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Planting Trees

  • Stefan Burr

Abstract

In 1821, John Jackson published this mathematical conundrum in a book of problems called Rational Amusement for Winter Evenings [4]. 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).

Keywords

Parametric Representation Projective Transformation Artful Computer Program Winter Evening Natural Urge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Burr, S. A.; Grünbaum, B.; and Sloane, N. J. A. 1974. The Orchard Problem. Geometriae Dedicata 2: 397–424.CrossRefGoogle Scholar
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    Grünbaum, B. 1972. Arrangements and Spreads. Providence, R.I.: Amer. Math. Soc.Google Scholar
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    Jackson, J. 1821. Rational Amusement for Winter Evenings. London: Longman, Hurst, Rees, Orme, and Brown.Google Scholar
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    Kelley, L. M., and Moser, W. O.J. 1958. On the Number of Ordinary Lines Determined by n Points, Canad. J. Math. 10: 210–219.CrossRefGoogle Scholar
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    Sylvester, J. J. 1886. Problem 2572. Math Questions from the Educational Times 45: 127–128.Google Scholar

Copyright information

© Wadsworth International 1981

Authors and Affiliations

  • Stefan Burr
    • 1
  1. 1.City University of New YorkUSA

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