The Abomination of Tessellation

Tessellation. It sounds like something Captain Kirk would do to the dilithium crystals before rebooting his warp drive. Sounds complicated.

Of course it isn’t it is simply the fitting together of geometric shapes, at least that’s what I think it is.

Without tessellation there would be no tiling or mosaics and probably no wallpaper either and that’s far from uncomplicated. (I sat in chaplaincy the other day and watched a maths undergraduate attempt some sort of project or course work on wallpaper patterns it was so complicated she didn’t even get it.)

Fit this shape to that shape and this one. I sat there one evening trying to do this with a pencil and a brain. Fitting together octagons and squares pentagons and stars. For a while I wondered if this was what the prophet Daniel was going on about when he spoke of the “abomination of tessellation”.

Then all of a sudden something strange started to happen. I started to enjoy myself.

“Explain without drawing” my maths books said “why it may be possible to make a tessellation using a combination of equilateral triangles and regular 12 sided pologons”

So I did by working out what the angles on a 12 sided polygon were (150 degrees) then putting two of those together with an equilateral triangle (60 degrees) to make a tessellatingly possible 360.

“Now draw the tessellation”

So I did.

I decided to make the sides 20mm long and then spent hours carefully drawing out the shapes with my ruler and protractor. When my first the 12^th side of my first polygon met the first I felt a huge amount of satisfaction. Even more when having drawn the second polygon there was two sides of an equilateral triangle. The space for the third side was....wait for it....almost exactly 20mm wide.

The thing is though as satisfying as that was, actually what I really liked was mathematically proving it would work first.

Therein lies my problem.

I’m a wordsmith, an ideas man, a dyed-in-the-wool BA (actually I’m a BD but that is close enough)

I once visited Imperial College in London for a chaplains’ conference and was marginally impressed by the place until I thought “Yeah but this is all just for Maths and Science and that’s boring.”

What if I’ve changed? Behold! I am become geek! I’m not sure I’d like that.

In the past when some fresher came into chaplaincy and told me that there was a tessellating pattern on the pavement outside the Maths Department and that “that’s really cool!” I found it hard to agree purely because I had no idea what the word “tessellating” meant. They might as well have said there was some “pentomonchasm” or “gigglebumwhacking” or “dgissy-twatz”.

I don’t get excited because some experiment works. I don’t read XKCD. I don’t know how to code.

Musicians are cool. Great original tele is cool. Stuff that makes me laugh is cool. Mathematical proofs are not cool.

That’s just the person I am and, I think I like the person I am.