Consider the lowly square, a four-sided shape with sides of equal length meeting at right angles. The embodiment of what we’re referring to when we refer to square miles, square kilometers, square inches, or square whatevers. The two-dimensional version of any one-dimensional length.
A trivially easy shape to draw, all you need is a straight edge and a compass — the latter for ensuring your corners are right angles (see Plato’s Divided Line for more on using a straight edge and compass). The only simpler shape is the circle.
Yet the simple square threw early mathematicians into a serious tizzy!
You may remember learning way back in grade school that you can’t divide by zero. You may remember being told that 
I’ve mentioned before that, after ten years of retired idleness, this year I’ve applied myself to getting some long-standing items off my TODO list. I’m a lazy beaver, not a busy one, but I’ve been less lazy than usual in 2023. (Perhaps, in part, because, on several counts, I can’t believe it’s actually 2023. I remember a time when 2001 seemed far off… in the future.)
This is one of those geeky posts more a “Dear Diary” (or “Dear Lab Notebook”) entry than a post I expect anyone anywhere will get anything out of. This — in part — is about how we define numbers using set theory, so it’s pretty niche and rarified. Tuning out is understandable; this is extra-credit reading.
Or do I mean Logic Square? Because it works either way. The Logic Square (or Square Logic) in question is a logic game created by 
It’s been a while, but the two previous posts in this series (
At some point in our early math education, we’re told that anything to the power of zero evaluates to one. 1°=1 and 5°=1 and 99°=1. Basically, x°=1 for all x. It’s typically presented as just a rule about taking anything to the power of zero, but it’s actually derived from a more basic rule about exponents.
Logos con carne 