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Magic Hexagons — Magic Moments

Published online by Cambridge University Press:  01 August 2016

David King  and
John Baker
David King
Affiliation:
8 Fieldsend Close, Mottram Rise, Stalybridge SK15 2UF
John Baker
Affiliation:
214 Tarata Road, Guanaba, Queensland, Australia 4210
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Extract

A ‘magic’ hexagon has rows of numbers in three directions that add to the same total. It is possible to construct such a hexagon from a honeycomb array of hexagons and from an array of triangles (Figure 1). There is known to be only one magic hexagon formed from hexagons. However, numerous magic arrangements are possible for the hexagon of triangles and these arrangements have many additional interesting properties. In this article we give the reasons why such configurations are possible, we look at the number of arrangements possible when there are 2 triangles on each side of the hexagon and we show that in general the arrangements are balanced in many ways – including that they are physically balanced, a property we call ‘magic moments’.

Type
Articles
Information
The Mathematical Gazette , Volume 90 , Issue 518 , July 2006 , pp. 235 - 248
Copyright
Copyright © The Mathematical Association 2006

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References

1. Trigg, C. W. A Unique Magic Hexagon, Reer. Math. Mag., (January 1964)Google Scholar
2. Bolt, B. Eggleton, R. and Gilks, J. The Magic Hexagram, Math. Gaz. 75 (1991), pp 141–142.Google Scholar
3. Dudeney, H. E. Amusements in Mathematics, Thomas Nelson (1917) pp. 119–127.Google Scholar
4. Andrews, W. S. Magic Squares and Cubes, Open Court Publishing (1917) chapters IV and VIII.Google Scholar
5. Weisstein, E. W. Magic Square, From Math World-A Wolfram Web Resource, http://mathworld.wolfram.com/MagicSquare.html (2004).Google Scholar
6. Baker, J. E. Hexagonia, from Natural Maths, http://www.naturalmaths.com.au/hexagonia (2004),Google Scholar
7. Baker, J. E. and King, D. R. The use of visual schema to find properties of a hexagon, Visual Mathematics (Vol. 6, No. 3, 2004) at http://members.tripod.com/vismath.Google Scholar
8. MacMahon, P. A. Proceedings of the Royal Institution of Great Britain, (1892) Vol 17, No. 96, pp 50–61.Google Scholar
9. King, D. R. Hall of Hexagons, http://www.drking.plus.com/hexagons (2004).Google Scholar