A triangle is one of the basic shapes of geometry: a two-dimensional figure with three vertices and three sides which are straight line segments. Triangle - Types of triangles. Triangles can be classified according to the relative lengths of their sides: In an equilateral triangle all sides are of equal length. An equilateral triangle is also equiangular, i.e. all its internal angles are equal—namely, 60°; it is a regular polygon In an isosceles triangle two sid ...

Including:

• Triangle - Types of triangles
• Triangle - Basic facts
• Triangle - Points lines and circles associated with a triangle
• Triangle - Computing the area of a triangle
• Triangle - Using geometry
• Triangle - Using vectors
• Triangle - Using trigonometry
• Triangle - Using coordinates
• Triangle - Using Heron's formula
• Triangle - Using the side lengths and a numerically stable formula
• Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia - Triangle

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Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia II - Triangle - Computing the area of a triangle

Triangles can be classified according to the relative lengths of their sides: In an equilateral triangle all sides are of equal length. An equilateral triangle is also equiangular, i.e. all its internal angles are equal—namely, 60°; it is a regular polygon In an isosceles triangle two sides are of equal length. An isosceles triangle also has two equal internal angles (namely, the angles where each of the equal sides meets the third side). In a scalene triangle all sides have different lengths. The internal angles ...

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Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia II - Triangle - Types of triangles

There are hundreds of different constructions that find a special point inside a triangle, satisfying some unique property: see the references section for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangl ...

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Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points, lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia II - Triangle - Points, lines and circles associated with a triangle

There are hundreds of different constructions that find a special point inside a triangle, satisfying some unique property: see the references section for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangl ...

See also:

Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia II - Triangle - Points lines and circles associated with a triangle

There are hundreds of different constructions that find a special point inside a triangle, satisfying some unique property: see the references section for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangl ...

See also:

Triangle, Triangle - Types of triangles, Triangle - Basic facts, Triangle - Points lines and circles associated with a triangle, Triangle - Computing the area of a triangle, Triangle - Using geometry, Triangle - Using vectors, Triangle - Using trigonometry, Triangle - Using coordinates, Triangle - Using Heron's formula, Triangle - Using the side lengths and a numerically stable formula, Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia II - Triangle - Points lines and circles associated with a triangle

In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) the opposite side or an extension of the opposite side. The intersection between the (extended) side and the altitude is called the foot of the altitude. This opposite side is called the base of the altitude. The length of the altitude is the distance between the base and the vertex. In an isosceles triangle (a triangle with two congruent sides), the altitude having the incongruent side as ...

Read more here: » Altitude triangle: Encyclopedia - Altitude triangle

The Bermuda Triangle (sometimes known as Devil's Triangle) is a 1.5-million-square-mile (4,000,000 km²) area of ocean roughly defined by Bermuda, Puerto Rico, and the southern tip of Florida. Some believe it is a paranormal site in which the laws of physics are violated or altered. It is said that within this area a number of ships and airplanes have disappeared under highly unusual circumstances. The United States Coast Guard and others disagree with the assessment of paranormal activity, arguing that the number of incidents involving lost ships and airplanes is no larger than ...

Including:

• Bermuda Triangle - History of the Bermuda Triangle
• Bermuda Triangle - First citations
• Bermuda Triangle - Popularized by Berlitz
• Bermuda Triangle - Scientific explanations
• Bermuda Triangle - Skeptical responses
• Bermuda Triangle - Kusche's research
• Bermuda Triangle - Methane hydrates
• Bermuda Triangle - Freak waves
• Bermuda Triangle - Famous incidents
• Bermuda Triangle - Flight 19
• Bermuda Triangle - Depictions on Television
• Bermuda Triangle - Cultural references

Read more here: » Bermuda Triangle: Encyclopedia - Bermuda Triangle

Black triangles are a kind of Unidentified Flying Object (UFO) that have been observed in the skies since the 1970s (and possibly earlier), to the present day. They have appeared more commonly over cities of the United States, and England, but have been spotted world wide including a mass sighting over St. Petersburg, Russia on February 19, 1997. Since then, hundreds of observers have reported enormous, totally silent, black triangular craft hovering or slowly cruising at low altitudes over cities and highways, usually at night ...

Including:

• Black triangles - Reported sightings
• Black triangles - Typical sightings
• Black triangles - Illinois police sighting incident
• Black triangles - Rendlesham Forest incident
• Black triangles - Phoenix lights incident
• Black triangles - The Belgian Air Force report
• Black triangles - The TR-3A and TR-3B
• Black triangles - Other theories
• Black triangles - Black triangles in fiction

Read more here: » Black triangles: Encyclopedia - Black triangles

Due to the special nature of the blood supply to the human nose and surrounding area, it is possible for retrograde infections from the nasal area to spread to the brain. For this reason, the area from the corners of the mouth to the bridge of the nose, including the nose and maxilla, is known to doctors as the danger triangle of the face. Other related archivesblood, brain, human, maxilla, nose, retrograde infections

Read more here: » Danger triangle of the face: Encyclopedia - Danger triangle of the face

In geometry, the circumcircle of a given two-dimensional geometric shape is a circle which contains the shape completely within it. For a triangle, it is the unique circle containing all three vertices. The center of this circumcircle is known as the shape's circumcenter. Note that although the circumcircle of an acute triangle is indeed the smallest circle containing this triangle, this is not true of obtuse triangles. Circumcircle - Cyclic polygons. At least three ver ...

Including:

• Circumcircle - Cyclic polygons
• Circumcircle - Circumcircles of triangles
• Circumcircle - Circumcircle equation
• Circumcircle - Circumcircle of circles

Read more here: » Circumcircle: Encyclopedia - Circumcircle

Charles Frambach Berlitz (November 20, 1914, New York City - December 18, 2003) was an author known for his books about anomalous phenomena. Many of the "facts" cited in his books are considered highly questionable by people who looked up the incidents in question. For example, Larry Kusche found that some ships claimed by Berlitz to have sunk in the Bermuda Triangle sank somewhere else, others did not even exist, and for still others, the weather was not as sunny as Berlitz said. He was the grandson of Maximilien Berlitz (Maximilian), and ...

Including:

• Charles Berlitz - Books

Read more here: » Charles Berlitz: Encyclopedia - Charles Berlitz

In geometry, two shapes are called congruent if one can be transformed into the other by an isometry, i.e. a combination of translations, rotations and reflections. Note: This article is about congruences in geometry. For notions of congruence in algebra, see congruence relation. Congruence geometry - Definition of congruence in analytic geometry. In a Euclidean system, congruence is fundamental; it's the counterpart of an equals sign in numerical analysis. In analytic geometry, congru ...

Including:

• Congruence geometry - Definition of congruence in analytic geometry
• Congruence geometry - Congruence of triangles

Read more here: » Congruence geometry: Encyclopedia - Congruence geometry

Pascal's triangle has many uses in binomial expansions. For example (x + 1)2 = 1x2 + 2x + 12. Notice the coefficients are the third row of Pascal's triangle: 1, 2, 1. In general, when a binomial is raised to a positive integer power we have: (x + y)n = a0xn + a1xn−1y + a2xn−2y< ...

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Pascal's triangle, Pascal's triangle - The triangle, Pascal's triangle - Uses of Pascal's triangle, Pascal's triangle - Properties of Pascal's triangle, Pascal's triangle - Geometric properties of Pascal's triangle, Pascal's triangle - Pascal's triangle and the matrix exponential, Pascal's triangle - History

Read more here: » Pascal's triangle: Encyclopedia II - Pascal's triangle - Uses of Pascal's triangle

Some simple patterns are immediately apparent in Pascal's triangle: The diagonals going along the left and right edges contain only 1s. The diagonals next to the edge diagonals contain the natural numbers in order. Moving inwards, the next pair of diagonals contain the triangle numbers in order. The next pair of diagonals contain the tetrahedral numbers in order, and the next pair give pentatope numbers. In general, each next pair of diagonals contains the next higher dimensional "d-triangle" numbers, whic ...

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Pascal's triangle, Pascal's triangle - The triangle, Pascal's triangle - Uses of Pascal's triangle, Pascal's triangle - Properties of Pascal's triangle, Pascal's triangle - Geometric properties of Pascal's triangle, Pascal's triangle - Pascal's triangle and the matrix exponential, Pascal's triangle - History

Read more here: » Pascal's triangle: Encyclopedia II - Pascal's triangle - Properties of Pascal's triangle

The Triangles - Latest Activity. On August 20, 2005 The Triangles released their newest creation, Magic Johnson, which is named after the famous basketball player Magic Johnson. It is being distributed by Half A Cow, an independent record label from Australia. This album contains the single Let's Replace the Cityscapes which has been receiving airplay on Triple J and 3RRR. ...

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The Triangles, The Triangles - History, The Triangles - Latest Activity, The Triangles - Band Members, The Triangles - Discography

Read more here: » The Triangles: Encyclopedia II - The Triangles - History

Pascal's triangle can be used as a lookup table for the number of arbitrarily dimensioned elements within a single arbitrarily dimensioned version of a triangle (known as a simplex). For example, consider the 3rd line of the triangle, with values 1, 3, 3, 1. A 2-dimensional triangle has one 2-dimensional element (itself), 3 1-dimensional elements (lines, or edges), and 3 0-dimensional elements (vertices, or corners). The meaning of the final number (1) is more difficult to explain (but see below). Continuing with our example, a tetrah ...

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Pascal's triangle, Pascal's triangle - The triangle, Pascal's triangle - Uses of Pascal's triangle, Pascal's triangle - Properties of Pascal's triangle, Pascal's triangle - Geometric properties of Pascal's triangle, Pascal's triangle - Pascal's triangle and the matrix exponential, Pascal's triangle - History

Read more here: » Pascal's triangle: Encyclopedia II - Pascal's triangle - Geometric properties of Pascal's triangle

Bermuda Triangle - First citations. The first mention of any disappearances in the area was made in 1950 by E.V.W. Jones as a sidebar on the Associated Press wire service regarding recent ship losses in the area. Jones' article notes the "mysterious disappearances" of ships, airplanes and small boats in the region and ascribes it the name "The Devil's Sea". It was mentioned again in 1952 in a Fate magazine article by George X. Sand, who outlined several "strange marine disappearances". The term "Bermuda Triangle ...

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Bermuda Triangle, Bermuda Triangle - History of the Bermuda Triangle, Bermuda Triangle - First citations, Bermuda Triangle - Popularized by Berlitz, Bermuda Triangle - Scientific explanations, Bermuda Triangle - Skeptical responses, Bermuda Triangle - Kusche's research, Bermuda Triangle - Methane hydrates, Bermuda Triangle - Freak waves, Bermuda Triangle - Famous incidents, Bermuda Triangle - Flight 19, Bermuda Triangle - Depictions on Television, Bermuda Triangle - Cultural references

Read more here: » Bermuda Triangle: Encyclopedia II - Bermuda Triangle - History of the Bermuda Triangle

If the legs aren't locked in, there are many options how to escape the choke. Depending on the position, it is possible to simply stand up, or to roll out. The arm inbetween the legs can be pulled out, and if the opponent was holding guard, the guard can be passed into side mount. Escaping the triangle choke once the legs are properly locked in the triangle formation is difficult. The opponent can start applying the choke, and it is no longer possible to stand up or roll out. A commonly used tactic in this situation is to stand up wit ...

See also:

Triangle choke, Triangle choke - Escaping the triangle choke

Read more here: » Triangle choke: Encyclopedia II - Triangle choke - Escaping the triangle choke

The channel, which had been launched only a few years before, hoped to garner a reputation as a relatively avant-garde alternative to the existing terrestrial stations. It compiled a list of provocative films, generally art-house and mostly in foreign languages, and entered into negotiation with independent TV regulator the IBA with an eye to showing them. The films, all of which had been theatrically exhibited under British Board of Film Classification "18" ratings, had never been shown on British television until that point. Their content ...

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Red triangle, Red triangle - The red triangle broadcasts, Red triangle - The films, Red triangle - Legacy

Read more here: » Red triangle: Encyclopedia II - Red triangle - The red triangle broadcasts