A modern proof, which uses algebra and trigonometry and is quite unlike the one provided by Heron, follows. Let a, b, c be the sides of the triangle and A, B, C the angles opposite those sides. We have by the law of cosines. From this we get with some algebra . The altitude of the triangle on base a has length bsin(C), and it follows Here the sim ...

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Heron's formula, Heron's formula - Numerical stability, Heron's formula - History, Heron's formula - Proof, Heron's formula - Generalizations

Read more here: » Heron's formula: Encyclopedia II - Heron's formula - Proof

The case n = 1 of the above has been known for a long time. Proclus, in his commentary to the 47th Proposition of the first book of Euclid's Elements, describes it as follows: Certain methods for the discovery of triangles of this kind are handed down, one which they refer to Plato, and another to Pythagoras. (The latter) starts from odd numbers. For it makes the odd number the smaller of the sides about the right angle; then it takes the square of it, subtracts unity and makes half the difference the greater of the sides ab ...

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Pythagorean triple, Pythagorean triple - Generating Pythagorean triples, Pythagorean triple - A special case: the Platonic sequence

Read more here: » Pythagorean triple: Encyclopedia II - Pythagorean triple - A special case: the Platonic sequence

Heron's formula as given above is numerically unstable for triangles with a very small angle. A stable alternative involves arranging the lengths of the sides so that: a ≥ b ≥ c and computing The brackets in the above formula are required in order to prevent numerical instability in the evaluation. ...

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Heron's formula, Heron's formula - Numerical stability, Heron's formula - History, Heron's formula - Proof, Heron's formula - Generalizations

Read more here: » Heron's formula: Encyclopedia II - Heron's formula - Numerical stability

Hubbard refers to a sharp reduction of any of the points of this triangle as an "ARC break": Upsets with people or things come about because of the lessening or sundering of affinity, reality or communication [...] because if one discovers which of the three points of understanding have been cut, one can bring about a rapid recovery in the person's state of mind. (Scientology 0-8) In Scientology, upset and anger are referred to as an ARC break. People who are upset are referred to ...

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ARC Scientology, ARC Scientology - The concept of ARC, ARC Scientology - The ARC Triangle, ARC Scientology - The ARC Break, ARC Scientology - Use in conversation by Scientologists

Read more here: » ARC Scientology: Encyclopedia II - ARC Scientology - The ARC Break

The instructor leading the flight was US Navy Lieutenant Charles C. Taylor, an experienced Pacific Theatre pilot but who had not long been at Fort Lauderdale and was unfamiliar with the area. The trainee pilots had little experience in Avengers, but had trained at Fort Lauderdale and knew the area well. Flight 19 was undertaking a routine over-water navigation/bombing exercise, similar to one completed a few hours earlier by another flight. (The enlisted men in the aircraft were taking part in advanced combat aircrew training). Called ...

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Flight 19, Flight 19 - Mission crew and disappearance, Flight 19 - Search, Flight 19 - Bermuda Triangle connection

Read more here: » Flight 19: Encyclopedia II - Flight 19 - Mission crew and disappearance

Earlier, as it became obvious the flight was indeed lost, numerous air bases, aircraft and merchant ships were alerted. Several aircraft were dispatched to search for the Avengers and guide them back if they could locate them. One of the aircraft was the PBM-5 Martin Mariner (Buno 59-225) which took off at 19:37 with a crew of 13 from Banana Beach Naval Air Station at Cocoa Beach , (now called Patrick Air Force Base). The aircraft radioed a routine message to its base a few minutes later, but was never heard from again because i ...

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Flight 19, Flight 19 - Mission crew and disappearance, Flight 19 - Search, Flight 19 - Bermuda Triangle connection

Read more here: » Flight 19: Encyclopedia II - Flight 19 - Search

TRIANGLE: In Ceremonial Magick, a three sided figure used to contain a spirit, intelligence, demon, or whatever has been evoked; it is part of the method of protection for the person or persons who have evoked the entity.

(See also: TRIANGLE, Witchcraft, Wicca, Paganism, Pagan Dictionary)

Double Triangle. See SIX-POINTED STAR

(See also: Double Triangle, Mysticism, Mysticism Dictionary, Occultism, Occultism Dictionary)

Interlaced Triangles. See SEAL OF THE THEOSOPHICAL SOCIETY; SIX-POINTED STAR

(See also: Interlaced Triangles, Mysticism, Mysticism Dictionary, Occultism, Occultism Dictionary)

Bermuda Triangle

Geographically, the Triangle, situated SW of the US, is formed by connecting with Bermuda, Puerto Rico, and a point west of Florida. Many people involved in esoteric and UFO studies believe the Triangle is a supernaturally dangerous area, with many ships and airplanes disappearing in the Triangle in the 20th century.

(See also: Bermuda Triangle, New Age Spirituality, Body Mind and Soul)

Triangle An emblem of the triad or three-in-one, expressing more than the three dots alone: the points, lines, and the whole figure give a septenate composed of two triads and a monad.

The triangle also symbolizes twin rays proceeding from a central point, and when the other ends of these lines are joined, the base line signifies that which is produced by the interaction and interblending of the two formative rays. The apex, the side lines, and the base thus represent the three chief stages of cosmic evolution. The idea is further elaborated in the square pyramid.

The Pythagoreans recognized the triangle as the first regular rectilinear figure, as three is the first odd number -- the one being considered as the origin and unit, out of which all subsequent parts flow. The usual form of the triangle in symbology is equilateral, with the apex up or down. The circle, triangle, and square form another important triad representing stages in evolution. For interlaced triangles,

See also SIX-POINTED STAR

(See also: Triangle, Mysticism, Mysticism Dictionary, Body mind and Soul)

Definition and meaning of Triangle Shirtwaist factory:

Triangle Shirtwaist factory

The tragic death of 150 women employees at New York's Triangle Shirtwaist factory in 1911, caused by locked doors and the absence of fire escapes, led to the passage of stricter building codes and factory-inspection laws to protect workers.

(Source: Madrid Waddington High School )

Also see these pages:  American History, American History Sitemap, History, History Sitemap

Circle

(See also: Triangle, Magick, Mysticism, Mysticism Dictionary, Body Mind and Soul, )

Triangle

• To dream of a triangle, foretells separation from friends, and love affairs will terminate in disagreements.

Source: 10 000 Dream Interpretations, by Gustavus Hindman Miller

(See also: Dream Archives, Meaning of Dreams, Dream Interpretation, Dream Dictionary, Dream Dictionary - Triangle, Meaning of Dreams about Triangle, Dream Interpretation Triangle)

Triangle Dream Symbols:

(Source: Myths - Dreams - Symbols)

Related pages: Dream Symbols, Dream Interpretation, Dream Symbol Triangle, Dream Dictionary Triangle, Meaning of dreams about Triangle, Dream Interpretation Triangle, Dream Analysis Triangle, Dreaming of Triangle

Triangle, Trinity, Mind body and spirit, Mind body and mind