An American in Paris is scored for 3 flutes ( 3rd doubling on piccolo ), 2 oboes, English horn, 2 clarinets in B flat, bass clarinet in B flat, 2 bassoons, 4 horns in F, 3 trumpets in B flat, 3 trombones, tuba, timpani, snare drum, bass drum, triangle, wood block, cymbals, low and high tom-toms, xylophone, glockenspiel, celesta, 4 taxi horns resembling the pitches A, B, C and D, alto saxophone / soprano saxophone, tenor saxophone / soprano saxophone / alto saxophone, baritone saxophone / soprano saxophone / alto saxophone, and strings.

If one also removes the second postulate (" a line can be extended indefinitely ") then elliptic geometry arises, where there is no parallel through a point outside a line, and in which the interior angles of a triangle add up to more than 180 degrees.

There, a small peninsular area is still called " Angeln " today and is formed as a triangle drawn roughly from modern Flensburg on the Flensburger Fjord to the City of Schleswig and then to Maasholm, on the Schlei inlet.

The northern triangle of Times Square is technically Duffy Square, dedicated in 1937 to Chaplain Francis P. Duffy of New York City's " Fighting 69th " Infantry Regiment ; a memorial to Duffy is located there, along with a statue of George M. Cohan.

* In a diode, it is the positive terminal at the tail of the arrow symbol ( base of the triangle ), where current flows into the device.

In reality, this " triangle arbitrage " is so simple that it almost never occurs.

At the intersection with 72nd street, the triangle of tiny Verdi Square is surrounded by several notable apartment buildings, including The Ansonia, and the Florentine palazzo occupied by Apple Bank for Savings.

Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case.

The binomial coefficients appear as the entries of Pascal's triangle where each entry is the sum of the two above it.

: This is the third line in the Pascal: s triangle.

The goat's head is formed by the triangle of stars ι Cap, θ Cap, and ζ Cap.

* Other: Correspondences include blood, the guitar, thunder, drum beat rubies and in writing fire is sometimes represented by a red upwards triangle.

The alchemical symbol for air is an upward-pointing triangle, bisected by a horizontal line.

It is sometimes represented by its Tattva or by a downward pointing triangle with a horizontal line through it.

It is based on the semaphore symbols for " N " ( two flags held 45 degrees down on both sides, forming the triangle at the bottom ) and " D " ( two flags, one above the head and one at the feet, forming the vertical line ) ( for Nuclear Disarmament ) within a circle.

A river delta ( originally, the Nile River delta ) is so named because its shape approximates the upper-case letter delta ( the shape is a triangle ).

In mathematics and computational geometry, a Delaunay triangulation for a set P of points in a plane is a triangulation DT ( P ) such that no point in P is inside the circumcircle of any triangle in DT ( P ).

As mentioned above, if a triangle is non-Delaunay, we can flip one of its edges.

This leads to a straightforward algorithm: construct any triangulation of the points, and then flip edges until no triangle is non-Delaunay.

When a vertex v is added, we split in three the triangle that contains v, then we apply the flip algorithm.

A string tied at each end to the two pins and the tip of a pen is used to pull the loop taut so as to form a triangle.

Other figures, such as lines, triangles, or circles, are named by listing a sufficient number of points to pick them out unambiguously from the relevant figure, e. g., triangle ABC would typically be a triangle with vertices at points A, B, and C.

The three sides of the triangle are named as follows:

The book introduces the concept of spherical triangle ( figures formed of three great circle arcs, which he named " trilaterals ") and proves Menelaus ' theorem on collinearity of points on the edges of a triangle ( which may have been previously known ) and its analog for spherical triangles.

In Italy, it is referred to as Tartaglia's triangle, named for the Italian algebraist Niccolò Fontana Tartaglia ( 1500 – 77 ).

The triangle was later named after Pascal by Pierre Raymond de Montmort ( 1708 ) who called it " Table de M. Pascal pour les combinaisons " ( French: Table of Mr. Pascal for combinations ) and Abraham de Moivre ( 1730 ) who called it " Triangulum Arithmeticum PASCALIANUM " ( Latin: Pascal's Arithmetic Triangle ), which became the modern Western name.

A triangle wave is a non-sinusoidal waveform named for its triangular shape.

Gautier instead turned the plot into a simple love triangle between a man, d ' Albert, and his mistress, Rosette, who both fall in love with Madelaine de Maupin, who is disguised as a man named Théodore.

It is so named because it passes through nine significant concyclic points defined from the triangle.

In geometry, Heron's ( or Hero's ) formula, named after Heron of Alexandria, states that the area T of a triangle whose sides have lengths a, b, and c is

In geometry, the Euler line, named after Leonhard Euler, is a line determined from any triangle that is not equilateral ; it passes through several important points determined from the triangle.

* Book 1 contains Euclid's 10 axioms ( 5 named postulates — including the parallel postulate — and 5 named axioms ) and the basic propositions of geometry: the pons asinorum ( proposition 5 ), the Pythagorean theorem ( Proposition 47 ), equality of angles and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are " equal " ( have the same area ).

The theorem is named after Thales because he was said by ancient sources to have been the first to prove the theorem, using his own results that the base angles of an isosceles triangle are equal, and that the sum of angles in a triangle is equal to two right angles.

There was a love triangle among Lady, Tramp, and a Russian wolfhound named Boris ( who appears in the dog pound in the final version ).

The tomb of the unknown soldierEston SquareEston Square, the curiously named shopping area on the main road passing through Eston, forms more of a triangle than a square.

Caesar named Aquitania the triangle shaped territory between the Ocean, the Pyrenees and the Garonne river.

* Golden Triangle, Ottawa, named for the property triangle in Ottawa between Elgin Street and the Rideau Canal

The term " Einthoven's triangle " is named for him.

Based on a reading of Charmian's diary, Stasz identifies the third vertex of the triangle, Evan Graham, with two real-life men named Laurie Smith and Allan Dunn.

It is about the adventures of two polygons, an equilateral triangle named ' Triangle ', and a rhombus named ' Robert '.

As reported by editor Ruth Berman ( issue # 1, Inside Star Trek, July 1968, pp. 15 – 16 ), " ardent rock hound and amateur lapidary " Roddenberry came up with the Vulcan philosophy after he presented Leonard Nimoy with a unique " hand-crafted piece of jewelry ," a " pendent " ( sic ) of polished yellow gold ( circle ) and florentined white gold ( triangle ), with a stone of brilliant white fabulite — an artificial gem " developed by the laser industry and used in space mechanisms for its optical qualities ," and thus well-suited as a gift for an actor in a science fiction show.

It involved a typical triangle and ends happily ever after.

In 1995, after a decade of campaigning, a pink triangle plaque was installed at the Dachau Memorial Museum to commemorate the suffering of gay men and lesbians.

" The triangle became a symbol for the gay community after the Holocaust.

The park protects a wide range of biomes, including semi-arid woodland, subalpine heath, and eucalypt forests, and provides a habitat for a range of animals, including bats, birds, wallabies, quolls, and the unique red triangle slug ( Triboniophorus graeffei ), which is known to appear after rainfall.

While located outside of the village triangle, the general store was built by John F. Himes to serve one of the first new residential areas developed after the paper mill's plant expansion of 1878.

The shape was essentially an inverted triangle, with a wide-brimmed hat on top, a full upper body with puffed sleeves, no bustle, and a skirt that narrowed at the ankles ( the hobble skirt was a fad shortly after the end of the Victorian era ).

The pedal line of a triangle is sometimes called the " Simson line " after him.

In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle: after one node is colored blue and another green, the third vertex of the triangle is connected to vertices of both colors, preventing it from being assigned either color.

A Burrow ’ s triangle is excised from the skin between the medial border of the flap and the nasal dorsum ; the triangle can be cut either before or after the elevation of the nasolabial.

It ascends after emerging from the suboccipital triangle obliquely between the inferior oblique and semispinalis capitis muscle.

El Hierro is a 278. 5 km < sup > 2 </ sup > island, formed approx 1. 2 million year ago after three successive eruptions, the island emerged from the ocean as a triangle of basaltic dykes topped with a volcanic cone more than 2, 000 metres high.

In the end, Rice wasn't able to win the hearts of Los Angeles fans after being traded for fan-favorite, Eddie Jones with many citing suspect defense and Rice's inability to perform in the triangle offense.

In this variation of graph minor theory, a graph is always simplified after any edge contraction to eliminate its self-loops and multiple edges .< ref > is inconsistent about whether to allow self-loops and multiple adjacencies: he writes on p. 76 that " parallel edges and loops are allowed " but on p. 77 he states that " a graph is a forest if and only if it does not contain the triangle K < sub > 3 </ sub > as a minor ", true only for simple graphs .</ ref >

It was originally a triangle of land bounded by roads but after road improvements is now a small roundabout.

* All of the object balls are racked in a triangle with the apex ball on the, and the game opened with a hard break ( as in eight-ball ); the 1 ball is played from where it lies after the break ( unless pocketed on the break, in which case it is spotted back on the foot spot just as if it had been legally pocketed.

The FRELIMO flag, used for a brief period after the country gained its independence from Portugal, looks like the current flag but lacking the emblem, with green, black, and yellow horizontal stripes separated by white fimbriations and a red triangle in the hoist.