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 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 can be stored and ripened suitably

until it turns into honey.

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 of honey

to produce just 1 ounce of wax.

So they don't want to waste it.

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.

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.

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.