Square triangles

Thirty six is a square number that is also a triangular number. I don't understand what that means obviously, because I'm not a mathematician, but I'm sure it's very important, especially for our purposes here, because it means, in certain circumstances, squares can be triangles. Thanks, mathematics!

In order to do important research for this important post, I typed in 'square triangle numbers' to Google, a search which I highly recommend everyone does. Not that you'll see much of interest - just a list of numbers. But it's just particularly pleasingly to type in that rather non-sequiturial sequence of words into the search box and see what comes up. It's like hammering a square peg into a round hole, except, of course, the round hole is a triangle and the hole is not a hole, it's just an abstract Platonic concept outside of time and space. (This all reminds me of the time I said to the Baron, "how many holes does a donut have?" and she retaliated with, "what are holes even?", and I said - but NO, we definitely want to go down that rabbit triangle again.)

It must be rather pleasing to be a mathematician, going about, showing that squares are triangles, really, in effect squaring the rhetorical circle, and.... hang on. Mathematically, it turns out, not only can circular numbers be square numbers. But.... 

Automorphic number. In mathematics an automorphic number (sometimes referred to as a circular number) is a number whose square "ends" in the same digits as the number itself.

So circles HAVE TO BE squares. Not only that, but - circular numbers can sometimes be triangular numbers as well as squares (our old friend thirty six is one - six squared!). Whew! I certainly hope the mathematician who decided that gets to go home and eat their four square meals a day. Except that would be sixteen meals and they would die of indigestion, which might not be quite so good for their health. But apart from that I have almost no problem with the concept.

So, to conclude, squares are triangles except when they are circles. And sometimes, they are all three at once. Mathematics, hey? If you can't count on numbers, then....