Science Dragonfly's Eye


Mike Sterling for Canadian Community News

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One of the wonders of nature is the Dragonfly's eye, which is made up of hexagons like the beehive.

Why the hexagon?  For centuries researchers recognized that the hexagon seemed to have the right stuff, but why not another shape?

It came to be known that the hexagon was THE shape to achieve certain results that are best explained by an example.

Suppose that you had a floor that was let's say square.  The exact shape is not vital.  Suppose further that you wished to tile the floor in a consistent uniform pattern of a single shape and use the least mortar.  And  suppose further that you wanted the mortar to be at least some minimum width for strength purposes.  What shape would completely cover the area and use the least mortar?  The answer is the hexagon.  The proof of this fact took a long time to achieve, even though people believed it to be true..

Bees know it and so do chicken wire manufacturers. So how do bees know it?  How do Dragonflies know it?  The answer may be in a process that involves things called 'attractors'.  Processes tend to go toward a solution that is simple and economical.

Let's take into consideration 100 chicken wire manufacturers over a 100 year period.  Suppose that each company could buy the raw material at about the same price and wished to make the chicken wire so that it looked regular, was strong and used the least material to tessellate the area of the wire screen that would be sold in rolls.

It's clear that a company that used circles of the same radii would soon go out of business.  Another company might use squares and they too would not do well. The wire would be weak and use too much material.  Another might decide on triangles, but they too would fail due to using too much material, even though they would have good strong overall mesh. 

 Over time a few companies would survive and they would make their chicken wire out of hexagons.  So, if the companies had equally competent management, the winner would be the companies using hexagons with good management.

Hexagons are the simplest solution and the winners were attracted to them for cost and functional reasons.  So too does nature get attracted to the simple solutions.  You can see it in the workings of the Dragonfly's eye and the Sunflower.  How are they related?  See the video below to get an idea.  Click Here

Let's look at another example. NASA is putting a giant telescope way, way out in space.  It's going to be a replacement for the Hubble.  It will orbit the sun at the pace of the earth, but will be very far out.  The mirror is not one mirror because it would be too bulky, too fragile and too hard to polish to the right tolerance. 

NASA's James Webb Space Telescope Hexagonal Mirrors

NASA Engineers selected the hexagon for the shape of individual mirrors that form a matrix.  They need to be packed tightly together and need to be strong.  The hexagon is the obvious choice.  The new telescope will have a short life. 

If sometime in the future, space aliens come upon it, will they be surprised by its shape?  If they have an advanced spacecraft, they will not be surprised at all.   They will think..... "well, whoever built this thing selected the obvious shape."

So why are we so surprised about the beautiful Dragonfly's eye?  The marvel is that it is so connected to other attractors like the golden ratio.


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Monday, March 05, 2012