On a Heilbronn-type problem
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- 作者：Hansheng Diao ; Gangsong Leng ; Lin Si
- 关键词：Triangle ; Parallelogram ; Convex figure ; Area ; Soifer's problem ; Heilbronn's problem
- 刊名：Discrete Mathematics
- 出版年：2008
- 出版时间：6 September 2008
- 年：2008
- 卷：308
- 期：17
- 页码：3960-3981
- 全文大小：242 K
文摘
Let F be a convex figure with area |F| and let G(n,F) denote the smallest number such that from any n points of F we can get G(n,F) triangles with areas less than or equal to 65b93a4cb24b"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">|F|/4. In this article, to generalize some results of Soifer, we will prove that for any triangle T, G(5,T)=3; for any parallelogram P, G(5,P)=2; for any convex figure F, if 65b2d7bae6d40b5c736a97ef4d1af54"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">S(F)=6, then 5b052421815f207d167876413085b"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">G(6,F)=4.