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[Texts]## 51F: Metric Geometry |

- 51F05: Absolute planes
- 51F10: Absolute spaces
- 51F15: Reflection groups, reflection geometries, See also 20H10, 20H15; for Coxeter groups, See 20F55
- 51F20: Congruence and orthogonality, See also 20H05
- 51F25: Orthogonal and unitary groups, See also 20H05
- 51F99: None of the above but in this section

Parent field: 51: Geometry

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

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

- Given 3 known points in 3-space, and the distances from each known point to an unknown point, how to determine the position of the unknown point?
- Fortran code to determine location by triangulation. [Author hasn't given permission to post his name.]
- Determine present location from distances to three fixed points.
- Using the Cholesky factorization of a matrix to find an isometric embedding of a finite set of points.

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.
- Calculating position from three angles to fixed locations

Other files for 51F:

- Representing a rotation in R^3 using rotations around only two axes
- Extracting the axis of rotation from a 3x3 orthogonal matrix.
- Proving the analogue of the Pythagorean theorem in higher dimensions.
- Determine a Euclidean motion from shadows of 5 moved points
- Finding the Euclidean isometry best matching n pre- and post-point pairs
- When can this freely-moving linkage be constructed?
- Determine locations of points given all bipartite distances
- Points in the plane with only two distances between them

Last modified 2000/01/14 by Dave Rusin. Mail: