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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

Triangulation is used for many purposes, including surveying, navigation, astrometry, binocular vision and gun direction of weapons.

See: Parallax.

In advanced geometry, in the most general meaning, triangulation is a subdivision of a geometric object into simplicesTopology Geometry Geometry In geometry, a simplex is an n dimensional figure, being the convex hull of a set of n + 1) affinely independent points in some Euclidean space of dimension n or higher i. a set of points such that no m plane contains more than. In particular, in the plane it is a subdivision into triangles, 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 simplicesTopology Geometry Geometry In geometry, a simplex is an n dimensional figure, being the convex hull of a set of n + 1) affinely independent points in some Euclidean space of dimension n or higher i. a set of points such that no m plane contains more than such that:

1. any two simplices in T intersect in a common face or not at all;
2. any bounded set in intersects only finitely many simplices in T.

A triangulation of a discreteThe word discrete comes from the latin word discretus which means separate''. It is used with different meanings in different contexts: In perception a discrete entity is something that can be perceived individually and not as connected to, or part of som set of points is a triangulation of such that the set of points that are vertices of the subdividing simplices coincides with .

In computational geometryIn computer science, computational geometry is the study of algorithms to solve problems stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and the study of such problems is also con, triangulation may be performed for various objects.

• Polygon triangulationPolygon triangulation is a topic in computational geometry. It means the decomposition of a polygon into a set of triangles. A triangulation of a polygon P is its partition into non-overlapping triangles whose union is P . In the strictest sense, these tr
• Point set triangulationA triangulation of a set of points P is the triangulation of the convex hull of P with all points from P being among the vertices of the triangulation. Sometimes it is desirable to have a triangulation with special properties, e. in which the triangles ea

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.