Sylvester's Four-Point Problem in a Sector and its Relation to Weber Location Problem

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  • 扇形シルベスター4点問題とウェーバー問題端点解発生確率

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This paper obtains the probability that the optimal location of the unweighted Weber location problem is one of the demand points where demand points which are uniformly and independently distributed within a sector. When the number of the demand points is four, this problem is identical with the famous Sylvester's four-point problem. We solves this problem by use of Crofton's formula. We have extended the existing works this is because our results include the ones of circles and triangles as special cases. We also reveal that the probability is stable unless the angle of the sector is small by use of numerical simulation.

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