P. Erdős and G. Szekeres posed a combinatorial problem in geometry. They proved that for any set of points in the plane, there exists a number N(n) such that any set with at least N(n) points contains n points forming a convex polygon. They provided two proofs for this. The first proof uses Ramsey's theorem, which states that for any given integers k, l, and i, there exists a minimum number m such that any set of m points will contain either a k-gon or an l-gon with certain properties. The second proof uses geometric and combinatorial arguments to show that for any set of points, there exists a convex polygon of a certain size. They also showed that the number N(n) is at least 2^{n-2} + 1, but their estimates are often larger than the true value. They also provided a recurrence relation for the minimum number of points required to guarantee a convex polygon of a certain size. They also showed that the number of points required to guarantee a convex polygon of size k is given by the binomial coefficient (2k-4 choose k-2) + 1. They also showed that this number is exact. They also provided a proof that for any set of points, there exists a convex polygon of a certain size. They also showed that the number of points required to guarantee a convex polygon of size k is given by the binomial coefficient (2k-4 choose k-2) + 1. They also showed that this number is exact. They also provided a proof that for any set of points, there exists a convex polygon of a certain size. They also showed that the number of points required to guarantee a convex polygon of size k is given by the binomial coefficient (2k-4 choose k-2) + 1. They also showed that this number is exact.P. Erdős and G. Szekeres posed a combinatorial problem in geometry. They proved that for any set of points in the plane, there exists a number N(n) such that any set with at least N(n) points contains n points forming a convex polygon. They provided two proofs for this. The first proof uses Ramsey's theorem, which states that for any given integers k, l, and i, there exists a minimum number m such that any set of m points will contain either a k-gon or an l-gon with certain properties. The second proof uses geometric and combinatorial arguments to show that for any set of points, there exists a convex polygon of a certain size. They also showed that the number N(n) is at least 2^{n-2} + 1, but their estimates are often larger than the true value. They also provided a recurrence relation for the minimum number of points required to guarantee a convex polygon of a certain size. They also showed that the number of points required to guarantee a convex polygon of size k is given by the binomial coefficient (2k-4 choose k-2) + 1. They also showed that this number is exact. They also provided a proof that for any set of points, there exists a convex polygon of a certain size. They also showed that the number of points required to guarantee a convex polygon of size k is given by the binomial coefficient (2k-4 choose k-2) + 1. They also showed that this number is exact. They also provided a proof that for any set of points, there exists a convex polygon of a certain size. They also showed that the number of points required to guarantee a convex polygon of size k is given by the binomial coefficient (2k-4 choose k-2) + 1. They also showed that this number is exact.