Heilbronn Triangle Problem
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High Quality Content by WIKIPEDIA articles! In mathematics, the Heilbronn triangle problem is a typical question in the area of irregularities of distribution, within elementary geometry. Consider region D in the plane: a unit circle or general polygon the asymptotics of the problem, which are the interesting aspect, aren't dependent on the exact shape. Place a number n of distinct points (greater than three) within D: there are numerous triangles that can be constructed from three of those points. For a given configuration, we are interested knowing that there is some small triangle, and how…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, the Heilbronn triangle problem is a typical question in the area of irregularities of distribution, within elementary geometry. Consider region D in the plane: a unit circle or general polygon the asymptotics of the problem, which are the interesting aspect, aren't dependent on the exact shape. Place a number n of distinct points (greater than three) within D: there are numerous triangles that can be constructed from three of those points. For a given configuration, we are interested knowing that there is some small triangle, and how small. The Heilbronn triangle problem involves therefore the extremal case: minimum area from these points. The question was posed by Hans Heilbronn, of giving a lower bound for this minimum area, denoted by (n).