Periodic forests of stunted trees

@article{Miller1970PeriodicFO,
  title={Periodic forests of stunted trees},
  author={J. P. Miller},
  journal={Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences},
  year={1970},
  volume={266},
  pages={111 - 63}
}
  • J. P. Miller
  • Published 1970
  • Mathematics
  • Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
We may define a forest of stunted trees as follows: Consider an infinite background of nodes at the vertices of an infinite plane tessellation of equilateral triangles., and start from a straight line of nodes at unit distance apart, which we shall consider as the ground; other parallel lines of nodes are then spaced at successive levels of linearly increasing heights above the ground. Any node may be live (if a tree passes through it) or vacant otherwise. Any live node may give rise to a… Expand
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On rotational tessellations and copses
  • J. C. Miller
  • Mathematics
  • Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1980
This paper is a self-contained sequal to Miller (1970), entitled ‘Periodic forests of stunted trees’. It is concerned with ‘Copses’ and ‘Tessellations’ based on an infinite background of nodes at the… Expand
Periodic forest whose largest clearings are of size 3
  • H. ApSimon
  • Mathematics
  • Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1970
Miller has observed that there are a finite number of periodic forests whose largest clearings are of size 1 or 2, and an infinite number whose largest clearings are of size 4. In this note the basic… Expand
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Periodic forests whose largest clearings are of size n ≥ 4
  • H. ApSimon
  • Mathematics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1970
The number of distinct periodic forests whose largest clearings are of size n is known to be 1 (n = 1), 1 (n = 2), 12 (n = 3), and ∞ (n = 4). In this note it is shown that there exist an infinity of… Expand
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References

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Periodic forest whose largest clearings are of size 3
  • H. ApSimon
  • Mathematics
  • Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1970
Miller has observed that there are a finite number of periodic forests whose largest clearings are of size 1 or 2, and an infinite number whose largest clearings are of size 4. In this note the basic… Expand
An Introduction to the Theory of Numbers
This is the fifth edition of a work (first published in 1938) which has become the standard introduction to the subject. The book has grown out of lectures delivered by the authors at Oxford,… Expand
On a conjecture concerning the primes
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