A Really Cool Math Fact About the Squares

My kids are in Classical Conversations (CC), which we love. This year they learned the squares (a number times itself) to 15, and they learned them to a song. The information in CC is wonderful. I wish I knew all this stuff. But apparently when I was in elementary school the “educational experts” had decided that it was cruel to kids (or something) to make them memorize “useless information.” Harumph!

Anyway, I mentioned to my wife that I wish I could learn this stuff, so she asked me at dinner what I wanted to learn. I said, “the squares.” So they taught me the song. You can get it here, and here are the numbers:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

As I was thinking about these numbers and trying to learn the song, I remembered something I read in a Princeton Review book when I was studying for the GRE (this is one of the things that makes me grateful that I had to take the GRE, by the way, and one of the reasons I encourage students to study for it and really try to learn!).

Look at those numbers. Do you notice the space between them?

Between 1 and 4 are 3 points on the number line, then between 4 and 9 there are 5, between 9 and 16 there are 7, and it continues up by odd numbers as follows:

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29

That is cool. God made the world in an orderly fashion, and he built elegance and beauty into it, as though he expected people to come along and search out all his wisdom to marvel at his glory.

“In the beginning was the Word, and the Word was with God, and the Word was God” (John 1:1).

“The heavens declare the glory of God, and the sky above proclaims his handiwork” (Psalm 19:1).