triangle

Definitions

  • The triangle spider
    The triangle spider
  • WordNet 3.6
    • n triangle a percussion instrument consisting of a metal bar bent in the shape of an open triangle
    • n triangle any of various triangular drafting instruments used to draw straight lines at specified angles
    • n Triangle a small northern constellation near Perseus between Andromeda and Aries
    • n triangle a three-sided polygon
    • n triangle something approximating the shape of a triangle "the coastline of Chile and Argentina and Brazil forms two legs of a triangle"
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Webster's Revised Unabridged Dictionary
  • Interesting fact: There is an area located off the south-eastern Atlantic coast of the United States called the "Bermuda Triangle." It is known for a high rate of unexplained losses of ships, small boats, and aircraft, which has led some people to believe that this triangle has supernatural powers
    • Triangle A draughtsman's square in the form of a right-angled triangle.
    • Triangle (Geom) A figure bounded by three lines, and containing three angles.
    • Triangle (Mus) A kind of frame formed of three poles stuck in the ground and united at the top, to which soldiers were bound when undergoing corporal punishment, -- now disused.
    • Triangle (Astron) A small constellation near the South Pole, containing three bright stars.
    • Triangle (Astron) A small constellation situated between Aries and Andromeda.
    • Triangle (Mus) An instrument of percussion, usually made of a rod of steel, bent into the form of a triangle, open at one angle, and sounded by being struck with a small metallic rod.
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Century Dictionary and Cyclopedia
  • Interesting fact: The Times Square "time ball" is named the "Star of Hope". It was specially made for this year and contains 504 glass crystals cut into triangles, 600 light bulbs, 96 big lights, and 92 mirrors.
    • n triangle A triangular box-fish, as Sectophrys trigonus, of the family Ostraciidæ of the West Indies.
    • n triangle In angling, an arrangement of three fish-hooks bound together with the points outward, forming a triangle.
    • triangle Three-cornered; three-angled; triangular.
    • n triangle In geometry, a figure composed of three lines which meet two by two in three points, called the vertiees of the triangle; especially, a rectilinear figure of this description. The lines measured in the shortest way from vertex to vertex are called the sides of the triangle. The angles between the sides at the vertices measured so that each subtends a side are called the angles of the triangle.
    • n triangle Any three-cornered or three-sided figure, body, or arrangement; anything having a triangular form or bounding a three-sided space.
    • n triangle A musical instrument of percussion, made of a rod of polished steel bent into the form of a triangle, and open at one of its angles. It is sounded by being struck with a small steel rod. It is frequently used in modern orchestral music for brilliant and sparkling effects.
    • n triangle [capitalized] In astron, same as Triangulum.
    • n triangle Eccles., a symbol of the Trinity. The equilateral triangle, as symbolizing the Trinity, is of frequent occurrence, in various combinations, in Christian ornament.
    • n triangle A chest made in triangular form to hold a priest's cope.
    • n triangle A three-cornered straight-edge, with one right angle and the other angles more or less acute, used in conjunction with the T-square for drawing parallel, perpendicular, or diagonal lines.
    • n triangle A kind of gin for raising heavy weights, formed by three spars joined at top. See gin, 2 .
    • n triangle Milit., formerly, in the British army, a sort of frame formed of three halberds stuck in the ground and united at the top, to which soldiers were bound to be flogged: generally in the plural.
    • n triangle In ceramics, a form of the stilt consisting of three metal pins held together in the form of a triangle. See stilt, 5.
    • n triangle One of certain tortricid moths: an English collectors' name. Tortrix rufana is the red triangle.
    • n triangle In entomology, a large three-sided cell found in the wings of many dragon-flies. It lies near the middle of the basal half of the wing, and its form and relations to the other cells, both of the anterior and posterior wings, are of much value in classification. It is often called the discoidal triangle, to distinguish it from the internal triangle, which adjoins it on the inner side, and the anal triangle, which lies close to the anal border of the wing.
    • n triangle See conjugate triangles, under conjugate.
    • n triangle A triangle whose sides are rectilinear.
    • n triangle the circumscribed circle;
    • n triangle the inscribed and the three escribed circles;
    • n triangle the Feuerback or nine-point circle;
    • n triangle the Brocard or seven-point circle;
    • n triangle the Tucker or triplicate-ratio cirde;
    • n triangle the sine triple-angle circle (constructed as follows: on the sides of the triangle ABC take D and D' on BC, E and E' on AC, F and F' on AB such that the angle AEF =AF'E' =A, BFD =BD'F' =B, CDE =CE'D' =C; then the circle in question passes through D, D', E, E', F, F', and DD': EE': FF'=sin 3A: sin 3B: sin 3C)
    • n triangle the Taylor or six-point circle, which passes through the six feet of perpendiculars drawn to the sides from feet of perpendiculars on the sides from the vertices of the triangle
    • n triangle the Spieker circle, or circle inscribed in the triangle whose vertices are the mid-points of the sides of the primitive triangle. See circle.
    • n triangle the centroid, or intersection of median lines
    • n triangle the orthocenter, or intersection of perpendiculars from the angles upon the opposite sides
    • n triangle the circumcenter, or center of the circumscribed circle
    • n triangle the center of the Feuerbach circle;
    • n triangle the incenter, or center of the inscribed circle
    • n triangle the radical center of the escribed circles;
    • n triangle the symmedian, Grebe, or Lemoine point, the intersection of the three lines each bisecting a side and bisecting a perpendicular from an angle upon a side
    • n triangle the Spieker point, or mid-point between the circumcenter and incenter
    • n triangle the Brocard points, two points of the Brocard circle (which see, under circle) (through the symmedian point S of any triangle ABC lines are drawn parallel to the sides of the latter, meeting these sides in D and D' on BC, E and E' on AC, F and F' on AB, so that D, S. E' are collinear, as well as E, S, F' and F, S, D'; then the three lines through A parallel to FD, through B parallel to DE, and through C parallel to EF meet in one Brocard point P, while the lines through A parallel to D' E', through B parallel to E'F', and through C parallel to F' D' meet in the other Brocard point P')
    • n triangle (10) the center of the triplicate-ratio circle; besides others.
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Chambers's Twentieth Century Dictionary
  • Interesting fact: The oldest patented company logo is the red triangle of Bass beers
    • n Triangle trī′ang-gl (math.) a plane figure with three angles and three sides: a musical instrument of percussion, formed of a steel rod bent in triangle-form, open at one angle: a frame of three halberds stuck in the ground to which soldiers were formerly bound to be flogged (generally pl.)
    • ***

Quotations

  • Charles De Montesquieu
    Charles%20De%20Montesquieu
    “If triangles made a god, they would give him three sides.”
  • Cecil Myers
    Cecil Myers
    “Successful marriage is always a triangle: a man, a woman, and God.”
  • Henry David Thoreau
    Henry%20David%20Thoreau
    “The stars are the apexes of what triangles!”

Etymology

Webster's Revised Unabridged Dictionary
L. triangulum, fr. triangulus, triangular; tri-,see Tri-) + angulus, angle: cf. F. triangle,. See Angle a corner
Chambers's Twentieth Century Dictionary
Fr.,—L. triangulumtres, three, angulus, an angle.

Usage

In literature:

The tip of the triangle in the paper was not the bull's-eye.
"Sergeant York And His People" by Sam Cowan
When he had made the round, he took his place in the Triangle of Science, and the ball stopped at his feet.
"The Mummy and Miss Nitocris" by George Griffith
You can tell Bandy Wobster he can keep his triangles for his parrots swingin' on.
"My Man Sandy" by J. B. Salmond
The last mentioned waters the plains of Assam at the eastern angle of the triangle.
"From Pole to Pole" by Sven Anders Hedin
Discoidal triangle: Odonata - see triangle.
"Explanation of Terms Used in Entomology" by John. B. Smith
At that hour precisely Mr. Hicks came out and hammered on a triangle as vigorously as if it were necessary.
"The Dude Wrangler" by Caroline Lockhart
One large triangle in the vent of the bait was sufficient tackle.
"Lines in Pleasant Places" by William Senior
Double triangle; median triangle 721 330.
"Archeological Expedition to Arizona in 1895" by Jesse Walter Fewkes
We started off together on our triangles.
"High Adventure" by James Norman Hall
You will see three red lamps burning in a triangle.
"Jack O' Judgment" by Edgar Wallace
With a rope made fast around his waist, he had been to the standing-room to look out for the triangle of lights on the Fatime.
"Asiatic Breezes" by Oliver Optic
He stared at the circled-triangle marks on the backs of his hands, deeply disturbed.
"The Alembic Plot" by Ann Wilson
Moore is third in the order of the triangle.
"My Recollections of Lord Byron" by Teresa Guiccioli
Why, do you know, Bessie has become a Red Triangle worker now, as she and her mother had been transferred to that service.
"Air Service Boys Flying for Victory" by Charles Amory Beach
It may be cut in squares, rounds or triangles to suit the fancy.
"The Golden Age Cook Book" by Henrietta Latham Dwight
Forming the third corner of the triangle, was the little interpreter.
"Panther Eye" by Roy J. Snell
Triangles of fried toast in between look and taste well at breakfast.
"Dishes & Beverages of the Old South" by Martha McCulloch Williams
To simplify calculation, he divided the orbit into triangles, and tried if making the triangles equal would do.
"Pioneers of Science" by Oliver Lodge
The last three form a beautiful little triangle.
"Pleasures of the telescope" by Garrett Serviss
The position as a whole between Auberive and Souain described a vast triangle.
"The Story of the Great War, Volume IV (of 8)"
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In poetry:

Pull up! the East will soon be red,
The wild duck westward fly,
And make above my anxious head,
Triangles in the sky.
"To The Hills!" by Govinda Krishna Chettur
I am nothing but the empty net which has gone on ahead
of human eyes, dead in those darknesses,
of fingers accustomed to the triangle, longitudes
on the timid globe of an orange.
"Enigmas" by Pablo Neruda
I climbed a forest path and found
A dim cave in the dripping ground,
Where dwelt the spirit of cool sound,
Who wrought with crystal triangles,
And hollowed foam of rippled bells,
A music of mysterious spells.
"The Forest Way" by Madison Julius Cawein
Now, dyed with burning carbuncle, a Limbo-litten pane,
Within its wall of storm, the West opens to hill and plain,
On which the wild geese ink themselves, a far triangled train;
And then the shuttering clouds close down--and night is here again.
"Sunset In Autumn" by Madison Julius Cawein

In news:

What may be lesser known, however, is that the Triangle is increasingly becoming the place to study food as well.
This may sound a little crazy but there's a group in the Triangle dying to help someone fix up their home, for free.
Shannon and Erin Hammett of Starkville are happy to announce the birth of their daughter, Kendall Reese Hammett on June 29, 2010, at Baptist Memorial Hospital, Golden Triangle.
PHOTO COURTESY OF THE TRIANGLE.
Pop culture with a Triangle twist.
Woman sues Neiman's for fraud in love triangle.
Research Triangle Park, NC (5 March 2008).
In the Iron Triangle After you have spent some days searching for the secret of political legitimacy in Miami and West Palm Beach, you want to go further.
Central / Football Triangle football's incredibly awesome day: was it for real.
Thomas Montgomery Pleads Guilty to Killing His Rival in Internet Love Triangle.
On Wednesday afternoon, I was on an Orange Line train from Federal Triangle to Vienna.
MMA fighter submits opponent with rare inverted triangle choke.
The Triangle will discover this week the dirty little secret of the NHL All-Star Game: What actually happens on the ice is the least important part of the entire weekend.
This gorgeous goat may greet you at Triangle L Ranch.
The Triangle United Soccer Association will hold tryouts May 21-23 for boys and girls teams.
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In science:

Top inset: accuracy of the WF with all the density-density Jastrow independently minimized (same symbols as before) and with the analytic parametrization (L = 18, empty triangles, and L = 82, full triangles).
Variational description of Mott insulators
On the other hand, given X > 0 we have, by Lemma 2.3, a unique pro jective equivalence class of a triangle ABC inscribed into a triangle abc.
Moduli spaces of convex projective structures on surfaces
For every triangle of the triangulation one can construct a pair of triangles using the number in the center as a parameter and using Lemma 2.3.
Moduli spaces of convex projective structures on surfaces
These lines cut the triangle co(∆n ) into small (unitary) triangles as we depicted on the above Picture.
A simple proof of associativity and commutativity of LR-coefficients (or the hive ring)
Given a cubic graph Γ with an orientation O , we construct SO (Γ, O) by associating to each vertex an ideal triangle, and gluing neighboring triangles.
Poisson--Dirichlet distribution for random Belyi surfaces
For every nondegenerate triangle in any metric space, there is an associated tree with three endpoints (a tripod) whose edge lengths match the triangle.
Thin triangles and a multiplicative ergodic theorem for Teichm\"uller geometry
Since separate up-pointing triangles are independent this amounts to a problem on a single triangle.
Random Cluster Models on the Triangular Lattice
The idea is to proceed by induction on the number of triangles N which we regard as embedded in the larger space of M triangles, N − M of which are automatically empty.
Random Cluster Models on the Triangular Lattice
The example shows that even if the edges of the 3 triangles are compatible over the base vertices, there is no common vertex joining the 3 triangles.
Constructing the hyperdefinable group from the group configuration
Suppose that Maker can win the triangle game on some collection of triangles on v ≤ 14 vertices and with maximum density less then 9/5.
Positional games on random graphs
Thus, gauge fields will be allowed to have large deviations from the identity on large triangles, but will be tightly constrained on small triangles.
QCD, Symmetry Breaking and the Random Lattice
Now if for M1 the triangle lengths are equal to a, b, c and d, the triangle lengths for M2 are λa, λb, λc and λd.
Multiplicities of simple closed geodesics and hypersurfaces in Teichm\"uller space
At the ν -th step of algorithm A, we obtain the triangle ∆ from the triangle ∆∗ (∆).
Moments for generalized Farey-Brocot partitions
For triangle ∆ we consider the vertex α(∆) such that the common denominator q(α(∆)) is the smallest among all vertices of triangle ∆ (it may not be unique and in this case we fix one of the minimal vertices).
Moments for generalized Farey-Brocot partitions
Among the triangles from partition Tilm there are triangles with vertex a. (The number of these triangles is 2, 3, 5, or 8.) Some of these triangles ∆ may admit the property a = α(∆) and some may not.
Moments for generalized Farey-Brocot partitions
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