Jessica L. Nelson

Harvey Mudd College Mathematics 2004

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Thesis Proposal: On the Erdős Problem of Empty Convex Hexagons
Thesis Advisor: Prof. Lisette G. de Pillis
Second Reader: Prof. Arthur T. Benjamin
E-Mail: Contact Me

New Angles on the Empty Convex Hexagons Problem

Paul Erdős's Empty Hexagon Problem asks if there exists a positive integer H(6) such that for all sets of n ≥ H(6) points in general position on the plane (that is, no three points are on a line) at least one subset of six of the points form the vertices of an empty convex hexagon. The question of the existence and value of H(6) is open although values for H(3), H(4), and H(5) have been found and it is known that H(k) does not exist for k ≥ 7.

I was attracted to this problem in combinatorial geometry for its apparent simplicity of statement and subtle complexity. I hope to find elementary proofs of the existence of H(6) and of its value.