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  • Grinding Angle, 20°;. Whetting Angle, 25°
    Grinding Angle, 20°;. Whetting Angle, 25°
  • WordNet 3.6
    • v angle present with a bias "He biased his presentation so as to please the share holders"
    • v angle fish with a hook
    • v angle seek indirectly "fish for compliments"
    • v angle to incline or bend from a vertical position "She leaned over the banister"
    • v angle move or proceed at an angle "he angled his way into the room"
    • n angle a biased way of looking at or presenting something
    • n Angle a member of a Germanic people who conquered England and merged with the Saxons and Jutes to become Anglo-Saxons
    • n angle the space between two lines or planes that intersect; the inclination of one line to another; measured in degrees or radians
    • ***

Additional illustrations & photos:

Using a Handscrew to hold a Board at an Angle Using a Handscrew to hold a Board at an Angle
Angles Angles
Fishing with an Angle Fishing with an Angle
Right-angled Arc Lamp Right-angled Arc Lamp

Webster's Revised Unabridged Dictionary
  • Interesting fact: Even though a polar bears fur looks white it is actually colourless and is made with hollow tubes. The reason the bear looks white is because the rough inner surface of the tubes make light scatter and reflect at many different angles which gives the white appearance
    • Angle 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.""A fisher next his trembling angle bears."
    • Angle (Astrol) A name given to four of the twelve astrological “houses.”
    • Angle A projecting or sharp corner; an angular fragment. "Though but an angle reached him of the stone."
    • Angle (Geom) The difference of direction of two lines. In the lines meet, the point of meeting is the vertex of the angle.
    • Angle (Geom) The figure made by. two lines which meet.
    • Angle The inclosed space near the point where two lines meet; a corner; a nook. "Into the utmost angle of the world.""To search the tenderest angles of the heart."
    • Angle To fish with an angle (fishhook), or with hook and line.
    • v. t Angle To try to gain by some insinuating artifice; to allure. "He angled the people's hearts."
    • Angle To use some bait or artifice; to intrigue; to scheme; as, to angle for praise. "The hearts of all that he did angle for."
    • ***
Century Dictionary and Cyclopedia
  • Interesting fact: The reason why some people get a cowlick is because the growth of their hair is in a spiral pattern, which causes the hair to either stand straight up, or goes to a certain angle
    • n angle A fishing-hook: often in later use extended to include the line or tackle, and even the rod.
    • n angle One who or that which catches by stratagem or deceit.
    • n angle [From the verb.] The act of angling.
    • angle To fish with an angle, or with hook and line.
    • angle To try by artful means to catch or win over a person or thing, or to elicit an opinion: commonly with for.
    • angle To fish (a stream).
    • angle To fish for or try to catch, as with an angle or hook.
    • angle To lure or entice, as with bait.
    • n angle One of a Teutonic tribe which in the earliest period of its recorded history dwelt in the neighborhood of the district now called Angeln, in Schleswig-Holstein, and which in the fifth century and later, accompanied by kindred tribes, the Saxons, Jutes, and Frisians, crossed over to Britain and colonized the greater part of it. The Angles were the most numerous of these settlers, and founded the three kingdoms of East Anglia, Mercia, and Northumbria. From them the entire country derived its name England, the “land of the Angles.” See Anglian, Anglo-Saxon, and English.
    • n angle The difference in direction of two intersecting lines; the space included between two intersecting lines; the figure or projection formed by the meeting of two lines; a corner. In geometry, a plane angle is one formed by two lines, straight or curved, which meet in a plane; a rectilinear angle, one formed by two straight lines. The point where the lines meet is called the vertex of the angle, or the angular point, and the lines which contain the angle are called its sides or legs. The magnitude of the angle does not depend upon the length of the lines which form it, but merely on their relative positions. It is measured by the length of a circular arc of unit radius having for its center the vertex of the angle, or point of intersection of the sides. Thus, the angle FEA, fig. 1, is measured by 32 degrees of the circumference, or the arc AF. Angular magnitudes are also expressed in quadrants of four to the circumference, in hours of six to the quadrant, in sexagesimal degrees of 90 to the quadrant, (rarely) in centesimal degrees of 100 to the quadrant, etc. The arc whose length is equal to the radius subtends an angle of 57° 17′ 44″.8 nearly. Theoretically, the measure of an angle is the logarithm of the anharmonic ratio made by the two sides with the two tangents to the absolute intersecting at the vertex. Angles receive different names, according to their magnitude, their construction, their position, etc. When one straight line intersects another so as to make the four angles so formed equal, these angles are called right angles, and each is measured by an arc equal to one fourth of a circumference, or 90 degrees. Thus, ACD, fig. 2, is a right angle. An angle which is less than a right angle is acute, as ACE. An obtuse angle is one which is greater than a right angle, as ECB. Acute and obtuse angles are both called oblique, in opposition to right angles. A curvilinear angle is formed by the meeting of the tangents to two curved lines at their point of intersection. Adjacent or contiguous angles are such as have one leg common to both angles, both together being equal to two right angles. Thus, in fig. 2, ACE and ECB are adjacent angles. Conjugate angles are two angles having a common vertex and common legs, one being concave, the other convex. A straight angle is an angle of 180°. A reflex angle is the same as a convex angle. (See conjugate angles, above.) Exterior, external, or outward angles are the angles of any rectilinear figure without it, made by producing one of the sides at each vertex, the angles formed within the figure being called interior angles. When one line intersects a pair of lines in a plane, of the eight angles so formed, those which are between the pair are called interior, those without exterior. Of the interior angles, a pair for different sides of the intersecting line, and at different intersected lines, are called alternate (which see). See radian.
    • n angle Hence An angular projection; a projecting corner: as, the angles of a building.
    • n angle In astrology, the 1st, 4th, 7th, or 10th house.
    • n angle In anatomy, same as angulus.
    • n angle In heraldry, a charge representing a narrow band or ribbon bent in an angle.
    • n angle In projective geometry, a piece of a flat pencil bounded by two of the straights as sides. See the extract.
    • angle To lead off or deflect (a body or element) from a direction parallel or perpendicular to another body or element to which or from which it is to move: as, to angle a rope.
    • ***
Chambers's Twentieth Century Dictionary
  • Interesting fact: Every 14 years, Saturn's rings become briefly invisible to astronomers on Earth. At that time, the plane of the rings is tipped to that of the Earth's orbit, and they are seen edge-on. Since the ring's are so thin, they can't be seen at that angle.
    • n Angle ang′gl a corner: the point where two lines meet:
    • n Angle ang′gl a hook or bend: a fishing-rod with line and hook
    • v.i Angle to fish with an angle
    • v.t Angle to entice: to try to gain by some artifice
    • n Angle ang′gl (geom.) the inclination of two straight lines which meet, but are not in the same straight line: any outlying corner or nook
    • ***


  • George Santayana
    “To knock a thing down, especially if it is cocked at an arrogant angle, is a deep delight to the blood.”
  • Peter Conrad
    Peter Conrad
    “All that a city will ever allow you is an angle on it -- an oblique, indirect sample of what it contains, or what passes through it; a point of view.”
  • Daniel J. Boorstin
    “The traditional novel form continues to enlarge our experience in those very areas where the wide-angle lens and the Cinema screen tend to narrow it.”
  • Samuel Johnson
    “Fly fishing may be a very pleasant amusement; but angling or float fishing I can only compare to a stick and a string, with a worm at one end and a fool at the other.”
  • Izaak Walton
    Izaak Walton
    “Angling may be said to be so like the mathematics that it can never be fully learned.”
  • Lord Chesterfield
    “Modesty is the only sure bait when you angle for praise.”


From a different angle - If you look at something from a different angle, you look at it from a different point of view.


Webster's Revised Unabridged Dictionary
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,
Chambers's Twentieth Century Dictionary
Fr.—L. angulus; cog. with Gr. angkylos; both from root ank, to bend, seen also in Anchor, Ankle.


In literature:

Many other stories of his performances with "the angle" could be also related, but this may suffice.
"A History of Horncastle from the earliest period to the present time" by James Conway Walter
He had to look up at a sharp angle to see the storm front.
"The Flying Stingaree" by Harold Leland Goodwin
Stepping outside, he estimated the angle the borer made with the dirt floor.
"Astounding Stories, April, 1931" by Various
At its inferior, or lower angle, it is united to the coccyx.
"A Treatise on Anatomy, Physiology, and Hygiene (Revised Edition)" by Calvin Cutter
At right angles to the Palazzo Comunale is the cathedral, with the campanile projecting and flanking the facade to the south.
"The Shores of the Adriatic" by F. Hamilton Jackson
That masonry changes at the centre of the eighth arch from the sea angle on the Piazzetta side.
"The Stones of Venice, Volume I (of 3)" by John Ruskin
In the description of the Fig-tree angle, given in the eighth chapter of Vol.
"The Stones of Venice, Volume III (of 3)" by John Ruskin
Only so far as they were Angles; and, except in the parts near the Elbe, they were other than Angle.
"The Ethnology of the British Islands" by Robert Gordon Latham
Put around a frame and cover with glass, at an angle of thirty-five degrees to the sun.
"Soil Culture" by J. H. Walden
There followed a hiss and a howl, and a sulky retreat to the farther angle.
"The Recipe for Diamonds" by Charles John Cutcliffe Wright Hyne
The stern of the boat was down; the bow up, leaving us at an angle of about forty-five degrees.
""And they thought we wouldn't fight"" by Floyd Gibbons
The floor rose at an angle, indicating that the rocket was half over on its side.
"Astounding Stories, July, 1931" by Various
The bases of the two approached so near, that their sloping sides formed an angle with each other.
"The Boy Slaves" by Mayne Reid
The line of the Roman walls ran from the Tower straight to Aldgate; there making an angle, it continued to Bishopsgate.
"Old and New London" by Walter Thornbury
Standing up at its most aggressive angle, it seemed to challenge the world.
"The Girl in the Mirror" by Elizabeth Garver Jordan
They were at bottom at ninety feet, and the clean sand dropped away at an angle of about thirty degrees.
"The Wailing Octopus" by Harold Leland Goodwin
Scuta nearly oval, with their umbones at the rostral angle.
"A Monograph on the Sub-class Cirripedia (Volume 1 of 2)" by Charles Darwin
That lens must have a mighty wide angle, by the way.
"The Blue Ghost Mystery" by Harold Leland Goodwin
The end is ground V-shaped and to an angle of 60 degrees, which corresponds to the angle of a standard V-thread.
"Turning and Boring" by Franklin D. Jones
The wing of an aeroplane is normally set at an angle horizontally (or rather at an angle to the relative wind) varying from 0deg to 4deg.
"The New Gresham Encyclopedia. Vol. 1 Part 1" by Various

In poetry:

And I should raise in the east
A glass of water
Where any-angled light
Would congregate endlessly.
"Water" by Philip Larkin
Thus fell Harold, bracelet-giver;
Jesu rest his soul for ever;
Angles all from thrall deliver;
Miserere Domine.
"The Swan-Neck" by Charles Kingsley
Dawn in New York groans
on enormous fire escapes
searching between the angles
for spikenards of drafted anguish.
"Dawn" by Federico Garcia Lorca
Atom to its atom flies,
Every bevill'd angle fits,
Till at length fair Order sits
Enthroned on earth and skies.
"Chaos Crystallising" by Martin Farquhar Tupper

An angle bore dear Uncle Joe
To rest beyond the stars.
I miss him, oh! I miss him so, --
He had such good cigars.
"Uncle Joe" by Harry Graham
That all the jarring notes of life
Seem blending in a psalm,
And all the angles of its strife
Slow rounding into calm.
"My Psalm" by John Greenleaf Whittier

In news:

A scalloped-top fence is part feat of engineering and part study in the allure of graceful curves, while elsewhere, the geometry of lines and angles has its own appeal.
44.99 The M-Edge Incline 360, as its name implies, lets you easily rotate your iPad mini from landscape to portrait orientations, giving you multiple viewing angles in each.
We offer both straight and curved inclines available at 15, 30 or 45 degree angles.
PTAM27L series inclinometer is based on MEMS technology for single and dual axis tilt angle measurement.
Inclinometer Benton Graphics Trenton NJ USA Benton Graphics introduces Flipcheck, a pocket-sized inclinometer for press operators to check contact and set angles.
Senators to inquire about gov contractor angle in secret service scandal.
We've already covered, from a variety of angles, the potential options for the Sixers with their first-round pick at No 16 overall.
Loved his angle on the world.
2005 Chevy Silverado Left Side Angle.
2005 Chevy Silverado Left Front Angle.
Invisibility devices up till now have involved metamaterial devices that were " invisible " only from one angle or to microwaves but not visible light.
Since the inception of hydraulic ironworkers, the traditional machine came with at least three main tools: a punch for punching holes in plate or angle iron.
A new angle on a historic event, what it says about us and why we should have paid for it.
The displays offer 28 views to ensure smooth picture quality, while the 150-degree viewing angle gives guests the freedom to see the 3D content off axis.
FORT MYERS, Florida (AP)--What some see as the biofuel of the future starts out as short, thick stems with a few leaves sticking out at sharp angles.

In science:

Since even most dangerous small angle scattering fits this simple picture, it seems plausible that Eq.(6.4) can be generalized to arbitrary scattering angle using Eq.(3.11) as the probability scattering.
Paraxial propagation of a quantum charge in a random magnetic field
Due to the rotational symmetry of the scatterer, the functions, F0 and F1, only depend on the scattering angle, θ, which is the angle between bk and bk′ .
Transport mean free path for Magneto-Transverse Light Diffusion: an alternative approach
This method works well when the pitch angle diffusion is a main process of the scattering, while it seems to have met some difficulties when the simpler case of pure large angle scattering is considered.
Application of random walk theory to the first order Fermi acceleration in shock waves
The pitch angle cosine of particle µ′ after scattering is determined according to the probability density function Pµ′ (µ′ ; v ′ ) independently of the pitch angle before scattering.
Application of random walk theory to the first order Fermi acceleration in shock waves
The probability densities of pitch angle at return for ν = 0.5 (a) PUW (µ′ ; µ′ 0 ) and (b) PDW (µ′ ; µ′ 0 ) for several values of the initial pitch angle µ′ 0 .
Application of random walk theory to the first order Fermi acceleration in shock waves
Allan et al. at Haverah Park in England studied the dependence of signals on primary energy Ep, perpendicular distance R of closest approach of the shower core, zenith angle θ, and angle α between the shower axis and the magnetic field vector.
Extensive Air Shower Radio Detection: Recent Results and Outlook
We express the contributions to the scattering amplitude multiplying the scalar quantities QL(R)i,j, using the following notation: k is the 3-momentum of the χ in the C.M. frame and θ is the scattering angle in the C.M. frame, i.e. the angle between the incident electron and the final-state χ− .
Prototype Graphs for radiative Corrections to Polarized Chargino or Neutralino Production in Electron-Positron Annihilation
This is indeed the case for all scattering angles θs, which we find somewhat surprising, since one might have expected the geometrical optics approximation to break down for the largest scattering angles.
Design of one-dimensional Lambertian diffusers of light
Energies and solid angles for n “unrestricted” momenta are produced independently, with a flat distribution of the angles in cos θ, the polar angle, and φ, the azimuthal angle.
AMEGIC++ 1.0, A Matrix Element Generator In C++
The algorithm then is to generate k0 and cos θ (the angle between k and one of the two initial momenta) in the c.m. frame of the initial momenta according to dA, distribute the polar angle uniformly and boost the three– momentum system back to the frame where the initial momenta were given.
AMEGIC++ 1.0, A Matrix Element Generator In C++
Once we are given the incidence angle θ0, we construct the refraction angle θ1 much in the same way.
Constructing Fresnel reflection coefficients by ruler and compass
The construction allows one to show at a simple glance the variation of these coefficients with the angle of incidence and the peculiarities of the parallel polarization when crossing the Brewster angle.
Constructing Fresnel reflection coefficients by ruler and compass
The validation cuts were then applied to the data, and for each photon of each event the Cherenkov angle θc and the azimuthal angle φc were reconstructed individually using the algorithm described in .
Experimental study of a proximity focusing Cherenkov counter prototype for the AMS experiment
In the first algorithm, a cluster is identified as a set of Cherenkov angles in which the angular distance between any two hit angles is smaller than a fixed value δθ1 . A clustering weight wi proportional to the number of contiguous hits is associated to each θci angle.
Experimental study of a proximity focusing Cherenkov counter prototype for the AMS experiment
The individual azimuthal angles φc defined below in the detector frame, can be expressed to give new azimutal ψc angles in the tra jectory frame.
Experimental study of a proximity focusing Cherenkov counter prototype for the AMS experiment