Triangulation and Trilateration
Triangulation is a very interesting concept which has been applied in many diverse fields to achieve results.
In geometry triangulation is basically a technique to locate the position of a point by drawing triangles from other points whose positions are known.
Triangulation is best illustrated with an example. Say you have two points (0,0) and (5,0) on a 2D plane which are known to you. You are required to find the location of a third point somewhere on the plane. By some mechanism the observer at 0,0 and the observer at (5,0) are able to observe the angle between the base line and the line to the unknown point. Take these angles as alpha and beta.
Based on these angles the perpendicular distance and the distance of the offsets can be easily calculated using basic trigonomentry.
Another similar concept is that of trilateration. If we take the previous example, but instead of the angles being known, we know the distance between the unknown point and the known points, then we can draw circles from the known points having radius equal to the distance between unknown and known points respectively. The point where the two circles intersect is the unknown point. This concept can be extended to 3 dimensions to locate a point in 3D. GPS satellites use the same concept to track a person’s location using 3 satellites .
In social sciences one can have increased confidence on a result if there are multiple studies come up with the same result. Similarly this concept can be used to verify many claims in other domains.
