Слова на English для '(mathematics, less common) Cartesian coordinates.'
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noun
- one of three Cartesian coordinates that determine a position in space
- the magnitude of something in a particular direction (especially length or width or height)
- a construct whereby objects or individuals can be distinguished
- magnitude or extent
- (linear algebra) The number of elements of any basis of a vector space.
- (computing) Any of the independent ranges of indices in a multidimensional array.
- A construct whereby objects or individuals can be distinguished.
- (physics) One of the physical properties that are regarded as fundamental measures of a physical quantity, such as mass, length and time.
- (geometry) The number of independent coordinates needed to specify uniquely the location of a point in a space; also, any of such independent coordinates.
- (science fiction, fantasy) A universe or plane of existence.
- A single aspect of a given thing.
- A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.
verb
noun
- (cartography) An arbitrary point on Earth's surface, chosen as the zero for a system of coordinates.
- (anatomy) The proximal end of attachment of a muscle to a bone that will not be moved by the action of that muscle.
- (mathematics) The point at which the axes of a coordinate system intersect.
- The beginning of something.
- (in the plural) Ancestry.
- The source of a river, information, goods, etc.
- an event that is a beginning; a first part or stage of subsequent events
- the place where something begins, where it springs into being
- the source of something's existence or from which it derives or is derived
- the hereditary derivation of an individual
- the point of intersection of coordinate axes; where the values of the coordinates are all zero
- properties attributable to your ancestry
noun
- (mathematics) The coordinates of a point in three-dimensional space, measured as its Cartesian distance from the origin, the angle measured from the z-axis to a line joining the point to the origin, and the angle measured counterclockwise from the x-axis to this line.
- (mathematics) A system of coordinates using such measurements to indicate position.
- (mathematics) The coordinates of a point in a plane, measured as its Cartesian distance from the origin and the angle measured counterclockwise from the x-axis to a line joining the point to the origin.
noun
- (cartography) Initialism of cartographic reference system.
- (computing, aviation, travel) Initialism of central reservation system or computer reservation system.
- (pathology) Initialism of Chinese restaurant syndrome.
- (toxicology) Abbreviation of crotylsarin.
- (US, aviation) Initialism of (FAA) certified repair station.
- (pathology) Initialism of congenital rubella syndrome.
- (pathology) Initialism of chronic rhinosinusitis.
- (technology) Initialism of cold-rolled steel, steel that has been processed while remaining relatively cold, often coated in oil to prevent corrosion.
- (pathology) Initialism of cytokine release syndrome.
- (pathology) Initialism of constriction ring syndrome.
- (US, realtors) Initialism of certified residential specialist.
- (pathology) Initialism of cardiorenal syndrome.
name
phrase
noun
- (of a finite set of points) the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of a given finite set of points.
- (mathematical analysis, of a function) An analogue of the centre of gravity of a nonuniform body in which local density is replaced by a specified function (which can take negative values) and the place of the body's shape is taken by the function's domain.
- (statistics, cluster analysis, of a cluster of points) the arithmetic mean (alternatively, median) position of a cluster of points in a coordinate system based on some application-dependent measure of distance.
- (graph theory, of a tree) Given a tree of n nodes, either (1) a unique node whose removal would split the tree into subtrees of fewer than n/2 nodes, or (2) either of a pair of adjacent nodes such that removal of the edge connecting them would split the tree into two subtrees of exactly n/2 nodes.
- (geometry, specifically, of a triangle) The point of intersection of the three medians of a given triangle; the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of the three vertices.
- (geometry, physics, engineering, of an object or a geometrical figure) The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly dense body; the centre of gravity or centre of mass.
- the center of mass of an object of uniform density
adj
- (geometry) Of or relating to homogeneous coordinates.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
noun
- a mathematical function whose graph (in Cartesian coordinates with uniform scales) is a line in the plane.
- (mathematics) Any function whose value on the sum of two elements is the sum of the values of the function on the two elements and whose value on the product of a scalar times an element is the scalar times the value of the function on the element: f(ax+by)=af(x)+bf(y)
- (mathematics) Any function whose graph is a straight line: f(x)=ax+b
noun
- (mathematics) The z-coordinate (the last of the three terms by which a point is referred to, in a system of Cartesian coordinates for a three-dimensional space)
- An applied material; an application
- (mathematics) A line at right angles to the axis of a conic section that extends from the axis to the curve
verb
noun
- (mathematics) One of the four regions of the Cartesian plane bounded by the x-axis and y-axis.
- (geometry) One fourth of a circle or disc; a sector with an angle of 90°.
- (college basketball) One of the four categories of team wins and losses, as categorized by strength of schedule.
- (nautical) A measuring device with a graduated arc of 90° used in locating an altitude.
- One of the four sections made by dividing an area with two perpendicular lines.
- any of the four areas into which a plane is divided by two orthogonal coordinate axes
- a measuring instrument for measuring altitude of heavenly bodies
- a quarter of the circumference of a circle
- the area enclosed by two perpendicular radii of a circle
noun
- (geometry) The second of the two terms by which a point is referred to, in a system of fixed rectilinear coordinate (Cartesian coordinate) axes.
- (geometry) The vertical line representing an axis of a Cartesian coordinate system, on which the ordinate (sense above) is shown.
- the value of a coordinate on the vertical axis
adj
verb
- (transitive, statistics, ecology) To subject to the mathematical operation of ordination.
- (transitive) To align a series of objects.
- (transitive, uncommon) To ordain a priest, or consecrate a bishop.
- appoint to a clerical posts
- bring (components or parts) into proper or desirable coordination correlation
adj
noun
noun
adj
verb
- (ambitransitive) To match (objects, especially clothes).
- (transitive) To place in the same order or rank.
- (ambitransitive) To synchronize (activities).
- be co-ordinated
- bring into common action, movement, or condition
- bring (components or parts) into proper or desirable coordination correlation
- bring order and organization to
noun
- (cartography) Any of several systems of intersecting lines that allow the curved surface of the earth to be represented on a flat surface. The set of mathematics used to calculate coordinate positions.
- (perfumery) The distance the scent of a perfume radiates off the skin.
- (psychology) A belief or assumption that others have similar thoughts and experiences to one's own, including making accusations that would more fittingly apply to the accuser.
- (mathematics) A transformation which extracts a fragment of a mathematical object.
- (geometry) An image of an object on a surface of fewer dimensions.
- (photography) The image that a translucent object casts onto another object.
- The action of projecting or throwing or propelling something.
- A forecast or prognosis obtained by extrapolation
- (linear algebra) An idempotent linear transformation which maps vectors from a vector space onto a subspace.
- The display of an image by devices such as movie projector, video projector, overhead projector or slide projector.
- (grammar) The preservation of the properties of lexical items while generating the phrase structure of a sentence. See Projection principle.
- (category theory) A morphism from a categorical product to one of its (two) components.
- Something which projects, protrudes, juts out, sticks out, or stands out.
- the act of projecting out from something
- a planned undertaking
- the representation of a figure or solid on a plane as it would look from a particular direction
- the act of expelling or projecting or ejecting
- any solid convex shape that juts out from something
- a prediction made by extrapolating from past observations
- (psychiatry) a defense mechanism by which your own traits and emotions are attributed to someone else
- the acoustic phenomenon that gives sound a penetrating quality
- the projection of an image from a film onto a screen
- any structure that branches out from a central support
noun
- (differential geometry, topology) Synonym of coordinate chart.
- A ranked listing of competitors, as of recorded music.
- A map illustrating the geography of a specific phenomenon.
- A diagram.
- A graph.
- A written deed; a charter.
- A tabular presentation of data; a table.
- A navigator's map.
- A record of a patient's diagnosis, care instructions, and recent history.
- (usually plural) a listing of best-selling recorded music
- a visual display of information
- a map designed to assist navigation by air or sea
verb
- To enter (medical information) into a medical record.
- (transitive) To draw a chart or map of.
- (transitive) To draw or figure out (a route or plan).
- (intransitive, of a record or artist) To appear on a hit-recording chart.
- (transitive) To record systematically.
- make a chart of
- plan in detail
- represent by means of a graph
adj
- (mathematics, cartography) Of, or pertaining to, co-ordinates based on mutually orthogonal axes.
- Of, or pertaining to, Descartes, his mathematical methods, or his philosophy, especially with regard to its emphasis on logical analysis and its mechanistic interpretation of physical nature.
- of or relating to Rene Descartes or his works
noun
noun
noun
- (computer graphics) A point in 3D space, usually given in terms of its Cartesian coordinates.
- The point at which an axis meets a curve or surface.
- The highest point, top or apex of something.
- (graph theory) One of the elements of a graph joined or not by edges to other vertices.
- (anatomy) The highest surface on the skull; the crown of the head.
- (astrology) The point where the prime vertical meets the ecliptic in the western hemisphere of a natal chart.
- (particle physics) An interaction point.
- (optics) The point where the surface of a lens crosses the optical axis.
- (typography) A sharp downward point opposite a crotch, as in the letters "V" and "W" but not "Y".
- (mathematics) A point on the curve with a local minimum or maximum of curvature.
- The common point of the two rays that form an angle.
- the highest point (of something)
- the point of intersection of lines or the point opposite the base of a figure
noun
- (geometry) The coordinates of a point measured from an origin along a horizontal axis from left to right (the x-axis) and along a vertical axis from bottom to top (the y-axis). This can be extended to three-dimensions by the z-axis perpendicular to the x- and y-axes.
- one of the coordinates in a system of coordinates that locates a point on a plane or in space by its distance from two lines or three planes respectively; the two lines or the intersections of the three planes are the coordinate axes
noun
- (geometry) The first of the two terms by which a point is referred to, in a system of fixed rectilinear coordinate (Cartesian coordinate) axes.
- (geometry) The horizontal line representing an axis of a Cartesian coordinate system, on which the abscissa (sense above) is shown.
- the value of a coordinate on the horizontal axis
noun
- (mathematics, geometry) A surface, all of whose cross sections are elliptic or circular (including the sphere), that generalises the ellipse and in Cartesian coordinates (x, y, z) is a quadric with equation x²/a² + y²/b² + z²/c² = 1.
- (geography) Such a surface used as a model of the shape of the earth.
- a surface whose plane sections are all ellipses or circles
adj
adj
- (cartography) Of a map, equal-area.
- (geometry) Equal in measure but not admitting of superposition; applied to magnitudes.
- (mathematics, category theory) Of two categories, (informally) such that one is essentially a relabeling of the other; (formally) related by a pair of functors such the composition of the one with the other is naturally isomorphic to the identity functor.
- (mathematics) Relating to the corresponding elements of an equivalence relation.
- (chemistry) Having the equal ability to combine.
- Similar or identical in value, meaning or effect; virtually equal.
- (mathematics) Of two sets, having a one-to-one correspondence.
- being essentially equal to something
noun
- Anything that is virtually equal to something else, or has the same value, force, etc.
- (chemistry) An equivalent weight.
- a person or thing equal to another in value or measure or force or effect or significance etc
- the atomic weight of an element that has the same combining capacity as a given weight of another element; the standard is 8 for oxygen
verb
noun
- (cartography) A method of marking off maps into areas.
- (electronics) The third (or higher) electrode of a vacuum tube (triode or higher).
- (motor racing) The pattern of starting positions of the drivers for a race.
- A grating of parallel bars; a gridiron.
- A rectangular array of squares or rectangles of equal size, such as in a crossword puzzle.
- (electricity) A battery-plate somewhat like a grating, especially a zinc plate in a primary battery, or a lead plate in a secondary or storage battery.
- (computing) A system or structure of distributed computers working mostly on a peer-to-peer basis, used mainly to solve single and complex scientific or technical problems or to process data at high speeds (as in clusters).
- A system for delivery of electricity, consisting of various substations, transformers and generators, connected by wire.
- (theater, television) An openwork ceiling above the stage or studio, used for affixing lights etc.
- A tiling of the plane with regular polygons; a honeycomb.
- a cooking utensil of parallel metal bars; used to grill fish or meat
- a perforated or corrugated metal plate used in a storage battery as a conductor and support for the active material
- a system of high tension cables by which electrical power is distributed throughout a region
- an electrode placed between the cathode and anode of a vacuum tube to control the flow of electrons through the tube
- a pattern of regularly spaced horizontal and vertical lines
verb
noun
- one of three Cartesian coordinates that determine a position in space
- the magnitude of something in a particular direction (especially length or width or height)
- a construct whereby objects or individuals can be distinguished
- magnitude or extent
- (linear algebra) The number of elements of any basis of a vector space.
- (computing) Any of the independent ranges of indices in a multidimensional array.
- A construct whereby objects or individuals can be distinguished.
- (physics) One of the physical properties that are regarded as fundamental measures of a physical quantity, such as mass, length and time.
- (geometry) The number of independent coordinates needed to specify uniquely the location of a point in a space; also, any of such independent coordinates.
- (science fiction, fantasy) A universe or plane of existence.
- A single aspect of a given thing.
- A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.
verb
noun
- (cartography) An arbitrary point on Earth's surface, chosen as the zero for a system of coordinates.
- (anatomy) The proximal end of attachment of a muscle to a bone that will not be moved by the action of that muscle.
- (mathematics) The point at which the axes of a coordinate system intersect.
- The beginning of something.
- (in the plural) Ancestry.
- The source of a river, information, goods, etc.
- an event that is a beginning; a first part or stage of subsequent events
- the place where something begins, where it springs into being
- the source of something's existence or from which it derives or is derived
- the hereditary derivation of an individual
- the point of intersection of coordinate axes; where the values of the coordinates are all zero
- properties attributable to your ancestry
noun
- (mathematics) The coordinates of a point in three-dimensional space, measured as its Cartesian distance from the origin, the angle measured from the z-axis to a line joining the point to the origin, and the angle measured counterclockwise from the x-axis to this line.
- (mathematics) A system of coordinates using such measurements to indicate position.
- (mathematics) The coordinates of a point in a plane, measured as its Cartesian distance from the origin and the angle measured counterclockwise from the x-axis to a line joining the point to the origin.
noun
- (cartography) Initialism of cartographic reference system.
- (computing, aviation, travel) Initialism of central reservation system or computer reservation system.
- (pathology) Initialism of Chinese restaurant syndrome.
- (toxicology) Abbreviation of crotylsarin.
- (US, aviation) Initialism of (FAA) certified repair station.
- (pathology) Initialism of congenital rubella syndrome.
- (pathology) Initialism of chronic rhinosinusitis.
- (technology) Initialism of cold-rolled steel, steel that has been processed while remaining relatively cold, often coated in oil to prevent corrosion.
- (pathology) Initialism of cytokine release syndrome.
- (pathology) Initialism of constriction ring syndrome.
- (US, realtors) Initialism of certified residential specialist.
- (pathology) Initialism of cardiorenal syndrome.
name
phrase
noun
- (of a finite set of points) the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of a given finite set of points.
- (mathematical analysis, of a function) An analogue of the centre of gravity of a nonuniform body in which local density is replaced by a specified function (which can take negative values) and the place of the body's shape is taken by the function's domain.
- (statistics, cluster analysis, of a cluster of points) the arithmetic mean (alternatively, median) position of a cluster of points in a coordinate system based on some application-dependent measure of distance.
- (graph theory, of a tree) Given a tree of n nodes, either (1) a unique node whose removal would split the tree into subtrees of fewer than n/2 nodes, or (2) either of a pair of adjacent nodes such that removal of the edge connecting them would split the tree into two subtrees of exactly n/2 nodes.
- (geometry, specifically, of a triangle) The point of intersection of the three medians of a given triangle; the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of the three vertices.
- (geometry, physics, engineering, of an object or a geometrical figure) The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly dense body; the centre of gravity or centre of mass.
- the center of mass of an object of uniform density
noun
- a mathematical function whose graph (in Cartesian coordinates with uniform scales) is a line in the plane.
- (mathematics) Any function whose value on the sum of two elements is the sum of the values of the function on the two elements and whose value on the product of a scalar times an element is the scalar times the value of the function on the element: f(ax+by)=af(x)+bf(y)
- (mathematics) Any function whose graph is a straight line: f(x)=ax+b
noun
- (mathematics) The z-coordinate (the last of the three terms by which a point is referred to, in a system of Cartesian coordinates for a three-dimensional space)
- An applied material; an application
- (mathematics) A line at right angles to the axis of a conic section that extends from the axis to the curve
verb
noun
- (mathematics) One of the four regions of the Cartesian plane bounded by the x-axis and y-axis.
- (geometry) One fourth of a circle or disc; a sector with an angle of 90°.
- (college basketball) One of the four categories of team wins and losses, as categorized by strength of schedule.
- (nautical) A measuring device with a graduated arc of 90° used in locating an altitude.
- One of the four sections made by dividing an area with two perpendicular lines.
- any of the four areas into which a plane is divided by two orthogonal coordinate axes
- a measuring instrument for measuring altitude of heavenly bodies
- a quarter of the circumference of a circle
- the area enclosed by two perpendicular radii of a circle
noun
- (geometry) The second of the two terms by which a point is referred to, in a system of fixed rectilinear coordinate (Cartesian coordinate) axes.
- (geometry) The vertical line representing an axis of a Cartesian coordinate system, on which the ordinate (sense above) is shown.
- the value of a coordinate on the vertical axis
adj
verb
- (transitive, statistics, ecology) To subject to the mathematical operation of ordination.
- (transitive) To align a series of objects.
- (transitive, uncommon) To ordain a priest, or consecrate a bishop.
- appoint to a clerical posts
- bring (components or parts) into proper or desirable coordination correlation
noun
adj
verb
- (ambitransitive) To match (objects, especially clothes).
- (transitive) To place in the same order or rank.
- (ambitransitive) To synchronize (activities).
- be co-ordinated
- bring into common action, movement, or condition
- bring (components or parts) into proper or desirable coordination correlation
- bring order and organization to
noun
- (cartography) Any of several systems of intersecting lines that allow the curved surface of the earth to be represented on a flat surface. The set of mathematics used to calculate coordinate positions.
- (perfumery) The distance the scent of a perfume radiates off the skin.
- (psychology) A belief or assumption that others have similar thoughts and experiences to one's own, including making accusations that would more fittingly apply to the accuser.
- (mathematics) A transformation which extracts a fragment of a mathematical object.
- (geometry) An image of an object on a surface of fewer dimensions.
- (photography) The image that a translucent object casts onto another object.
- The action of projecting or throwing or propelling something.
- A forecast or prognosis obtained by extrapolation
- (linear algebra) An idempotent linear transformation which maps vectors from a vector space onto a subspace.
- The display of an image by devices such as movie projector, video projector, overhead projector or slide projector.
- (grammar) The preservation of the properties of lexical items while generating the phrase structure of a sentence. See Projection principle.
- (category theory) A morphism from a categorical product to one of its (two) components.
- Something which projects, protrudes, juts out, sticks out, or stands out.
- the act of projecting out from something
- a planned undertaking
- the representation of a figure or solid on a plane as it would look from a particular direction
- the act of expelling or projecting or ejecting
- any solid convex shape that juts out from something
- a prediction made by extrapolating from past observations
- (psychiatry) a defense mechanism by which your own traits and emotions are attributed to someone else
- the acoustic phenomenon that gives sound a penetrating quality
- the projection of an image from a film onto a screen
- any structure that branches out from a central support
noun
- (differential geometry, topology) Synonym of coordinate chart.
- A ranked listing of competitors, as of recorded music.
- A map illustrating the geography of a specific phenomenon.
- A diagram.
- A graph.
- A written deed; a charter.
- A tabular presentation of data; a table.
- A navigator's map.
- A record of a patient's diagnosis, care instructions, and recent history.
- (usually plural) a listing of best-selling recorded music
- a visual display of information
- a map designed to assist navigation by air or sea
verb
- To enter (medical information) into a medical record.
- (transitive) To draw a chart or map of.
- (transitive) To draw or figure out (a route or plan).
- (intransitive, of a record or artist) To appear on a hit-recording chart.
- (transitive) To record systematically.
- make a chart of
- plan in detail
- represent by means of a graph
noun
noun
- (computer graphics) A point in 3D space, usually given in terms of its Cartesian coordinates.
- The point at which an axis meets a curve or surface.
- The highest point, top or apex of something.
- (graph theory) One of the elements of a graph joined or not by edges to other vertices.
- (anatomy) The highest surface on the skull; the crown of the head.
- (astrology) The point where the prime vertical meets the ecliptic in the western hemisphere of a natal chart.
- (particle physics) An interaction point.
- (optics) The point where the surface of a lens crosses the optical axis.
- (typography) A sharp downward point opposite a crotch, as in the letters "V" and "W" but not "Y".
- (mathematics) A point on the curve with a local minimum or maximum of curvature.
- The common point of the two rays that form an angle.
- the highest point (of something)
- the point of intersection of lines or the point opposite the base of a figure
noun
- (geometry) The coordinates of a point measured from an origin along a horizontal axis from left to right (the x-axis) and along a vertical axis from bottom to top (the y-axis). This can be extended to three-dimensions by the z-axis perpendicular to the x- and y-axes.
- one of the coordinates in a system of coordinates that locates a point on a plane or in space by its distance from two lines or three planes respectively; the two lines or the intersections of the three planes are the coordinate axes
noun
- (geometry) The first of the two terms by which a point is referred to, in a system of fixed rectilinear coordinate (Cartesian coordinate) axes.
- (geometry) The horizontal line representing an axis of a Cartesian coordinate system, on which the abscissa (sense above) is shown.
- the value of a coordinate on the horizontal axis
noun
- (mathematics, geometry) A surface, all of whose cross sections are elliptic or circular (including the sphere), that generalises the ellipse and in Cartesian coordinates (x, y, z) is a quadric with equation x²/a² + y²/b² + z²/c² = 1.
- (geography) Such a surface used as a model of the shape of the earth.
- a surface whose plane sections are all ellipses or circles
adj
noun
- (cartography) A method of marking off maps into areas.
- (electronics) The third (or higher) electrode of a vacuum tube (triode or higher).
- (motor racing) The pattern of starting positions of the drivers for a race.
- A grating of parallel bars; a gridiron.
- A rectangular array of squares or rectangles of equal size, such as in a crossword puzzle.
- (electricity) A battery-plate somewhat like a grating, especially a zinc plate in a primary battery, or a lead plate in a secondary or storage battery.
- (computing) A system or structure of distributed computers working mostly on a peer-to-peer basis, used mainly to solve single and complex scientific or technical problems or to process data at high speeds (as in clusters).
- A system for delivery of electricity, consisting of various substations, transformers and generators, connected by wire.
- (theater, television) An openwork ceiling above the stage or studio, used for affixing lights etc.
- A tiling of the plane with regular polygons; a honeycomb.
- a cooking utensil of parallel metal bars; used to grill fish or meat
- a perforated or corrugated metal plate used in a storage battery as a conductor and support for the active material
- a system of high tension cables by which electrical power is distributed throughout a region
- an electrode placed between the cathode and anode of a vacuum tube to control the flow of electrons through the tube
- a pattern of regularly spaced horizontal and vertical lines
verb
adj
- (geometry) Of or relating to homogeneous coordinates.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
adj
noun
adj
- (mathematics, cartography) Of, or pertaining to, co-ordinates based on mutually orthogonal axes.
- Of, or pertaining to, Descartes, his mathematical methods, or his philosophy, especially with regard to its emphasis on logical analysis and its mechanistic interpretation of physical nature.
- of or relating to Rene Descartes or his works
noun
adj
- (cartography) Of a map, equal-area.
- (geometry) Equal in measure but not admitting of superposition; applied to magnitudes.
- (mathematics, category theory) Of two categories, (informally) such that one is essentially a relabeling of the other; (formally) related by a pair of functors such the composition of the one with the other is naturally isomorphic to the identity functor.
- (mathematics) Relating to the corresponding elements of an equivalence relation.
- (chemistry) Having the equal ability to combine.
- Similar or identical in value, meaning or effect; virtually equal.
- (mathematics) Of two sets, having a one-to-one correspondence.
- being essentially equal to something
noun
- Anything that is virtually equal to something else, or has the same value, force, etc.
- (chemistry) An equivalent weight.
- a person or thing equal to another in value or measure or force or effect or significance etc
- the atomic weight of an element that has the same combining capacity as a given weight of another element; the standard is 8 for oxygen