Distance Geometry Notes
نویسنده
چکیده
Introduction. This paper is concerned with several disconnected developments in distance geometry. §1 deals with the congruent imbedding of metric spaces in euclidean or Hubert spaces. By showing that the validity of the Pythagorean theorem insures the essentially euclidean character of the metric, the basic role this theorem plays in euclidean geometry is seen to be fully justified. In §2 the circle and ^-dimensional sphere are considered with respect to the property of covering euclidean subsets. The concluding section presents an algebraic-geometric proof of the quasi congruence order property of the En which, by making use of determinants, achieves a considerable abbreviation of the two proofs of this important result hitherto published. The desired purely algebraic proof has not yet been obtained.
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