Sums of Distances Between Points on a Sphere
نویسندگان
چکیده
منابع مشابه
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...
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In this paper, we tackle the extension of aggregations of distances in R to the fuzzy numbers and fuzzy points and we investigate the fullfilment of the conditions of a fuzzy metric.
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We show that for m points and n lines in R2, the number of distinct distances between the points and the lines is Ω(m1/5n3/5), as long as m1/2 ≤ n ≤ m2. We also prove that for any m points in the plane, not all on a line, the number of distances between these points and the lines that they span is Ω(m4/3). The problem of bounding the number of distinct point-line distances can be reduced to the...
متن کاملOn distinct sums and distinct distances
The paper (Discrete Comput. Geom. 25 (2001) 629) of Solymosi and Tóth implicitly raised the following arithmetic problem. Consider n pairwise disjoint s element sets and form all ð 2Þn sums of pairs of elements of the same set. What is the minimum number of distinct sums one can get this way? This paper proves that the number of distinct sums is at least ns ; where ds 1⁄4 1=cJs=2n is defined in...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.2307/2037644