Hexagon

Mrs Parsons, a spanner?

Geometric Hexagon

A hexagon

That has put a spanner in the works.

An hexagon has six sides.

A hexagon has six sides.

I'll draw it as a little hexagon.

So once again, I like to just draw a hexagon.

Let's just draw a hexagon and count the triangles in it.

The sum of the interior angles of this hexagon, of any hexagon, whether it's regular or not, are going to be 4 times 180 and that's 720 degrees.

Problem 50 What is the measure of an exterior angle of a regular hexagon?

And it's a regular hexagon, so all the interior angles are going to be the same.

Maybe wrap it into a hexagon with a nice symmetric sort of cycle to the flappy parts.

In fact, there's enough space here to keep wrapping the strip, and then your hexagon is pretty stable.

Using triangulation or tessolation, what is the minimum number of triangles you can use to represent this hexagon?

And since it's shaped like a hexagon and you flex it and flex rhymes with hex, hexaflexagon it is.

If you look at the hexagon, for instance, it's like an amoeba, which is constantly changing its own profile.

With four, you make a square, you make a pentagon, you make a hexagon, you make all these kind of polygons.

A regular hexagon tells us that all of the sides are the same, it's equilateral, and all of the angles are the same, equiangular.

And then, since hexagons have six way symmetry, you decide to try this three way fold the other way, with flappy parts up, and are collapsing it down when suddenly the inside of your hexagon decides to open right up.