Depth of segments and circles through points enclosing many points: a note

Details Depth of segments and circles through points enclosing many points: a note Depth of segments and circles through points enclosing many points: a note

2008-03-07

arxiv.org/abs/0803.1088v1

Mathematics

Combinatorics

5 pages, 2 figures

Scientific paper

Neumann-Lara and Urrutia showed in 1985 that in any set of n points in the plane in general positionthere is always a pair of points such that any circle through them contains at least (n-2)/60 points. In a series of papers, this result was subsequently improved till n/4.7, which is currently the best known lower bound. In this paper we propose a new approach to the problem that allows us, by using known results about j-facets of sets of points in $R^3$, to give a simple proof of a somehow stronger result: there is always a pair of points such that any circle through them has, both inside and outside, at least n/4.7 points.

Affiliated with

Also associated with

No associations

Rating

Depth of segments and circles through points enclosing many points: a note does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Depth of segments and circles through points enclosing many points: a note, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Depth of segments and circles through points enclosing many points: a note will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-253017