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In discrete geometry, the original orchard-planting problem asks for the maximum number of 3-point lines attainable by a configuration of points in the plane. It is also called the tree-planting problem or simply the orchard problem. There are also investigations into how many k-point lines there can be. Hallard T. Croft and Paul Erdős proved ''t''''k'' > ''c'' ''n''2 / ''k''3, where ''n'' is the number of points and ''t''''k'' is the number of ''k''-point lines.〔''The Handbook of Combinatorics'', edited by László Lovász, Ron Graham, et al, in the chapter titled ''Extremal Problems in Combinatorial Geometry'' by Paul Erdős and George B. Purdy.〕 Their construction contains some m-point lines, where m > k. One can also ask the question if these are not allowed. ==Integer sequence== Define ''t''3orchard(''n'') to be the maximum number of 3-point lines attainable with a configuration of ''n'' points. For an arbitrary number of points, ''n'', ''t''3orchard(''n'') was shown to be (1/6)''n''2 − O(n) in 1974. The first few values of ''t''3orchard(''n'') are given in the following table . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Orchard-planting problem」の詳細全文を読む スポンサード リンク
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