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2015 Spring Symposium on Undergraduate Research and Community... has ended
Wednesday, April 22 • 2:45pm - 3:05pm
A Study of the Occurrence of Convex Sets Among Points in the Plane

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In 1935 Esther Klein proposed the following question to two of her colleagues, Paul Erdős and George Szekeres: How many points in general position are necessary to guarantee a set of four points that define a convex quadrilateral? This was quickly proven to be five. The generalization of this problem, known as The Happy Ending Problem, has been far more difficult to prove. The basic question is, how many points in general position are necessary to guarantee a set of n points that define a convex n-gon? Erdős and Szekeres were able to prove such a number exists for all n, although an exact value is only known for n less than or equal to six. In researching this problem we have focused on determining combinatorically the minimum number of convex quadrilaterals defined by any number of points in general position.

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Wednesday April 22, 2015 2:45pm - 3:05pm
123 Zeis Hall

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