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# 51F: Metric Geometry

## Introduction

We use this as the repository for remarks on triangulation, that is, determining locations from sightings. (Triangulation in the sense of subdividing into triangles is discussed with polyhedra, and computational geometry, as well as PL-topology).

## Subfields

• 51F05: Absolute planes
• 51F10: Absolute spaces
• 51F15: Reflection groups, reflection geometries, See also 20H10, 20H15; for Coxeter groups, See 20F55
• 51F99: None of the above but in this section

Parent field: 51: Geometry

Browse all (old) classifications for this area at the AMS.

## Selected topics at this site

A common question is this: how can you determine positions if you know the distances to three other points? A couple of relevant threads:

Here's an interesting mix of practical and theoretical considerations, of algebra and geometry. A USENET poster asked if one could determine positions within a triangle knowing the angles of sighting to the vertices of the triangle, and how one could compute this.

• The original posting and a (pretty predictable) response. In this discussion the problem was purely geometrical.
• An explanation of the practical origins of the triangulation problem.
• A follow-up post giving a ruler-and-compass solution to the triangulation problem at hand.

Other files for 51F: