1.a biased way of looking at or presenting something
2.the space between two lines or planes that intersect; the inclination of one line to another; measured in degrees or radians
3.the point where three areas or surfaces meet or intersect"the corners of a cube"
4.an interior angle formed by two meeting walls"a piano was in one corner of the room"
1.a member of a Germanic people who conquered England and merged with the Saxons and Jutes to become Anglo-Saxons
1.present with a bias"He biased his presentation so as to please the share holders"
2.fish with a hook
3.seek indirectly"fish for compliments"
4.to incline or bend from a vertical position"She leaned over the banister"
5.move or proceed at an angle"he angled his way into the room"
AngleAn"gle (ăṉ"g'l), n. [F. angle, L. angulus angle, corner; akin to uncus hook, Gr. 'agky`los bent, crooked, angular, 'a`gkos a bend or hollow, AS. angel hook, fish-hook, G. angel, and F. anchor.]
1. The inclosed space near the point where two lines meet; a corner; a nook.
Into the utmost angle of the world. Spenser.
To search the tenderest angles of the heart. Milton.
2. (Geom.) (a) The figure made by. two lines which meet. (b) The difference of direction of two lines. In the lines meet, the point of meeting is the vertex of the angle.
3. A projecting or sharp corner; an angular fragment.
Though but an angle reached him of the stone. Dryden.
4. (Astrol.) A name given to four of the twelve astrological “houses.” [Obs.] Chaucer.
5. [AS. angel.] A fishhook; tackle for catching fish, consisting of a line, hook, and bait, with or without a rod.
Give me mine angle: we 'll to the river there. Shak.
A fisher next his trembling angle bears. Pope.
Acute angle, one less than a right angle, or less than 90°. -- Adjacent or Contiguous angles, such as have one leg common to both angles. -- Alternate angles. See Alternate. -- Angle bar. (a) (Carp.) An upright bar at the angle where two faces of a polygonal or bay window meet. Knight. (b) (Mach.) Same as Angle iron. -- Angle bead (Arch.), a bead worked on or fixed to the angle of any architectural work, esp. for protecting an angle of a wall. -- Angle brace, Angle tie (Carp.), a brace across an interior angle of a wooden frame, forming the hypothenuse and securing the two side pieces together. Knight. -- Angle iron (Mach.), a rolled bar or plate of iron having one or more angles, used for forming the corners, or connecting or sustaining the sides of an iron structure to which it is riveted. -- Angle leaf (Arch.), a detail in the form of a leaf, more or less conventionalized, used to decorate and sometimes to strengthen an angle. -- Angle meter, an instrument for measuring angles, esp. for ascertaining the dip of strata. -- Angle shaft (Arch.), an enriched angle bead, often having a capital or base, or both. -- Curvilineal angle, one formed by two curved lines. -- External angles, angles formed by the sides of any right-lined figure, when the sides are produced or lengthened. -- Facial angle. See under Facial. -- Internal angles, those which are within any right-lined figure. -- Mixtilineal angle, one formed by a right line with a curved line. -- Oblique angle, one acute or obtuse, in opposition to a right angle. -- Obtuse angle, one greater than a right angle, or more than 90°. -- Optic angle. See under Optic. -- Rectilineal or Right-lined angle, one formed by two right lines. -- Right angle, one formed by a right line falling on another perpendicularly, or an angle of 90° (measured by a quarter circle). -- Solid angle, the figure formed by the meeting of three or more plane angles at one point. -- Spherical angle, one made by the meeting of two arcs of great circles, which mutually cut one another on the surface of a globe or sphere. -- Visual angle, the angle formed by two rays of light, or two straight lines drawn from the extreme points of an object to the center of the eye. -- For Angles of commutation, draught, incidence, reflection, refraction, position, repose, fraction, see Commutation, Draught, Incidence, Reflection, Refraction, etc.
AngleAn"gle (�), v. i. [imp. & p. p. Angled (�); p. pr. & vb. n. Angling (�).]
1. To fish with an angle (fishhook), or with hook and line.
2. To use some bait or artifice; to intrigue; to scheme; as, to angle for praise.
The hearts of all that he did angle for. Shak.
AngleAn"gle, v. t. To try to gain by some insinuating artifice; to allure. [Obs.] “He angled the people's hearts.” Sir P. Sidney.
Angle Class I • Angle Class II • Angle Class III • Angle's Classification • Angle-closure glaucoma (primary)(residual stage) acute • Angle-closure glaucoma (primary)(residual stage) chronic • Angle-closure glaucoma (primary)(residual stage) intermittent • angle bracket • angle brackets • angle iron • angle lock • angle of attack • angle of depression • angle of dip • angle of extinction • angle of field • angle of incidence • angle of inclination • angle of reflection • angle of refraction • angle of sideslip • angle of sight • angle of thread • angle of tilt • angle of total reflection • angle of view • angle shot • angle-closure glaucoma • angle-park • face angle • high-angle fire • high-angle gun • internal angle • right angle • round angle • straight angle
peuple ancien envahisseur (fr)[Classe]
peuple européen (fr)[Classe...]
habitant d'un lieu précis (fr)[Classe...]
peuple ancien anglo-saxon (fr)[Classe]
angle (n.) [figurative]
figure à deux dimensions (fr)[Classe]
figure géométrique (fr)[Classe]
building block, unit[Desc]
construction; building; edifice[ClasseHyper.]
construction; edifice; building[ClasseHyper.]
prendre un animal (fr)[Classe]
sortir qqch ou qqn de l'eau (fr)[Classe]
angle (v. intr.)
poisson de mer courant (fr)[ClasseParExt.]
gadoid; gadoid fish[ClasseTaxo.]
family Lophiidae, Lophiidae[membre]
angle (v. intr.)
angle (v. intr.)
tilt; list; inclination; lean; leaning[ClasseHyper.]
flexion, flexure - bender - bend, crook, curve, turn, twist - bend, crease, crimp, flexure, fold, plication - bendable, pliable, pliant, waxy - lean - angle, lean, slant, tilt, tip - rock, shake, sway - rock, sway - oscillate, sway, swing - cant, cant over, pitch, slant, tilt - careen, shift, tilt, wobble - careen, keel, lurch, reel, stagger, swag - bumpy, jolting, jolty, jumpy, rocky, rough - incline, pitch, slant, slope, slope down - heel, list - slant - angulate - angle - angular, angulate - angular[Dérivé]
angle (v. intr.)
action, motion, move, movement - locomotion, travel - locomotion, motive power, motivity - motion, movement - change of location, travel - traveler, traveller - mover - locomotive, locomotor, locomotory - angle - angulate - angle, lean, slant, tilt, tip - angular, angulate - angular[Dérivé]
stay in place[Ant.]
angle (v. intr.)
In geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles are usually presumed to be in a Euclidean plane, but are also defined in non-Euclidean geometry.
Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc by its radius. In the case of an angle (figure), the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any point and its image by the rotation.
The word angle comes from the Latin word angulus, meaning "a corner". The word angulus is a diminutive, of which the primitive form, angus, does not occur in Latin. Cognate words are the Greek ἀγκύλος (ankylοs), meaning "crooked, curved," and the English word "ankle". Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow".
Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was used by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.
The size of an angle is characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are called congruent angles.
In some contexts, such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts, such as identifying a point on a spiral curve or describing the cumulative rotation of an object in two dimensions relative to a reference orientation, angles that differ by a non-zero multiple of a full turn are not equivalent.
In order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The length of the arc s is then divided by the radius of the arc r, and possibly multiplied by a scaling constant k (which depends on the units of measurement that are chosen):
The value of θ thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio s/r is unaltered.
Units used to represent angles are listed below in descending magnitude order. Of these units, the degree and the radian are by far the most commonly used. Angles expressed in radians are dimensionless for the purposes of dimensional analysis.
Most units of angular measurement are defined such that one turn (i.e. one full circle) is equal to n units, for some whole number n. The two exceptions are the radian and the diameter part. For example, in the case of degrees, n = 360. A turn of n units is obtained by setting k = n/(2π) in the formula above. (Proof. The formula above can be rewritten as k = θr/s. One turn, for which θ = n units, corresponds to an arc equal in length to the circle's circumference, which is 2πr, so s = 2πr. Substituting n for θ and 2πr for s in the formula, results in k = nr/(2πr) = n/(2π).)
Although the definition of the measurement of an angle does not support the concept of a negative angle, it is frequently useful to impose a convention that allows positive and negative angular values to represent orientations and/or rotations in opposite directions relative to some reference.
In a two dimensional Cartesian coordinate system, angles are typically defined relative to the positive x-axis with positive angles representing rotations toward the positive y-axis and negative angles representing rotations toward the negative y-axis. When Cartesian coordinates are represented as they commonly are, with the x-axis rightward and the y-axis upward, positive rotations are counterclockwise and negative rotations are clockwise.
In many contexts, an angle of −θ is effectively equivalent to an angle of "one full turn minus θ". For example, an orientation represented as − 45° is effectively equivalent to an orientation represented as 360° − 45° or 315°. However, a rotation of − 45° would not be the same as a rotation of 315°.
In three dimensional geometry, "clockwise" and "counterclockwise" have no absolute meaning, so the direction of positive and negative angles must be defined relative to some reference, which is typically a vector passing through the angle's vertex and perpendicular to the plane in which the rays of the angle lie.
In navigation, bearings are measured relative to north. By convention, viewed from above, bearing angle are positive clockwise, so a bearing of 45° corresponds to a north-east orientation. Negative bearings are not used in navigation, so a north-west orientation corresponds to a bearing of 315°.
There are several alternatives to measuring the size of an angle by the corresponding angle of rotation. The grade of a slope, or gradient is equal to the tangent of the angle, or sometimes the sine. Gradients are often expressed as a percentage. For very small values (less than 5%), the grade of a slope is approximately the measure of an angle in radians.
In rational geometry the spread between two lines is defined at the square of sine of the angle between the lines. Since the sine of an angle and the sine of its supplementary angle are the same any angle of rotation that maps one of the lines into the other leads to the same value of the spread between the lines.
Astronomers measure angular separation of objects in degrees from their point of observation.
These measurements clearly depend on the individual subject, and the above should be treated as rough approximations only.
In mathematical expressions, it is common to use Greek letters (α, β, γ, θ, φ, ...) to serve as variables standing for the size of some angle. (To avoid confusion with its other meaning, the symbol π is typically not used for this purpose.) Lower case roman letters (a, b, c, ...) are also used. See the figures in this article for examples.
In geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB and AC (i.e. the lines from point A to point B and point A to point C) is denoted ∠BAC or BÂC. Sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex ("angle A").
Potentially, an angle denoted, say, ∠BAC might refer to any of four angles: the clockwise angle from B to C, the anticlockwise angle from B to C, the clockwise angle from C to B, or the anticlockwise angle from C to B, where the direction in which the angle is measured determines its sign (see Positive and negative angles). However, in many geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant, and no ambiguity arises. Otherwise, a convention may be adopted so that ∠BAC always refers to the anticlockwise (positive) angle from B to C, and ∠CAB to the anticlockwise (positive) angle from C to B.
The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection. Various names (now rarely, if ever, used) have been given to particular cases:—amphicyrtic (Gr. ἀμφί, on both sides, κυρτός, convex) or cissoidal (Gr. κισσός, ivy), biconvex; xystroidal or sistroidal (Gr. ξυστρίς, a tool for scraping), concavo-convex; amphicoelic (Gr. κοίλη, a hollow) or angulus lunularis, biconcave.
To define angles in an abstract real inner product space, we replace the Euclidean dot product ( · ) by the inner product , i.e.
In a complex inner product space, the expression for the cosine above may give non-real values, so it is replaced with
or, more commonly, using the absolute value, with
The latter definition ignores the direction of the vectors and thus describes the angle between one-dimensional subspaces and spanned by the vectors and correspondingly.
The definition of the angle between one-dimensional subspaces and given by
In geography, the location of any point on the Earth can be identified using a geographic coordinate system. This system specifies the latitude and longitude of any location in terms of angles subtended at the centre of the Earth, using the equator and (usually) the Greenwich meridian as references.
In astronomy, a given point on the celestial sphere (that is, the apparent position of an astronomical object) can be identified using any of several astronomical coordinate systems, where the references vary according to the particular system. Astronomers measure the angular separation of two stars by imagining two lines through the centre of the Earth, each intersecting one of the stars. The angle between those lines can be measured, and is the angular separation between the two stars.
Astronomers also measure the apparent size of objects as an angular diameter. For example, the full moon has an angular diameter of approximately 0.5°, when viewed from Earth. One could say, "The Moon's diameter subtends an angle of half a degree." The small-angle formula can be used to convert such an angular measurement into a distance/size ratio.
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