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Point sets with many unit circles

โœ Scribed by Heiko Harborth; Ingrid Mengersen


Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
269 KB
Volume
60
Category
Article
ISSN
0012-365X

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โœฆ Synopsis


Every three of n points in the plane determine a circle. The maximum number f(n) of congruent circles is determined for n < 7: f(3) = 1, f(4) =f(5) = 4, f(6) = 8, f(7) = 12.


๐Ÿ“œ SIMILAR VOLUMES


Circles through two points that always e
โœ H. Edelsbrunner; N. Hasan; R. Seidel; X. J. Shen ๐Ÿ“‚ Article ๐Ÿ“… 1989 ๐Ÿ› Springer ๐ŸŒ English โš– 485 KB

This paper proves that any set of n points in the plane contains two points such that any circle through those two points encloses at least n(1/2 -1/,fi2) + O(1) ~ n/4-7 points of the set. The main ingredients used in the proof of this result are edge counting formulas for k-order Voronoi diagrams a

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