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Partitions of planar sets into small triangles

✍ Scribed by Andrew M Odlyzko; János Pintz; Kenneth B Stolarsky

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
440 KB
Volume
57
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Given 3n points in the unit square, n >12, they determine n triangles whose vertices exhaust the given 3n points in many ways. Choose the n triangles so that the sum of their areas is minimal, and let a*(n) be the maximum value of this minimum over all configurations of 3n points. Then n-~<< a*(n)<< n-~ is deduced using results on the Heilbronn triangle problem. If the triangles are required to be area disjoint it is not even dear that the sum of their areas tends to zero; this open question is examined in a slightly more general setting.

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