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. Erd˜os posed the problem of determining the minimumnumber g ( n ) such that any set of g ( n ) points in general positionin the plane contains an empty convex n -gon. In 1978, Harborthproved that g (5) = 10. We reprove the result in a geometric ap-proach. 1. IntroductionDue to the importance in computer graphics, geometric modellings,motion planing, and other areas, the study of the convex polygons hasa renewed interest, recently. In this paper, we reprove a known resultrelated to the Erd˜os and Szekeres problem which is a classic problemcounting empty convex k -gons in planar points sets.In 1935, Erd˜os and Szekeres posed the problem of determining thesmallest positive integer f ( n ) so that any set of at least f ( n ) points inopened position in the plane contains a convex n -gon and also conjec-tured that f ( n ) = 2 ni 2 +1 for all n ‚ 3[1]. Until now, the problem hasbeen solved for the values n = 3 ; 4 ; and 5 only ([4]). For larger valuesof n , the best known upper bound

EMPTY CONVEX 5-GONS IN PLANAR POINT SETS