[Continuing my theme of revealing things to undermine what little confidence the world has in me...]
The other day my second grade son was watching a cartoon about blocks that do math. It was on Netflix I think; he has mastered all the streaming apps on the TV, and when he has free-viewing time (when Mommy and Daddy need a break) he is more than capable of selecting a show to watch, so I was not paying much attention to how we go there. [Wow, I'm really knocking it out of the park with this introductory paragraph! How can the reader not want to see where this is going?] In this instance, it was something that seemed more toward teaching pre-schoolers or kindergarteners about math--well below where he is in school, but maybe he gets nostalgic for that period of his life; it was at least educational, and certainly far less bad than a lot of shows he could have selected.
As I noted, I was only vaguely paying attention and likely because of that seeing the blocks make square shapes made me think about squaring numbers--1x1, 2x2, 3x3, etc.--and remembered that a number squared is the only way when represented with blocks that it creates a literal square; the units on the vertical axis and horizontal axis obviously must be the same or it's merely a rectangle. [Finally got to the topic, proving that first paragraph was a digression before I even started. Readers love that.]
Squaring numbers is a concept still a few years in the future for my son, but obviously way from way back in elementary school (probably) for me. Still, I hadn't thought of it in such rudimentary terms since... well, probably since I was in elementary school over four decades ago. [Yowza! I am old.]
I then paused and thought about the results of those squared numbers:
1, 4, 9, 16, 25, 36, 49, 64, 81...
And how they incremented in a pattern--by 3, then 5, then 7, then 9, then 11, etc.