Take a moment to imagine a square. Draw one if you’d like. Look at it. Turn it. It’s perfect; as they all are. Your square is one of the infinite number of squares you could have chosen. It is unique. No other square has its length, width, or area. Depending on how mindful you were of detail while you were drawing, you may not be aware of its dimensions. You may not have taken much care to draw accurate angles at the corners, but that’s all right. It’s not the drawing that is important, but the idea it represents. Your square might have its flaws. One side may seem longer than another, or one of the angles may not look exactly as planned. Perhaps you took the time and constructed your square making its flaws apparent only if magnified to a great degree. That is fine. The idea is perfect, and if you say your polygon is a square, then so be it.
Your square has no scale associated with its size. It is as large or as small as you wish. Imagine your square expanding or contracting to become any other square. It could be so small that you have to hold it very close to see its shape. It could also be large enough that you have to soar high above it to keep its entirety within your vision. Between those two ideas exist an infinite number of squares that are similar to your own. Your square, though unique, is simultaneously one of them and all of them. Indeed, to draw one is to draw all. These are the things that run through my mind during sleepless nights as I stare at the ceiling. I know–I’m concerned as well. But as long as I am going to the trouble of thinking about it, I may as well share it with the rest of you. My intent for this blog is to share ideas about squares, the students who study them, why they should study them, and the efforts educators make to facilitate their study. Over the course of the next year (or at least the next 36 or 49 weeks), I will devote a weekly article dedicated to squares, their use, importance, and, yes, even their beauty. As ridiculous and nonsensical as this sounds, each will address a different topic related to squares. I invite you to follow, share, and join me on my quest for all things squared.