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A mathematical question "Riddle"

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The question is:

Why do bees store its honey in hexagonal shapes? Why not a triangle? A square??

The answer is obtained mathematically.

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I gave it a bit of thought but then I Googled it. I won't spoil it for you guys, but it is quite interesting and actually not that complex.

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i cannot see your imageshack pictures :(

it's because when you put them altogether there's no wasted space unlike when you use circles. if you use other shapes the areas will be smaller.

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I read a bit about circle packing a while back and this reminded me of how hexagonal packing is the most efficient way of packing equal circles. Maybe it has something to do with that? :P I still haven't looked up the actual answer, BTW, if I get bored I might take another look at this tomorrow.

Edit: Also, to tile something like regular octagons, for example, on a plane would require extra squares in some spaces, as opposed to using hexagons, triangles or squares (I can't think of any others right now). Out of the three, hexagons seem like they would provide the most rigid structure since the way squares line up doesn't look like it would be quite as rigid, and tiling triangles would form hexagons out of the triangles anyway.

Edited by aldld

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Assumptions:

1- equilateral triangle is the most rigid geometrical shape and you can fit six of them in one a regular hexagon. Therefore in the end it will all be strong.

2- If my idea in part one is correct. Then the shape no matter if it is rotated it will be the same. I wanted to insert the Center of Gravity concept. But you only said mathematically

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Also to consider I'm pretty sure that I have observed that bunches of soap bubbles form hexagons as well. Memories are fuzzy so I could be wrong. So when packing a bunch of spheres that are attracted to form a solid shape it seems that hexagons are ideal. I guess that you would want to balance the max internal area that can be formed without losing space between the shapes.

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The answer is:

We have a triangle, a square, and a hexagon that have the same area.

The perimeter of the hexagon will be the shortest of them although it has the same area.

Now it is easily proven mathematically.

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Guest Positron

Ok, this is easy, but I'll post it anyways :D

21234 X 0.51235

Yeah, and of course no calculators...

Edited by Klaus.A

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Ok, this is easy, but I'll post it anyways :D

21234 X 0.51235

Yeah, and of course no calculators...

one? XD

edit: wait no, I thought it was 21234 X 0.51234

0.5 I really put some effort into this lol

Edited by rFumachi

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