Talk:Distance geometry

Molecules structure

It seems that the term is only used for molecules structure?? Tosha 18:14, 3 October 2005 (UTC)

Applications

Probably, the most "real-life application" is GPS? — Mikhail Ryazanov (talk) 08:18, 24 January 2011 (UTC)

Destruction of material by Toninowiki

A series of edits were done on this article on November 11 by user:Toninowiki, who destroyed all references to higher dimensions, which are crucial to the point of the article. Now someone in another forum is telling me that my link to this article is not much appreciated because it doesn't go into higher dimensions. I've restored the material that was destroyed. Michael Hardy (talk) 21:22, 25 January 2014 (UTC)

This article could use a good deal of improvement

There are numerous symbols used in the article that are nowhere defined.

This is a terrible idea for an encyclopedia article.

I hope someone can define in the article the symbols t_A, t_B, t_C, and d_ij, among others. 2601:200:C000:1A0:D814:9114:E269:A7A7 (talk) 18:51, 28 April 2022 (UTC)

They're defined: Template:Tq and d is defined in the sentence beginning Template:Tq MrOllie (talk) 18:55, 28 April 2022 (UTC)

Content error

Under “Characterization via Cayley–Menger determinants” it is noted that the following results are proved in Blumenthal's book [12].

Unfortunately, that's wrong. The results presented by Wikipedia only roughly reflect Blumenthal's work and contain errors.

This can easily be checked by means of a simple counterexample: According to Blumenthal, the semimetric space with the distance matrix

0 3 4 8

3 0 1 4

4 1 0 2

8 4 2 0

cannot be embedded in any space Rⁿ, but according to the Wikipedia article it can, namely for n=3.

The Cayley-Menger determinants given by the principal submatrices with elements of the 4, the first 3 and the first 2 lines satisfy the embedding conditions of Wikipedia. However, the remaining three triangles of the potential tetrahedron do not fulfill the triangle inequality.

These misrepresentations of the central theorem of distance geometry are not peanuts.

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K2357W (talk) 09:24, 2 July 2022 (UTC)