Triangulation Guide, Meaning , Facts, Information and Description
In trigonometry and elementary geometry, triangulation is the process of finding a 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 reference points.
Some identities often used (valid only in flat or euclidean geometry):
- The sum of the angles of a triangle is π (180 degrees).
- The law of sines
- The law of cosines
- The Pythagorean theorem
See: Parallax.
In advanced geometry, in the most general meaning, triangulation is a subdivision of a geometric object into simplices. In particular, in the plane it is a subdivision into triangless, hence the name.
Different branches of geometry use slightly differing definitions of the term.
A triangulation T of is a subdivision of into (n+1)-dimensional simplices such that:
- any two simplices in T intersect in a common face or not at all;
- any bounded set in intersects only finitely many simplices in T.
In computational geometry, triangulation may be performed for various objects.
Topology generalizes this notion in a natural way as follows. A triangulation of a topological space is a simplicial complex , homeomorphic to , together with a homeomorphism .
Triangulation is useful in determining the properties of a topological space.
In the social sciences, triangulation is often used to indicate that more than one method is used in a study with a view to double (or triple) checking results. This is also called "cross examination". The idea is that we can be more confident with a result if different methods lead to the same result.
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