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Honeybees are fascinating creatures for a number of reasons:
蜜蜂是一种非常迷人的生物，原因有如下几个：
their incredible work ethic, the sugary sweet syrup they produce and their intricate social structure.
它们有难以置信的工作准则，它们能酿造含糖的甜浆，以及它们错综复杂的社会结构。
But another reason is that honeybees are, in fact, excellent mathematicians.
然而事实上，还有另外一个原因是蜜蜂是出色的数学家。
Scientists claim the tiny insects can calculate angles, and can even comprehend the roundness of the Earth.
科学家们声称这些小虫子们能计算角度，甚至意识到地球是圆的。
But there's particular mathematical bee genius behind the most important aspect of honeybee life: the hive.
不过蜜蜂还有一个特殊的数学天赋，这也是蜜蜂一生中最重要的一方面：蜂巢。
Just like humans, bees need food and shelter to stay alive.
就像人类一样，蜜蜂也需要食物和居所来维持生存。
The hive is not only the bees' home, but doubles as a place to store their honey.
蜂巢不仅仅是蜜蜂们的家，还是它们贮藏蜂蜜的地方。
Since it's so central to survival, honeybees have to perfect the hive's architectural design.
因为这是生存的核心部分，蜜蜂们不得不让他们蜂巢的建筑设计完美无瑕。
If you examine any piece of honeycomb, you'll see that it's constructed from tightly packed hexagonal, or six-sided, cells.
如果你考量蜂房的任何一处，你会发现它是由紧凑的六角或六边小巢室构成的。
Of all the possible designs, why do honeybees choose this one?
在所有可能的设计里，为什么蜜蜂们要选择这个呢？
To understand, you need to think like a bee.
为了找到答案，你必须要像一只蜜蜂一样去思考。
Bees need a secure place for their entire colony to live.
蜜蜂们需要一个安全的地方来支撑整个群体的生活。
Similarly, there needs to be a place where their nectar can be stored and ripened suitably until it turns into honey.
同样，它们需要一个地方使它们的花蜜可以适宜地贮藏起来，并且适当成熟，直到变成蜂蜜。
That means there's a need for some serious space efficiency.
那意味着有效利用空间的重要性。
A good solution is to build little storage units, or cells, just big enough for a bee to fit into,
一个好的解决办法是建造小的贮藏单元或者小巢室，仅仅能让一只蜜蜂进出就足够了，
which can also double as the containers in which nectar is stored: The bees' very own honey jars.
它同时还可以充当贮藏花蜜的容器：蜜蜂们自己的蜂蜜罐子。
The next thing, is to decide what the little cells should be made out of.
接下来的事情是决定这些小巢室应该用什么来建造。
Bees don't have beaks or arms to pick up things, but they are capable of producing wax.
蜜蜂们没有喙或者手臂来拿起物品，但是他们有能力生产蜂蜡。
The thing is, producing it is a lot of hard work.
问题是，生产蜂蜡是一项繁重的工作。
Bees have to consume 8 ounces of honey to produce just 1 ounce of wax. So they don't want to waste it.
蜜蜂们不得不消耗8盎司的蜂蜜来生产仅仅1盎司的蜂蜡。所以他们不想浪费。
So, they need a design that allows them to store the largest possible amount of honey using the least amount of wax.
因此他们需要一个允许他们贮藏最大量蜂蜜的设计，同时只用最少的蜂蜡。
What shape does that? Imagining for a minute that all bees had to attend architecture academy and go to math class.
那是个什么形状呢？想象一下所有的蜜蜂不得不去建筑学院上数学课。
Let's say they asked their geometry teacher,
让我们假设，它们问它们的几何老师，
'What shape would give us the most space to store our honey, but require the least amount of wax?'
“哪种形状可以给我们最大的空间来贮藏我们的蜂蜜，但是只需要最少量的蜂蜡呢？”
And then geometry teacher replied, 'The shape that you're seeking is the circle.'
然后几何老师回答道：“你们寻找的形状是圆形。”
Leaving the bees to return to their trial construction site and begin building their honeycomb using circular cells.
离开的蜜蜂们回到它们自己的试验建造基地，开始用一个个的圆形小巢室来建造它们的蜂房。
After a while, some of them might have noticed a problem with their design: small gaps between the cells.
不一会儿，一些蜜蜂可能发现了它们设计上的一个问题：小巢室之间的小缝隙。
'We can't even fit in there! That's wasted space!' they might have thought.
“我们甚至不能进出那里了！那样是浪费空间！”它们可能会这样想。
So, ignoring the geometry lesson, and taking matters into their own hands,
所以，忽略几何课，它们决定自己处理这个问题，
the bees went back to the drawing board to rethink their beehive design.
这些蜜蜂们回到画板上，重新思考它们蜂巢的设计。
One suggested triangles, 'We can use triangles. Look! They fit together perfectly.'
有一只蜜蜂建议用三角形，“我们可以用三角形。看！三角形之间匹配得很完美。”
Another bee suggested squares. Finally, a third bee piped up and said,
另一只蜜蜂建议用正方形。最后，第三只蜜蜂高声说道：
'Pentagons don't seem to work, but hexagons do!
“五边形好像不行，但是六边形可以！
We want the one that will use the least amount of wax and be able to store the most amount of honey.
我们需要一个形状使用最少量的蜂蜡并且可以贮藏最大量的蜂蜜。
Yes, I think that's the hexagon.' 'Why?' 'It looks more like the circle than the others.'
是的，我认为那是六边形。”“为什么？”“它比其他形状看起来更像圆形。”
'But how do we know for sure?'
“但是我们怎么能确定呢？”
To find out, the industrious insect architects calculated the areas of the triangle, the square and the hexagon
为了找到答案，勤劳的昆虫建筑师们计算了三角形、正方形和六边形的面积
and found that the hexagon was, in fact, the shape that gave them the most storage space.
它们发现事实上六边形可以提供最多的贮藏空间。
They agreed on an ideal size and returned to work.
它们同意这个完美的形状并且重新回到工作中。
The space efficient comb that is a bee's trademark today,
如今，这个有效利用空间的蜂房是蜜蜂的标志，
is probably the result of this trial and error, but over long periods of evolutionary history. However, it paid off.
它可能是不断尝试和更正的结果，而在长期的进化过程中，蜜蜂取得了成功。
Peek into any hive -- with your protective goggles and netting on, of course -- and you'll see the end result:
观察一下任何一个蜂巢，当然要带上你的护目镜和网状面罩，你会看到最终的结果：
a beautiful compact honeycomb that any architect would have be proud to design.
一个美丽且紧实的蜂房，任何一个建筑师都将引以为傲的设计。
