On Distinct Distances from a Vertex of a Convex Polygon
نویسندگان
چکیده
منابع مشابه
The number of distinct distances from a vertex of a convex polygon
Erdős conjectured in 1946 that every n-point set P in convex position in the plane contains a point that determines at least bn/2c distinct distances to the other points of P . The best known lower bound due to Dumitrescu (2006) is 13n/36−O(1). In the present note, we slightly improve on this result to (13/36 + ε)n − O(1) for ε ≈ 1/23000. Our main ingredient is an improved bound on the maximum ...
متن کاملOn unit distances in a convex polygon
For any convex quadrilateral, the sum of the lengths of the diagonals is greater than the corresponding sum of a pair of opposite sides, and all four of its interior angles cannot be simultaneously acute. In this article, we use these two properties to estimate the number of unit distance edges in convex n-gons and we: (i) exhibit three large groups of cycles formed by unit distance edges that ...
متن کاملa study on the design of bio-ethanol process from date wastes of sistan and baluchistan province
اتانول کاربردهای متنوعی در صنایع لاستیک سازی، رنگسازی، حلالها ومکمل سوخت خودرو دارد. اتانول برخلاف نفت از جمله مواد تجدیدپذیر محسوب می شود که مشکلات زیست محیطی و آلودگی نیز ایجاد نمی کند. استفاده از اتانول به عنوان مکمل سوختخودروها از جمله مهمترین مصارف صنعتی این ماده بشمار می رود. با توجه به این موضوع تحقیق و توسعه در زمینه تولید اتانول با درجه خلوص بالا در سطح جهان، و نه تنها در کشور های پیشر...
Distinct Distances on a Sphere
We prove that a set of N points on a two dimensional sphere satisfying a discrete energy condition determines at least a constant times N distinct distances. Homogeneous sets in the sense of Solymosi and Vu easily satisfy this condition, as do other sets that in the sense that will be made precise below respect the curvature properties of the sphere. The classical Erdös distance conjecture (EDC...
متن کاملA note on distinct distances
We show that, for a constant-degree algebraic curve γ in R, every set of n points on γ spans at least Ω(n) distinct distances, unless γ is an algebraic helix (see Definition 1.1). This improves the earlier bound Ω(n) of Charalambides [2]. We also show that, for every set P of n points that lie on a d-dimensional constantdegree algebraic variety V in R, there exists a subset S ⊂ P of size at lea...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2006
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-006-1262-y