Consider triangle ABC …

I’ve been diverted by a nice little maths result that was only discovered in the early 1990s. Take a triangle, and divide each side into three. Now connect each of the pairs of trisection points to the vertex opposite (these are the black lines in the picture). These lines create a hexagon in the middle of the triangle.

The cute result is that this hexagon is always 1/10 of the area of the original triangle.

The really cool thing is to construct the figure in a dynamic geometry program. When you’ve built it, you can grab a vertex (corner) of the triangle, and wiggle it around all over the place, making the triangle as big or as small or as  distorted as you like (sorry, but you can’t do this with the blog picture) … and still the hexagon — which has also been distorted — remains 1/10 of the area of the original triangle.

So pretty …

And then there are loads of possibilities for generalising …

Unfortunately the ambiguities of my working life are such that this is more play than work, and so I am feeling a bit guilty for doing this instead of writing a conference paper that is due in on Monday and which I haven’t even started. I know which I’d rather do!