Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Saturday, April 21, 2007

Carrying On

A real world honeycomb! Observe that the diagram from lesson 43 is actually a hexagonal tiling of the plane. For larger NxN matrices there are more central hexagons on the largest scale. By tweaking the geometry one could make the pattern regular as in the bee's honeycomb.


Blogger nige said...

Wow! That hexagonal honeycomb is identical to the vacuum structure in James Clerk Maxwell's famous 1861 papers on electromagnetism: Fig 2 on page 38 (by PDF reader pagination, not numbers on scanned pages) of On Physical Lines of Force. By J.C. Maxwell, Professor of Natural Philosophy in King's College, London, Part II. - The Theory of Molecular Vertices applied to Electric Currents, available online here. Maybe Maxwell's model was based on the buzz of a beehive?

April 22, 2007 12:47 AM  
Blogger Kea said...

Hi Nigel. Yes, that's true. I was going to mention Maxwell's paper, but I am glad that you have spotted it beforehand. Thanks for the link.

April 22, 2007 10:06 AM  
Blogger Doug said...

I do not have access to this paper, but look at a 1986 abstract for mathematical modeling of the honeycomb with Fourier Transformation:

Journal of Mathematical Biology
'Mathematical model of honeycomb construction' MR Bell et al

April 23, 2007 12:06 AM  
Blogger L. Riofrio said...

This suggests a connection with that hexagon on Saturn's North pole, which is a location of magnetic fields.

April 24, 2007 2:48 PM  

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