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
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.
A triangulation of a discrete set of points is a triangulation of such that the set of points that are vertices of the subdividing simplices coincides with P.
In computational geometry, triangulation may be performed for various objects.
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.