Update 2000-07-05

Magic Penny Golden Hexagon of Patagonia (10 Centavo Argentina)

For any objects of circular cross section, the same number can be arranged in a close packed regular hexagon of side x objects, or in a square grid of side y objects, provided the following equation is obeyed, and x and y are integers.

On 2000 June 28 the first seven numbers of the Magic Penny Patagonia Golden Hexagon Series were submitted to NJA (Neil) Sloane for possible inclusion in his renowned Encyclopedia of Sequences hosted on the ATT server. An email was also sent to Steven Finch of Mathsoft asking if he had any knowledge of the series being published previously. As a result of the ensuing correspondence in which we learnt that Martin Gardner had referred to this series of numbers in his book "Time Travel and other Mathematical Bewilderments (Freeman NY 1988), the series has now been expanded and several probably hitherto unpublished numbers have been posted on the internet (2000-07-04).

By 0800 hrs the following day (2000-07-05) we had obtained a photocopy of Chapter Two of Gardner´s book from the library of Brunel University, London. The chapter entitled "Hexes and Stars" is beautifully written and illustrated and must be essential reading for all interested in mathematical patterns. The mathematics underlying the series is all there, together with the above equation. It is gratifying that playing with coins can lead to similar conclusions and diagrams. Thank you Martin Gardner and Neil and Steven and Brunel. More information will be posted here once we have checked the copyright with the publishers.

see www.research.att.com/~njas/sequences (A 001570, A001922, A006051)
      www.mathsoft.com

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