{
  "id": "math/9906001",
  "version": "v4",
  "published": "1999-06-01T02:30:38.000Z",
  "updated": "2000-06-22T01:14:13.000Z",
  "title": "A discrete form of the Beckman-Quarles theorem for rational eight-space",
  "authors": [
    "Apoloniusz Tyszka"
  ],
  "comment": "added Remark 4 by Joseph Zaks, to appear in Aequationes Math",
  "journal": "Aequationes Mathematicae 62 (2001), pp. 85-93",
  "categories": [
    "math.MG"
  ],
  "abstract": "Let Q denote the field of rational numbers. Let F \\subseteq R is a euclidean field. We prove that: (1) if x,y \\in F^n (n>1) and |x-y| is constructible by means of ruler and compass then there exists a finite set S(x,y) \\subseteq F^n containing x and y such that each map from S(x,y) to R^n preserving unit distance preserves the distance between x and y, (2) if x,y \\in Q^8 then there exists a finite set S(x,y) \\subseteq Q^8 containing x and y such that each map from S(x,y) to R^8 preserving unit distance preserves the distance between x and y.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2000-06-22T01:14:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51M05",
      "05C12"
    ],
    "keywords": [
      "beckman-quarles theorem",
      "rational eight-space",
      "discrete form",
      "preserving unit distance preserves",
      "finite set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......6001T"
    }
  }
}