Honeybees are fascinating creatures  for a number of reasons:

蜜蜂會是如此迷人的生物有如下理由：

But another reason is  that honeybees are, in fact,

Scientists claim the tiny insects  can calculate angles,

科學家聲稱這些小昆蟲可以計算角度，

and can even comprehend the roundness of the Earth.

But there&#39;s particular mathematical bee genius

behind the most important aspect  of honeybee life: the hive.

就藏在他們的生活環境中：蜂巢。

Just like humans, bees need food and shelter to stay alive.

就像人類，蜜蜂需要食物與住所。

but doubles as a place to store their honey.

honeybees have to perfect the hive&#39;s architectural design.

蜜蜂需要設計一個完美的建築結構。

you&#39;ll see that it&#39;s constructed from

tightly packed hexagonal,  or six-sided, cells.

To understand, you need to think like a bee.

想要了解，你必須從蜜蜂的角度思考

Bees need a secure place  for their entire colony to live.

蜜蜂需要一個安全的地方讓他們群體生存。

where their nectar can  be stored and ripened suitably

That means there&#39;s a need for some serious space efficiency.

這意味著他們要一個可充分利用的空間

A good solution is to build little storage units, or cells,

好的解決方法就是建造一個小儲藏處，

which can also double as the containers in which nectar is stored:

The next thing, is to decide what the little cells should be made out of.

接著，要決定這些小房間應該用什麼做成，

Bees don&#39;t have beaks or arms to pick up things,

蜜蜂並沒有鳥喙或手臂來撿東西。

The thing is, producing it  is a lot of hard work.

So, they need a design  that allows them to store

允許他們儲存最大數量的蜂蜜，

Imagining for a minute  that all bees had to

attend architecture academy  and go to math class.

Let&#39;s say they asked  their geometry teacher,

讓我們假設他問他們的幾何學老師。

&quot;What shape would give us the most space to store our honey,

什麼形狀會提供最大的空間來儲存蜂蜜，

but require the least amount of wax?&quot;

&quot;The shape that you&#39;re seeking  is the circle.&quot;

Leaving the bees to return to their trial constrution site

and begin building their honeycomb using circular cells.

而且開始用圓形小格子來建造蜂巢。

After a while, some of them  might have noticed

會有些小縫隙在圓形小格子之間。

That&#39;s wasted space!&quot; they might have thought.

&quot;We can use triangles. Look!  They fit together perfectly.&quot;

我們可以用三角形。注意，三角形可以完美的結合在一起。

&quot;Pentagons don&#39;t seem to work,  but hexagons do!

五邊形沒辦法不留空隙，但六邊形可以。

We want the one that will use  the least amount of wax

我們需要一個使用最少數量的蠟

and be able to store  the most amount of honey.

Yes, I think that&#39;s the hexagon.&quot;

&quot;It looks more like the circle  than the others.&quot;

他看起來比其他的形狀更像圓。

但我們怎麼確定這形狀最好呢？

To find out, the industrious  insect architects

為了了解，這些勤勞的蜜蜂建築師

calculated the areas of the triangle, the square and the hexagon

分別計算三角形、正方形和六邊形的面積，

the shape that gave them the most storage space.

They agreed on an ideal size  and returned to work.

他們都同意這個理想的設計而且回到工作場地。

The space efficient comb that  is a bee&#39;s trademark today,

這個高度利用的空間是蜜蜂的特徵。

is probably the result  of this trial and error,

也許這結果是透過多次的嘗試與錯誤才得到，

but over long periods  of evolutionary history.

with your protective goggles  and netting on, of course --

and you&#39;ll see the end result:  a beautiful compact honeycomb

你會看到到這最終的成果：一個完美緊密的蜂巢，

that any architect would have  be proud to design.

任何設計師都會對這設計感到佩服。

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