Hexagons, part I

We interrupt our regularly scheduled series to present to you the amazing hexagon.

Here is a regular hexagon:

You might say, “Tom, what’s so special about a hexagon?” Let me tell you:

1. It has the most number of sides (6) of any regular polygon that can be tiled (there other polygons with more sides such as some decagons that can be tiled, but they won’t be “regular”).
2. They have a very special relationship to circles, which I will get into at a later time.
3. Hexagons appear in nature in many places and ways:
1. A honeycomb is made of hundreds or thousands of hexagons;
2. The north pole of Saturn has a hexagonal cloud pattern.
3. Snowflakes have hexagonal crystal structures.

The fact of the matter is, hexagons appear in nature so much because they make efficient use of space.

Here’s an interesting fact about regular hexagons.  Let’s take a regular hexagon and draw a circle around it such that the vertices of the hexagon are all on the circle’s edge, like so:

Let me tell you an interesting property of the hexagon in the above figure: the sides of the hexagon are all equal to the radius of the circle it inscribes!

So, we’re going to talk about hexagons a little.