A discrete form of the Beckman-Quarles theorem for rational eight-space
| dc.creator | Tyszka, Apoloniusz | |
| dc.date | 1999-06-01 | |
| dc.date | 2000-06-22 | |
| dc.date.accessioned | 2026-07-07T05:29:19Z | |
| dc.date.available | 2026-07-07T05:29:19Z | |
| dc.description | 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. | |
| dc.description | added Remark 4 by Joseph Zaks, to appear in Aequationes Math | |
| dc.identifier | https://arxiv.org/abs/math/9906001 | |
| dc.identifier | http://arxiv.org/abs/math/9906001 | |
| dc.identifier | Aequationes Mathematicae 62 (2001), pp. 85-93 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78595 | |
| dc.subject | Metric Geometry | |
| dc.subject | 51M05 (Primary), 05C12 (Secondary) | |
| dc.title | A discrete form of the Beckman-Quarles theorem for rational eight-space | |
| dc.type | text |