cartesian coordinate system, along which the ordinate is measured z-axisin a three-dimensional Cartesian coordinate system, the axis that is perpendicular to the x-axis and the y-axis and that is used to measure or plot the values of z zerothe integer denoted by the symbol 0; nought ▷ See mathematics
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