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On points with arbitrarily assigned mutual distances

Published online by Cambridge University Press:  24 October 2008

H. S. M. Coxeter  and
J. A. Todd
H. S. M. Coxeter
Affiliation:
Trinity College
J. A. Todd
Affiliation:
Trinity College
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Extract

Let SsTt denote a space of s + t dimensions with the property that the square of the distance between any two points

is of the form

where s of the ε's are equal to + 1 and t of them to — 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 30 , Issue 1 , January 1934 , pp. 1 - 3
Copyright
Copyright © Cambridge Philosophical Society 1934

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References

* Cf. Coxeter, , Proc. Camb. Phil. Soc. 29 (1933), 3, 4.CrossRefGoogle Scholar

* It is worth noticing that the B's, unlike the A's, are necessarily independent.

† This is the accurate statement of the remark made in parentheses in the first paragraph of the paper previously cited.

* Sommerville, D. M. Y., Geometry of n dimensions (London, 1929), 124–125.Google Scholar

† Cf. Wald, A., Ergebnisse eines mathematisches Kolloquiums, 5 (1932/1933), 36.Google Scholar His results are equivalent to ours if it is assumed that we can always find, in some complex metric space, n + 1 points with arbitrarily assigned mutual distances.