So How's Your Hex Life?

Though curves may be cute, 
And sexy, to boot, 
Their plainness just leads me to yawn, 
But ask for designs, 
With six perfect lines, 
And I'll give you the bold hexagon!The Bard of beBee

OK, I can read your minds.  

"This time Boddie's lost it and gone completely start raving mad!  What's all this nonsense about sexy curves versus six sided steel symbols?  Is this an updated version of that old pseudo-Scots TV commercial for tools, 'You canna hand a man a grander spanner'?"

Well, I promise you, there are no tools in this blog ..... other than the one who's writing it!

No, rather I'm about to show you that there is a certain beauty, even sexiness, about six straight lines of virtually identical length,  linked in rotation and forming six congruent angles between each successive pair, each of 120 degrees (or for the mathematically more astute, 2xPi /3 radians). 

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Before I proceed further, I really need to go back several months to when quite a few of our more esteemed bee bloggers were praising the "curves and slings of outrageous architecture", whereas I was languishing inside a flimsy fortress, fabricating a somewhat limp defence of the engineering profession, the poor sods who have to build these fantasmagorical flourishes of the architect's imagination.

The congratulatory, curve-commending comments were flying fast and free, backwards and forwards, like a fiddler's elbow. And there was many the sage who, in awesome appreciation of the natural beauty of these arches, bends and wiggles, boldly pronounced that .....  

"There are no straight lines in nature."
the many and the multitudinous, yet mistakingly misdirected

Well, here's the rub, after some not inconsiderable research, I am about to reveal to you, my precious and previously misdirected readers, that there are many, many straight lines in nature, and the most amazing, astounding, astonishing and awe-inspiring of them are to be found in neatly interlocking layers of hexagons.

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Let me then introduce you to the fascination of the naturally occurring hexagon, as revealed by Mother Nature and her wonderful world of creatures and natural phenomena.

But first, the most obvious on this platform of buzzing apiarists, and perhaps the most fascinatingly and fastidiously formed and fabricated ..... 

Yes, my hive hugging heroes, the humble honey bee stores honey (along with the occasional queen bee's eggs and pollen) in perfectly hexagonal honeycombs. But are these little winged workers "heaven-intructed mathematicians", as William Kirby would have had us believe in 1852, or, as Darwin suspected, are they merely using their evolved and inherited instincts?

Wouldn't circular cross sectional units (ie cylinders) be much simpler for them to construct, even though this would leave heaps of gaps?  Or how about cells constructed of equal sided triangles or squares if they have an affinity with straight sided edges, and if all of the plane being constructed is to be used for storage? 

Well we now know, through mathematics and engineering verification, that hexagonal cells require the shortest total wall length and, furthermore, according to such modern research, that the hexagon uses the least amount of material to hold the most weight. Not bad for an insect that hasn't had any formal mathematics tuition. Or is there something more 'natural' being formed here?

Perhaps Mother Nature just naturally loves making hexagonal arrays of cells? Let's look at some more samples from nature.

1. Bubble Rafts

2. Columnar Basalt

There are many famous examples around the world of how basalt cools from its original molten lava to form hexagonal columns.  The pictures above are from the Giant's Causeway (in Northern Ireland), and then there's Fingal's Cave off the west coast of Scotland.  

The same natural cooling process also applies to drying mud or cracking paint or the cracking (as no doubt observed by our Canadian friends) in permafrost.

And Mother Nature does all this without a batchelor's degree in science, technology, engineering or mathematics (STEM), not to mention a master's or doctorate.

3. Turtles and Giraffes

The various units comprising the individual components and patterns of animals like the turtle and giraffe are predominantly hexagonal, albeit somewhat different in size and sometimes plus or minus a side or two, but it would appear that again Mother Nature is utilising the most efficient geometrical patterns to cover curved surfaces. 

4. What Else?

And I haven't even touched upon the following natural hexagons:

• the cellular structure of insect eyes, such as the dragonfly; or
• the magical shapes of snowflakes; or
• the carbon chains, such as present in our DNA and the nicely packed organic material comprising our flesh; or, slightly further afield
• the cloud formation above the North Pole of Saturn - "beam me up, Scotty!"

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Now let's be quite clear. I'm not saying that curves aren't worth contemplating, nor that they're not candidates for clever and cost effective construction.  After all arches, domes, arcades, vaults and viaducts, all curvaceous construction complexities, have been features of grand architecture for thousands of years. 

Furthermore, I'm not saying that curves have no point. 

But let's give Mother nature her due and accept that, when it comes to economy of effort, maximising available space, and increasing strength and stiffness while minimising increase in weight, there's nothing like the HEXAGON. After all, 6 trillion honey bees, worldwide, can't be wrong, can they?

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Useful Links

When not researching the weird or the wonderful, the comical or the cultured, the sinful or the serious, I chase my creative side, the results of which can be seen as selected photographs of my travels on my website at:

http://ken-boddie.squarespace.com

The author of the above, Ken Boddie, besides being a sometime poet and occasional writer, is an enthusiastic photographer, rarely leisure-travelling without his Canon, and loves to interact with other like-minded people with diverse interests.

Ken's three day work week (part time commitment) as a consulting engineer allows him to follow his photography interests, and to plan trips to an ever increasing list of countries and places of scenic beauty and cultural diversity.