In 1821, John Jackson published this mathematical conundrum in a book of problems called Rational Amusement for Winter Evenings . These days, verse is not as popular, and a modern-day puzzle poser might even dispense with the trees, saying: Arrange nine points on a plane so that there occur ten rows of three points. When a mathematician encounters such a problem, he feels a natural urge to generalize it and then wants to make it more precise. This leads to the following version: Given a positive integer p, how can p points (p ≥ 3) be arranged on a plane, no four in a straight line, so that the number of straight lines with three points on them is maximized? We will call this maximal number of lines l(p).
KeywordsParametric Representation Projective Transformation Artful Computer Program Winter Evening Natural Urge
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