A Constructive Approach to Sylvester's Conjecture
| dc.creator | Plato,Jan | |
| dc.date | 2005 | |
| dc.date.accessioned | 2024-02-06T12:54:05Z | |
| dc.date.available | 2024-02-06T12:54:05Z | |
| dc.description | Sylvester's conjecture states that, given n distinct noncollinear points in a plane, there exists a connecting line of two of the points such that no other point is incident with the line. First a proof is given of the six-point Sylvester conjecture from a constructive axiomatization of plane incidence geometry. Next ordering principles are studied that are needed for the seven-point case. This results in a symmetrically ordered plane affine geometry. A corollary is the axiom of complete quadrangles. Finally, it is shown that the problem admits of an arithmetic translation by which Sylvester's conjcture is decidable for any n. | |
| dc.format | text/html | |
| dc.identifier | https://doi.org/10.3217/jucs-011-12-2165 | |
| dc.identifier | https://lib.jucs.org/article/28551/ | |
| dc.identifier.uri | https://openrepository.mephi.ru/handle/123456789/8915 | |
| dc.language | en | |
| dc.publisher | Journal of Universal Computer Science | |
| dc.relation | info:eu-repo/semantics/altIdentifier/eissn/0948-6968 | |
| dc.relation | info:eu-repo/semantics/altIdentifier/pissn/0948-695X | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.rights | J.UCS License | |
| dc.source | JUCS - Journal of Universal Computer Science 11(12): 2165-2178 | |
| dc.subject | Sylvester's conjecture | |
| dc.subject | constructive geometry | |
| dc.subject | ordered geometry | |
| dc.title | A Constructive Approach to Sylvester's Conjecture | |
| dc.type | Research Article |