’n Veralgemeende Sylvester-Gallai Stelling
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie/South African Journal of Science and Technology
| Field | Value | |
| Title | ’n Veralgemeende Sylvester-Gallai Stelling A generalised Sylvester-Gallai Theorem | |
| Creator | Pretorius, L. M. Swanepoel, K. J. | |
| Description | Ons gee ’n algoritmiese bewys vir die kontrapositief van die volgende stelling wat onlangs deur die outeurs bewys is:Laat S ’n eindige versameling van punte in die vlak wees, met elke punt rooi, blou of met beide kleure gekleur. Veronderstel dat daar vir enige twee verskillende punte A en B in S wat ’n kleur k deel, ’n derde punt in S is wat (o.a.) die kleur anders as k het en wat saamlynig met A en B is. Dan is al die punte in S saamlynig.Hierdie stelling is ’n gemeenskaplike veralgemening van die Sylvester-Gallai Stelling en dieMotzkin- Rabin Stelling. We give an algorithmic proof for the contrapositive of the following theorem that has recently been proved by the authors:Let S be a finite set of points in the plane, with each point coloured red, blue or with both colours. Suppose that for any two distinct points A and B in S sharing a colour k, there is a third point in S which has (inter alia) the colour different from k and is collinear with A and B. Then all the points in S are collinear.This theorem is a generalization of both the Sylvester-Gallai Theorem and the Motzkin-Rabin Theorem. | |
| Publisher | AOSIS | |
| Date | 2007-09-21 | |
| Identifier | 10.4102/satnt.v26i1.118 | |
| Source | Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie; Vol 26, No 1 (2007); 8-13 Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie; Vol 26, No 1 (2007); 8-13 2222-4173 0254-3486 | |
| Language | eng | |
| Relation |
The following web links (URLs) may trigger a file download or direct you to an alternative webpage to gain access to a publication file format of the published article:
https://journals.satnt.aosis.co.za/index.php/satnt/article/view/118/90
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