Why do honeybees love hexagons? - Zack Patterson and Andy Peterson

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Honeybees are some of nature's finest mathematicians. Not only can they calculate angles and comprehend the roundness of the earth, these smart insects build and live in one of the most mathematically efficient architectural designs around: the beehive. Zack Patterson and Andy Peterson delve into the very smart geometry behind the honeybee's home.

Lesson by Zack Patterson and Andy Peterson, animation by TED-Ed.

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 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 construction 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.