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易　04分・・180wpm（母国では標準の説明速度）　 　2015/10/31 新出

字幕：上の動画は開始後 で字幕On/Off､ で言語選択。文字ｻｲｽﾞはｵﾌﾟｼｮﾝから｡
　　　　動画を見るとき、パソコンで画面全体を拡大するときれい。

★下記英文はブラウザ クロムのマウスオーバー辞書が使えます｡

Honeybees are fascinating creatures for a number of reasons: their incredible work ethic, the sugary sweet syrup they produce and their intricate social structure. But another reason is that honeybees are, in fact, excellent mathematicians.

Scientists claim（主張する） the tiny insects can calculate angles, and can even comprehend the roundness of the Earth. But there's particular mathematical bee genius behind the most important aspect of honeybee life: the hive. Just like humans, bees need food and shelter to stay alive. The hive is not only the bees' home, but doubles as a place to store their honey.

Since it's so central to survival, honeybees have to perfect the hive's architectural design. If you examine any piece of honeycomb, you'll see that it's constructed from tightly packed hexagonal, or six-sided, cells. Of all the possible designs, why do honeybees choose this one? To understand, you need to think like a bee. Bees need a secure place for their entire colony to live. Similarly, there needs to be a place where their nectar（花蜜） can be stored and ripened suitably until it turns into honey.
　nectar：本来は花蜜。　果肉飲料の意味もある（ネクター：森永の商標だったが解放）

That means there's a need for some serious space efficiency. A good solution is to build little storage units, or cells, just big enough for a bee to fit into, which can also double as the containers in which nectar is stored: The bees' very own honey jars.

The next thing, is to decide what the little cells should be made out of. Bees don't have beaks or arms to pick up things, but they are capable of producing wax. The thing is, producing it is a lot of hard work. Bees have to consume 8 ounces（230g） of honey to produce just 1 ounce（30g） of wax. So they don't want to waste it.
　　１ ounce [áuns]＝28.35g、 約30ｇで覚えるとよい

So, they need a design that allows them to store the largest possible amount of honey using the least amount of wax. What shape does that? Imagining for a minute that all bees had to attend architecture academy and go to math class. Let's say they asked their geometry teacher, "What shape would give us the most space to store our honey, but require the least amount of wax?" And then geometry teacher replied, "The shape that you're seeking is the circle."

Leaving the bees to return to their trial constrution site and begin building their honeycomb using circular cells. After a while, some of them might have noticed a problem with their design: small gaps between the cells. "We can't even fit in there! That's wasted space!" they might have thought.

So, ignoring the geometry lesson, and taking matters into their own hands, the bees went back to the drawing board to rethink their beehive design. One suggested triangles, "We can use triangles. Look! They fit together perfectly." Another bee suggested squares. Finally, a third bee piped up and said, "Pentagons don't seem to work, but hexagons do! We want the one that will use the least amount of wax and be able to store the most amount of honey.
　平面充填の正多角形は、三角形、四角形、六角形の三つのみ。（正でなければ複雑）

Yes, I think that's the hexagon." "Why?" "It looks more like the circle than the others." "But how do we know for sure?" To find out, the industrious insect architects calculated the areas of the triangle, the square and the hexagon and found that the hexagon was, in fact, the shape that gave them the most storage space.

They agreed on an ideal size and returned to work. The space efficient comb that is a bee's trademark today, is probably the result of this trial and error, but over long periods of evolutionary history. However, it paid off.
　pay off：自動詞では「うまくいく」。　他動詞では「完済する」、「清算解雇する」

Peek into any hive -- with your protective goggles and netting on, of course -- and you'll see the end result: a beautiful compact honeycomb that any architect would have be proud to design.