When you think of honeybees, you probably think of honey. However, most of us don't give much thought to the honeycomb, also known as a wax comb. This comb is an array of hexagonal compartments in which larvae (baby bees) develop. A queen bee can lay up to 3,000 eggs per day, so there are always thousands and thousands of larvae that need compartments in which to grow!
If you've ever seen a honeycomb before, then you may have noticed that it is composed of tightly-packed hexagons. Bees use this shape because it has a small surface area (how big the walls are) compared to its large volume (3-dimensional space that it contains). In other words, hexagons "wall off" a lot of space using only a little bit of wax.
Another way to look at constructing a bee hive is that wax is what is "costs" the bees to build a hive. Bees have to spend time and energy making wax, so it's not a good idea to waste it. Compartments are what they get out of their work. Since there are so many larvae that need room to grow, space is precious, so wasting it is not an option for bees!
Therefore, bees want to build the largest number of compartments possible by using the least amount of wax. Getting a lot by using the least amount of material is called efficiency.
The most efficient shape for boxing in a single compartment is a circle. However, circles are not that efficient if you have to make more than one compartment. This is because having circles next to each other (like a bunch of cookies on a dish) means that there will always be wasted space between the circles.
So, bees use hexagonal compartments, which contain almost as much volume as circular ones, but which do not waste any space. In other words, if you arrange hexagons in the right way, then there will be no space between the compartments, which means no wasted space!
Honeybees have been around for over 150 million years, but still, how did they manage to figure all this out? Well, they weren't sitting around measuring the surface areas of different shapes. Rather, different groups of bees tried different ways of building honeycombs. The bees that built the most efficient honeycombs were able to give more of their larvae a place to grow. So, that's how bees evolved to make hexagonal honeycomb.
Little Lion Experiment:
Get some play-dough or clay and roll out three smooth sheets which are about 5' across. Then, roll out a long coil and flatten it so that it is about 1/8' thick, 1' wide, and exactly 2 feet long. Using a butter knife, slice off the rough edges to make a 2-foot-long rectangle. Use a ruler to make sure that all parts of the rectangle are equally wide!
Cut the rectangle into three 8' strips. Stand a strip on its edge and bend it around to make a square. Use the second strip to make a triangle. Use the third strip to make a hexagon. Remember, you used the same amount of clay to make each shape, so all three have the same surface area.
Connect each of your three shapes to a 5' sheet so that you have three boxes without lids. Use a tiny bit of extra play-dough or clay to seal the cracks. Put your boxes over some newspaper in case they leak. Make sure that the boxes are still level with the table!
Now, we're ready to measure the volume. Fill the hexagonal box with sugar. This volume of sugar is equal to the volume of the box.
Then, carefully pour the sugar from the first box into the second box. You'll have leftover sugar since the second box has a smaller volume than the first box does.
Next, use the sugar from the second box to fill the third box. Judging by the amount of sugar needed to fill the second box versus the third box, which one has the larger volume?