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Honeybees are fascinating creatures [br]for a number of reasons:

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their incredible work ethic,

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the sugary sweet syrup they produce

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and their intricate social structure.

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But another reason is [br]that honeybees are, in fact,

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excellent mathematicians.

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Scientists claim the tiny insects [br]can calculate angles,

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and can even comprehend[br]the roundness of the Earth.

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But there's particular[br]mathematical bee genius

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behind the most important aspect [br]of honeybee life: the hive.

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

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The hive is not only the bees' home,

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but doubles as a place[br]to store their honey.

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Since it's so central to survival,

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honeybees have to perfect[br]the hive's architectural design.

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If you examine any piece of honeycomb,

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you'll see that it's constructed from

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tightly packed hexagonal, [br]or six-sided, cells.

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Of all the possible designs,

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why do honeybees choose this one?

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To understand, you need[br]to think like a bee.

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

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Similarly, there needs to be a place

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where their nectar can [br]be stored and ripened suitably

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until it turns into honey.

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That means there's a need[br]for some serious space efficiency.

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

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just big enough for a bee to fit into,

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

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The bees' very own honey jars.

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

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Bees don't have beaks[br]or arms to pick up things,

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but they are capable of producing wax.

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

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Bees have to consume 8 ounces of honey

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to produce just 1 ounce of wax.

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So they don't want to waste it.

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So, they need a design [br]that allows them to store

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the largest possible amount of honey

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using the least amount of wax.

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What shape does that?

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Imagining for a minute [br]that all bees had to

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attend architecture academy [br]and go to math class.

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Let's say they asked [br]their geometry teacher,

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"What shape would give us[br]the most space to store our honey,

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but require the least amount of wax?"

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And then geometry teacher replied,

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

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Leaving the bees to return[br]to their trial construction site

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and begin building their honeycomb[br]using circular cells.

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After a while, some of them [br]might have noticed

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a problem with their design:

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small gaps between the cells.

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"We can't even fit in there! [br]That's wasted space!"

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they might have thought.

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So, ignoring the geometry lesson,

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and taking matters into their own hands,

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the bees went back to the drawing board

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to rethink their beehive design.

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One suggested triangles,

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

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Another bee suggested squares.

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Finally, a third bee piped up and said,

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"Pentagons don't seem to work, [br]but hexagons do!

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We want the one that will use [br]the least amount of wax

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and be able to store [br]the most amount of honey.

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Yes, I think that's the hexagon."

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"Why?"

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"It looks more like the circle [br]than the others."

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"But how do we know for sure?"

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To find out, the industrious [br]insect architects

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calculated the areas of the triangle,[br]the square and the hexagon

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and found that the hexagon was, in fact,

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the shape that gave them[br]the most storage space.

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They agreed on an ideal size [br]and returned to work.

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The space efficient comb that [br]is a bee's trademark today,

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is probably the result [br]of this trial and error,

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but over long periods [br]of evolutionary history.

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However, it paid off.

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Peek into any hive --

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with your protective goggles [br]and netting on, of course --

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and you'll see the end result: [br]a beautiful compact honeycomb

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that any architect would have [br]be proud to design.