کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4648348 | 1342407 | 2012 | 10 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: The Lemma of Tangents reformulated The Lemma of Tangents reformulated](/preview/png/4648348.png)
The famous Lemma of Tangents describes a useful (algebraic) relation between the tangents through three points of an arc in a Desarguesian projective plane. Because the formulation of the lemma assumes the three points to have coordinates (1,0,0)(1,0,0), (0,1,0)(0,1,0) and (0,0,1)(0,0,1), it is sometimes not so evident to apply when studying arc subsets of more than three points.In this paper, we reformulate the Lemma of Tangents in a concise way which is independent of the chosen basis of the projective plane. We also express the consequences of this lemma for sets of more than three arc points in the form of linear equations. To show that our framework is helpful we provide a new and direct proof of the fact that every qq-arc in PG(2,q) must be part of a conic when qq is odd.
Journal: Discrete Mathematics - Volume 312, Issue 3, 6 February 2012, Pages 705–714