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why a hexagon?

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kazmcc 

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very good.....didn't understand a word at one point, but still, from what i did understand, very interesting lol
 

Skyhook 

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seems to be all looking at most efficient way to store honey, overlooking the fact that the cells hold larvae as well. If you had triangular cells, wouldn't you get triangular bees? And everyone knows that only happens in toblerone's apiaries...
 

Firegazer 

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Their article is mainly about the maths, which looks very elegant.

It seems to be a bit confused about the bee aspects though, which is strange considering they do mention the use of bubbles to check what happens when surface tension, alone, determines shapes.

Not surprisingly, the bubble mixture 'builds' hexagons, and even 'builds' the bottom of the cells (where they interlock with the reversed layer of cells) in the most efficient shape, predicted by the maths.

This isn't anything being clever, or 'learning' to build things efficiently - it's just physics. The molecules pull towards each other and any configuration other than the 'least tension' one will tend to move molecules in the direction of the 'least tension' one until everything reaches a balanced position. The only trick is to see the bee's comb as a liquid, rather than a solid. If it were a liquid, like the soap bubbles, the shapes would 'make' themselves.

Bubbles don't sit around thinking/considering and neither (in this case) do the bees. In Tautz's book, he points out that if a bee makes each cell by constructing a tube, using itself as the template, the tubes will naturally stack in a hexagonal array - try it with loo-roll middles. If those wax cylinders are then heated up a bit, to a temperature where they can flow - just slowly, and not for very long - they will form beautiful flat sided hexagons. The same happens at the bottom of the cells.

The bee has (apparently) 850,000 neurons in its body, most of which are involved with its complex eyes - at least 3 colour pixels per eye segment. It's not thinking about maths, it's following a simple rule-set to do this building. This might work:

1) need more space;
2) go to the edge of the comb;
3) climb into the cell;
4) if I fit in, start building a new cell next to this one;
5) add to the walls into I fit in;
6) if a cell I inspect has round walls and it isn't close to the edge, heat it up for a bit;

I think they do some strengthening of the top surface of the cell to give better rigidity too, but the hexagonal perfection of the comb is brought about by simple rule following, heating and basic physics.

This is the really clever bit, in my opinion: how instinctive behaviour coded into the bee's DNA sequence can produce something so efficient and perfect.

FG
 
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I can't get the link to work but if the item is about how hexagons are the most efficient way to sub-divide a surface it is not strictly correct. For an infinite plane it is true but for a surface with a boundary, e.g. a frame, then the most efficient system uses in places shapes which are just slightly different from a symetrical hexagon. The difference is only a fraction of a percent so the bees almost get it right!


I can't find a "proper" reference for this so Wiki will have to suffice: http://en.wikipedia.org/wiki/Circle_packing Look for the section called packing in bounded areas.
 

Firegazer 

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I think my argument is that they never build hexagons.

That would be too difficult for an insect with limited brain resources and lots of different behaviours to be capable of.

They build cylinders by rotating around, fitting the cell to their own body diameter, then warm things up to get a bit more overall volume, as hexagons form naturally. This is a very simple thing to do compared to building shapes in general and particularly compared to building different shapes according to some larger geographical context like 'edge of frame'.

FG

BTW checking up, it seems their eyes only account for 150,000 neurons or so, rather than the majority as I suggested - apologies.
 

Skyhook 

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This is the really clever bit, in my opinion: how instinctive behaviour coded into the bee's DNA sequence can produce something so efficient and perfect.
FG
And that, of course. applies to everything they do... which is why almost everything I learn about bees leaves me more and more amazed!bee-smillie
 

madasafish 

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And that, of course. applies to everything they do... which is why almost everything I learn about bees leaves me more and more amazed!

When human behaviour is also governed by our DNA, there is no cause for amazement.

See fibonacci sequences and the golden mean... which exists throughout nature.. (which determines human views of beauty)

I remember close packed hexgonal crystals from geology so hexagaons in beehives are only a duplication of mineral activity...
 

kazmcc 

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Wow, firegazer, thanks for explaining that to me......my mentor is going to be so stunned when I pop out that little pearl :) going to save it for when someone mentions the shape, miss big head lol
 

justme 

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Their article is mainly about the maths, which looks very elegant.

It seems to be a bit confused about the bee aspects though, which is strange considering they do mention the use of bubbles to check what happens when surface tension, alone, determines shapes.

Not surprisingly, the bubble mixture 'builds' hexagons, and even 'builds' the bottom of the cells (where they interlock with the reversed layer of cells) in the most efficient shape, predicted by the maths.

This isn't anything being clever, or 'learning' to build things efficiently - it's just physics. The molecules pull towards each other and any configuration other than the 'least tension' one will tend to move molecules in the direction of the 'least tension' one until everything reaches a balanced position. The only trick is to see the bee's comb as a liquid, rather than a solid. If it were a liquid, like the soap bubbles, the shapes would 'make' themselves.

Bubbles don't sit around thinking/considering and neither (in this case) do the bees. In Tautz's book, he points out that if a bee makes each cell by constructing a tube, using itself as the template, the tubes will naturally stack in a hexagonal array - try it with loo-roll middles. If those wax cylinders are then heated up a bit, to a temperature where they can flow - just slowly, and not for very long - they will form beautiful flat sided hexagons. The same happens at the bottom of the cells.

The bee has (apparently) 850,000 neurons in its body, most of which are involved with its complex eyes - at least 3 colour pixels per eye segment. It's not thinking about maths, it's following a simple rule-set to do this building. This might work:

1) need more space;
2) go to the edge of the comb;
3) climb into the cell;
4) if I fit in, start building a new cell next to this one;
5) add to the walls into I fit in;
6) if a cell I inspect has round walls and it isn't close to the edge, heat it up for a bit;

I think they do some strengthening of the top surface of the cell to give better rigidity too, but the hexagonal perfection of the comb is brought about by simple rule following, heating and basic physics.
This is the really clever bit, in my opinion: how instinctive behaviour coded into the bee's DNA sequence can produce something so efficient and perfect.

FG
This bit reminded me to ask, sorry off topic but, some of the comb in 1 of my hives has thickened top edges to the cells. Almost as if they had just started to seal them, but there are a lot in a patch that they've not used. Comb was built on small starter strips (as is most of mine) and is well below the starter strip. Any ideas anyone? Please. Di:.)?
 
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They have probably prepared the cells for the queen to lay in if these edges look matt coloured. It is normal and is a way of finding where the queen is likely to be near.
 
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Bent - but not necessarily mathematically...
 

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