On Monday, Cristina Santiestevan of Outlaw Garden shared a post about the geometry of gardening, introducing us to the idea of “hexagonal spacing.” This was such a cool idea that I thought I’d explore it further. I wanted to know the math behind it. In other words, why are hexagons so darned special?

Let’s start by with the bees. In research for a magazine assignment, I’ve done some reading about bees lately, and once again, I’m in absolute awe. These little guys are the linchpins of our ecosystem in a lot of ways. Not only does their pollen-collecting insure the reproduction of a variety of plant species (and therefore the survival of critters that depend on these plants), but their colonies are efficient little factories that seem to mirror human manufacturing — from the dance the workers do to relay directions to the best pollen to the efficiency of their job descriptions.

And then there are the hives. If you think of the bees as efficient — and they are — you can deign why the hive is made up of tiny hexagons. (Remember, a hexagon is a six-sided figure.) Not wanting to waste any space whatsoever, the bees figured it out: instead of making circular cells, which leave gaps around the sides, they create a tessellation of hexagons, which leave no empty space at all.

(A tessellation is the repetition of a geometric shape with no space between the figures. Think M.C. Escher or a tile floor.)

The same concept applies to gardening. Why waste space? As Cristina pointed out, choosing a hexagon-shaped planting scheme, you’ll get more plants in your beds. And if you’ve got an outlaw garden, like Cristina, it’s best to make the most of your space! Here’s how:

In regular rows, you plant 6″ apart in only two directions, getting nice, even rows. But if you consider six directions, you’re replicating the hexagon, instead of a square — and as a result maximizing your space (just like the honey bees). Cristina describes it as planting on the diagonal. Or you can think of each plant at the center of the hexagon. Then you can plant the others 6″ from the center in six directions — creating the vertices of the hexagon. (If you’ve ever looked carefully at a Grandmother’s Flower Garden quilt pattern, this idea might jump out at you. Not only is each plant the center of a hexagon, but it’s also the vertex of another hexagon.)

Did you see what I did there? Math *can* be described in a variety of ways! Look at the second diagram carefully, and see what jumps out at you — the hexagons or the diagonal rows?

So there you have it. We can learn a lot from a bee. And I can already think of times when this can be useful in other areas. How many more cookies can you fit on a cookie sheet, if you arrange them diagonally (or in a hexagon shape) rather than horizontal rows? What about kids desks in a classroom?

*Where can you apply the hexagon to make your space more efficient? Share your ideas in the comments section!*