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triangles | A Wisdom Archive on triangles | | triangles A selection of articles related to triangles | |
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triangles
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| ARTICLES RELATED TO triangles | | | |  triangles: Encyclopedia II - Triangle - Basic factsElementary facts about triangles were presented by Euclid in books 1-4 of his Elements around 300 BCE.
A triangle is a polygon and a 2-simplex (see polytope).
Two triangles are said to be similar if and only if the angles of one are equal to the corresponding angles of the other. In this case, the lengths of their corresponding sides are proportional. This occurs for example when two triangles share an angle and the sides opposite to that angle are parallel.
Using right triangles and the concept of similarity, the trigonometric functions sine and cosine can be defined. These are functions of an angle ...
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 - Basic facts |
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| | | | | triangles: Encyclopedia II - Pascal's triangle - Geometric properties of Pascal's triangle 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 ...
See also: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 |
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| | | | | triangles: Encyclopedia II - Bermuda Triangle - History of the Bermuda 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 ...
See also: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 |
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| | | | | | | | | | triangles: Encyclopedia II - Sierpinski triangle - Properties The Sierpinski triangle has Hausdorff dimension log(3)/log(2) ≈ 1.585, which follows from the fact that it is a union of three copies of itself, each scaled by a factor of 1/2.
If one takes Pascal's triangle with 2n rows and colors the even numbers white, and the odd numbers black, the result is an approximation to the Sierpinski triangle.
The area of a Sierpinski triangle is zero (in Lebesgue measure). This can been seen from the infinite iteration, where we remo ...
See also:Sierpinski triangle, Sierpinski triangle - Construction, Sierpinski triangle - Properties, Sierpinski triangle - Analogs in higher dimension, Sierpinski triangle - Self-assembly with DNA, Sierpinski triangle - Computer Program Read more here: » Sierpinski triangle: Encyclopedia II - Sierpinski triangle - Properties |
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| | | | | | | triangles: Encyclopedia II - Historic Triangle - Jamestown The first permanent English settlement in the New World which was established at Jamestown in 1607. Today, you can visit the Jamestown Festival Park and Jamestown Island attractions. Included are recreations of a native American village and colonial fort, and archaeological sites where current work is underway.
The are two major areas at Jamestown. The former Jamestown Festival Park, a living history museum which includes the replica ships and is operated by the Commonwealth of Virginia, and is now known as Jamestown Settlement. The National Park Service site which includes Jamestown Island and the ongoing archaeolo ...
See also:Historic Triangle, Historic Triangle - Colonial Parkway, Historic Triangle - Jamestown Ferry, Historic Triangle - Jamestown, Historic Triangle - Williamsburg, Historic Triangle - Yorktown, Historic Triangle - Commercial enterprises Read more here: » Historic Triangle: Encyclopedia II - Historic Triangle - Jamestown |
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| | | | | triangles: Encyclopedia II - Historic Triangle - Williamsburg In 1699, the capital of Virginia was moved from Jamestown to a location on high ground at Middle Plantation at the suggestion of students from the College of William and Mary, which had been established there in 1693. Middle Plantation was soon renamed Williamsburg, in honor of King William III and was a busy place until the American Revolution.
After the capital was moved to a more secure location at Richmond in 1780, Williamsburg became a largely forgotten and sleepy little town for almost 150 years. All that changed in the early 20 ...
See also:Historic Triangle, Historic Triangle - Colonial Parkway, Historic Triangle - Jamestown Ferry, Historic Triangle - Jamestown, Historic Triangle - Williamsburg, Historic Triangle - Yorktown, Historic Triangle - Commercial enterprises Read more here: » Historic Triangle: Encyclopedia II - Historic Triangle - Williamsburg |
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| | | | | triangles: Encyclopedia II - Black triangles - Reported sightings By mid-2004, there were almost 400 separate reports of flying triangles, wedges, or boomerangs clearly visible over densely populated areas and highways, mostly near the East and West Coast of the United States. This geographic distribution also matches the locations of U.S. Air Force bases, leading to suggestions that the craft either belong to the U.S. Air Force or are investigating Air Force installations.
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See also:Black triangles, 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 II - Black triangles - Reported sightings |
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| | | | | triangles: Encyclopedia II - Bermuda Triangle - Scientific explanations
Bermuda Triangle - Skeptical responses.
Critics have charged that Berlitz and others have exaggerated the "mysterious" aspects of some cases (Berlitz himself did not advocate any paranormal explanation), and argue that the Bermuda Triangle sees no more "disappearances" than any comparable area of the oceans. Of note, Lloyd's of London has determined the "triangle" to be no more dangerous than any other piece of the ocean, and does not charge unusual rates of insurance for ...
See also: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 - Scientific explanations |
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| | | | | triangles: Encyclopedia II - Bermuda Triangle - Famous incidents
Bermuda Triangle - Flight 19.
Main article: Flight 19
One of the best known Bermuda Triangle incidents concerns the loss of Flight 19, a squadron of five U.S. Navy TBM Avenger torpedo bombers on a training flight out of Fort Lauderdale, Florida, on December 5, 1945. According to Berlitz, the flight consisted of expert Marine Corps aviators who, after reporting a number of odd visual effects, simply disappeared, an account which isn't entirely true. Furthermore, Berlitz claims that becau ...
See also: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 - Famous incidents |
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| | | | | triangles: Encyclopedia II - Bermuda Triangle - Cultural references Barry Manilow sang a UK no. 15 hit in 1981 entitled Bermuda Triangle. It tells the story of a fictional holiday to the area where the singer's girlfriend elopes with a local, but he finds a more than adequate replacement, leading to the uplifting final refrain:
DC Comics’ Paradise Island city-state, controlled by Amazons and the home of Wonder Woman, is located there.
The Marvel Comics series Skul the Slayer was set in a world inhabited by people who had been swallowed by the Triangle, which was actually a trap created by aliens.
Milton Bradley released a boa ...
See also: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 - Cultural references |
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| | | | | triangles: Encyclopedia II - Black triangles - Other theories The remaining possibilities are
that they are previously unknown American aircraft, manned or unmanned, which are being deployed in a 'high-visibility' fashion, but without public notice for some reason;
that they belong to some nation or organization other than the United States, which wishes to display itself in this fashion;
that they are some sort of common error of identification of some 'conventional' aircraft or other phenomenon; however, this could not explain why their observation started only in the 1990s;
o ...
See also:Black triangles, 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 II - Black triangles - Other theories |
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| | | | | triangles: Encyclopedia II - The Triangle North Carolina - Cities The Triangle region, as defined for statistical purposes as the Raleigh-Durham-Cary-Dunn CSA is generally considered to comprise 7 counties of although the U.S. Census Bureau divided the region into 2 metropolitan statistical areas and 1 micropolitan area in 2003.
The Triangle North Carolina - Primary cities.
Raleigh
Durham
Cary
Chapel Hill, is not considered a primary city as far as the metropolitan statistical purposes anymore, but is 1 of th ...
See also:The Triangle North Carolina, The Triangle North Carolina - Counties, The Triangle North Carolina - Cities, The Triangle North Carolina - Primary cities, The Triangle North Carolina - Suburbs with more than 10000 inhabitants, The Triangle North Carolina - Suburbs with fewer than 10000 inhabitants, The Triangle North Carolina - Education, The Triangle North Carolina - Institutes of higher education, The Triangle North Carolina - Commerce, The Triangle North Carolina - Area major employers, The Triangle North Carolina - Area hospitals and medical centers, The Triangle North Carolina - Transportation, The Triangle North Carolina - Shopping Read more here: » The Triangle North Carolina: Encyclopedia II - The Triangle North Carolina - Cities |
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| | | | | triangles: Encyclopedia II - The Triangle North Carolina - Cities The Triangle region, as defined for statistical purposes as the Raleigh-Durham-Cary-Dunn CSA is generally considered to comprise 7 counties of although the U.S. Census Bureau divided the region into 2 metropolitan statistical areas and 1 micropolitan area in 2003.
The Triangle North Carolina - Primary cities.
Raleigh
Durham
Cary
Chapel Hill, is not considered a primary city as far as the metropolitan statistical purposes anymore, ...
See also:The Triangle North Carolina, The Triangle North Carolina - Counties, The Triangle North Carolina - Cities, The Triangle North Carolina - Primary cities, The Triangle North Carolina - Suburbs with more than 10000 inhabitants, The Triangle North Carolina - Suburbs with fewer than 10000 inhabitants, The Triangle North Carolina - Education, The Triangle North Carolina - Institutes of higher education, The Triangle North Carolina - Commerce, The Triangle North Carolina - Area major employers, The Triangle North Carolina - Area hospitals and medical centers, The Triangle North Carolina - Transportation, The Triangle North Carolina - Shopping Read more here: » The Triangle North Carolina: Encyclopedia II - The Triangle North Carolina - Cities |
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| | | | | triangles: Encyclopedia II - The Triangle North Carolina - Education The secondary education setup in the Triangle is similar that of the majority of the state of North Carolina, in which there are countywide system systems (the exception is Chapel Hill-Carrboro Schools). The largest in the region is the Wake County Public School System, which includes the cities of Raleigh and Cary. The other larger systems in the region rank as such: Durham County, Orange County, and rapidly growing Johnston County.
The Triangle North Carolina - Institutes of higher education.
Duke ...
See also:The Triangle North Carolina, The Triangle North Carolina - Counties, The Triangle North Carolina - Cities, The Triangle North Carolina - Primary cities, The Triangle North Carolina - Suburbs with more than 10000 inhabitants, The Triangle North Carolina - Suburbs with fewer than 10000 inhabitants, The Triangle North Carolina - Education, The Triangle North Carolina - Institutes of higher education, The Triangle North Carolina - Commerce, The Triangle North Carolina - Area major employers, The Triangle North Carolina - Area hospitals and medical centers, The Triangle North Carolina - Transportation, The Triangle North Carolina - Shopping Read more here: » The Triangle North Carolina: Encyclopedia II - The Triangle North Carolina - Education |
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