A parametrization of equilateral triangles having integer coordinates
| dc.creator | Ionascu, Eugen J. | |
| dc.date | 2006-08-02 | |
| dc.date.accessioned | 2026-07-07T07:21:19Z | |
| dc.date.available | 2026-07-07T07:21:19Z | |
| dc.description | We study the existence of equilateral triangles of given side lengths and with integer coordinates in dimension three. We show that such a triangle exists if and only if their side lengths are of the form $\sqrt{2(m^2-mn+n^2)}$ for some integers $m,n$. We also show a similar characterization for the sides of a regular tetrahedron in $\Z^3$: such a tetrahedron exists if and only if the sides are of the form $k\sqrt{2}$, for some $k\in\N$. The classification of all the equilateral triangles in $\Z^3$ contained in a given plane is studied and the beginning analysis is presented. A more general parametrization is proven under a special assumption. Some related questions are stated in the end. | |
| dc.description | 3 fugures, 17 pages, submitted to Integers | |
| dc.identifier | https://arxiv.org/abs/math/0608068 | |
| dc.identifier | http://arxiv.org/abs/math/0608068 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115259 | |
| dc.subject | Number Theory | |
| dc.subject | 11D09 | |
| dc.title | A parametrization of equilateral triangles having integer coordinates | |
| dc.type | text |