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The maximum number of unit distances in a convex n-gon

✍ Scribed by Zoltȧn Füredi

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
216 KB
Volume
55
Category
Article
ISSN
0097-3165

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Proof. Denote by f (n) the maximum number of times the unit distance can occur among n points in convex position in the plane. Let p 1 , p 2 , ..., p n , in this cyclic order, be the vertices of a convex polygon, for which the maximum is attained. Let G denote the geometric graph obtained by connect

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Minkowski space M d =(R d , || ||) is just R d with distances measured using a norm || ||. A norm || || is completely determined by its unit ball {x ¥ R d | ||x|| [ 1} which is a centrally symmetric convex body of the d-dimensional Euclidean space E d . In this note we give upper bounds for the maxi