see notes below.

 Standing Patagonia  Wheel Mandala of magnetic 1992 British 2p and 2011 British 5p coins
Standing Patagonia Wheel Mandala of magnetic 1992 British 2p and 2011 British 5p coins.
The 36 coins in this intriguing example of circle packing, are held together by the magnetic field generated by two Magic Penny magnets, reinforced by a neodynium magnet, below. No adhesives have been used.

This "nearly mathematically-perfect" pentagonal-centred array is made of coins of only two different diameters. It is well known that six 5p coins will pack exactly around another 5p coin to form a hexagonal rose. The fact that, five 2p coins will pack almost exactly around one 5p coin to form a pentagonal rose is providing considerable stimulus for packing creatitvity and geometrical investigation.

The diameter of the central 5p coin is 18.0mm. The diameter of the 2p coin is 25.9mm giving a ratio of approximately 1.439.

Using simple geometry, the ratio of diameters of a pentaganol rose of perfect fit is approximately 1.426, a value within 1 percent of the ratio of the actual coins!

Can such a packed circular pentagonal-centred array of 36 coins of only two different diameters ever be mathematically perfect?

If the array was made of coins of three different diameters what would the ratios of diameters have to be for the best fit? What would be the diameter of the smallest such perfect array with a 5p coin in the centre?
(The fact that the edge of the 5p coin is milled, whereas that of the 2p is smooth can be ignored!)

Keep watching -there is much much more to come!

© Marķa Victoria Canullo
Robin Linhope Willson
Ciencias y Artes Patagonia - Magic Penny Trust, 2012