Kobon Triangle Problem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura. The problem asks for the largest number N(k) of nonoverlapping triangles that can be produced by k straight line segments. Saburo Tamura proved that the largest integer not exceeding k(k 2)/3 provides an upper bound on the maximal number of nonoverlapping triangles realizable by k lines. This sequence is captured in the On-Line Encyclopedia of Integer Sequences ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura. The problem asks for the largest number N(k) of nonoverlapping triangles that can be produced by k straight line segments. Saburo Tamura proved that the largest integer not exceeding k(k 2)/3 provides an upper bound on the maximal number of nonoverlapping triangles realizable by k lines. This sequence is captured in the On-Line Encyclopedia of Integer Sequences as A032765. In 2007, a tighter upper bound was found by Johannes Bader and Gilles Clément, by proving that Tamura''s upper bound couldn''t be reached for any k congruent to 0 or 2 (mod 6).
