Triangulation
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In trigonometry and elementary geometry, triangulation is the process of finding coordinates and distance to a point by calculating the length of one side of a triangle, given measurements of angles and sides of the triangle formed by that point and two other known reference points, using the law of sines.
(In the figure at right, the third angle of the triangle (call it θ) is known to be 180-α-β, since the sum of the three angles in any triangle is known to be 180 degrees. The opposite-side for this (the third) angle is l, which is a known distance. Since, by the law of sines, the ratio sin(θ)/l is equal to that same ratio for the other two angles α and β, the lengths of any of the remaining two sides can be computed by algebra. Given either of these lengths, sine and cosine can be used to calculate the offsets in both the north/south and east/west axes from the corresponding observation point to the unknown point, thereby giving its final coordinates.)
Some identities often used (valid only in flat or euclidean geometry):
- The sum of the angles of a triangle is π rad or 180 degrees.
- The law of sines
- The law of cosines
- The Pythagorean theorem
Triangulation is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision and gun direction of weapons.
Many of these surveying problems involve the solution of large meshes of triangles, with hundreds or even thousands of observations. Complex triangulation problems involving real-world observations with errors require the solution of large systems of simultaneous equations to generate solutions.
Famous uses of triangulation have included the retriangulation of Great Britain.
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[edit] In chess
In the game of chess, triangulation refers to a tactical idea by which a player forces his opponent to move, thereby willingly losing a tempo. This device is a form of zugzwang. Triangulation is especially important in many endgames in which a stronger side can "stiffle" the weaker side by making the latter move to the unwanted squares.
[edit] In politics
In politics, triangulation refers to a stratagem whereby a politician associates an opposing view with other views that are so outlandish that third parties are alienated and so give the politician their support. Examples include associating anybody who questions any aspect of environmentalism with Big Oil so as to undermine their argument without having to actually engage with it, or associating trade unionism with communism, again to evade the question.
[edit] In business
In business, triangulation is an organizational practice where reporting and communication relationships between two individuals are compromised when a subordinate bypasses a supervisor to share prejudicial information with others in a hierarchy without the supervisor's knowledge. It is generally considered inappropriate or unethical, and jeopardizes relationships within the organization.
[edit] See also
- Multilateration, where a point is calculated using the time-difference-of-arrival between other known points
- Parallax
- Trilateration, where a point is calculated given its distances from other known points
- Trigonometry
- Trig point
- Triangulation Software
