their incredible work ethic,

有嚴格的工作原則、

the sugary sweet syrup they produce

生產甜蜜的糖漿、

and their intricate social structure.

還有錯綜複雜的社會結構。

But another reason is that honeybees are, in fact,

實際上還有另一個原因：

excellent mathematicians.

他們是優秀的數學家。

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.

甚至還了解地球是圓的。

But there's particular mathematical bee genius

他們最特別的數學天賦

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。

The hive is not only the bees' home,

蜂巢不單是蜜蜂的家，

but doubles as a place to store their honey.

但也是儲存蜂蜜的地方。

Since it's so central to survival,

因為生存空間如此重要

honeybees have to perfect the hive's architectural design.

蜜蜂需要設計一個完美的建築結構。

If you examine any piece of honeycomb,

如果你檢查蜂巢的任一部份

you'll see that it's constructed from

你會發現他們是由

tightly packed hexagonal, or six-sided, cells.

緊密排列的六邊形所構成。

Of all the possible designs,

在所有可能的設計中

why do honeybees choose this one?

為何蜜蜂要選擇這一個呢？

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。

Similarly, there needs to be a place

同理的，他們也需要一個地方

where their nectar can be stored and ripened suitably

使得採集的花蜜可以儲存

until it turns into honey.

待其成熟而變為蜂蜜。

That means there'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，

just big enough for a bee to fit into,

讓蜜蜂得以進出。

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

也可以儲存他們採集的蜂蜜。

The bees' very own honey jars.

這就是他們特有的蜂蜜罐。

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't have beaks or arms to pick up things,

蜜蜂並沒有鳥喙或手臂來撿東西。

but they are capable of producing wax.

但他們有能力可以製造蠟。

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

問題是製造蠟相當費工。

Bees have to consume 8 ounces of honey

蜜蜂需要消耗 8 盎司的蜂蜜

to produce just 1 ounce of wax.

來製造僅僅 1 盎司的蠟。

So they don't want to waste it.

因此不想要浪費蜂蜜。

So, they need a design that allows them to store

於是，他們需要一個設計

the largest possible amount of honey

允許他們儲存最大數量的蜂蜜，

using the least amount of wax.

且用最少的蠟。

What shape does that?

什麼形狀最適合呢？

Imagining for a minute that all bees had to

稍微想像所有的蜜蜂必須

attend architecture academy and go to math class.

參加建築與數學課程。

Let's say they asked their geometry teacher,

讓我們假設他問他們的幾何學老師。

"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?"

但用最少的蠟？

And then geometry teacher replied,

此時幾何學老師回答，

"The shape that you're seeking is the circle."

你在尋找的形狀是圓形，

Leaving the bees to return to their trial constrution site

讓我們回到他們的建築工地，

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

過了一陣子，有些蜜蜂察覺到

a problem with their design:

這樣的設計有些問題。

small gaps between the cells.

會有些小縫隙在圓形小格子之間。

"We can't even fit in there!

我們也無法使用這些小縫隙。

That's wasted space!" they might have thought.

他們覺得這些空間浪費了。

So, ignoring the geometry lesson,

所以，不管幾何學課程，

and taking matters into their own hands,

回到實務面來處理問題，

the bees went back to the drawing board

蜜蜂返回他們的建築設計圖，

to rethink their beehive design.

重新思考他們的蜂巢設計。

One suggested triangles,

其中一人建議用三角形，

"We can use triangles. Look! They fit together perfectly."

我們可以用三角形。注意，三角形可以完美的結合在一起。

Another bee suggested squares.

另一個蜜蜂提議正方形。

Finally, a third bee piped up and said,

最後，第三隻蜜蜂突然說：

"Pentagons don'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.

但可以儲存最多數量的蜂蜜。

Yes, I think that's the hexagon."

是的，我認為就是六邊形。

"Why?"

但為什麼呢？

"It looks more like the circle than the others."

他看起來比其他的形狀更像圓。

"But how do we know for sure?"

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，

and found that the hexagon was, in fact,

然後發現六邊形是

the shape that gave them the most storage space.

提供最大儲存空間的形狀。

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'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.

經過長時間演化的考驗。

However, it paid off.

不管怎樣，這是值得的。

Peek into any hive --

稍微偷瞄蜂巢的任一個地方，

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

當然，要記得戴上護目鏡，

and you'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。