One evening about a month ago, my six-year-old brother asked a question that was designed to stump the oldest of us. “What’s fifty times fifty?” He loves starting with the hardest number to multiply that he can fathom, and then multiply that by itself, the new number by itself again, and keep going—until even the calculator groans and returns an E+, ‘Overflow’, or simply starts showing uninterpretable decimals.
But since fifty times fifty isn’t too big, I set it up on the whiteboard for him and gave him the answer. “Two thousand five hundred.”
“So…what’s forty times forty?”
I can’t remember exactly how the conversation went from there, but we ended up calculating several squares in the 47-52 range. After looking at the ones on the board, I suddenly wondered if there was a pattern. If we could possibly predict the next one.
472 = 2,209
482 = 2,304 (difference from 472: 95)
492 = 2,401 (difference from 482: 97)
502 = 2,500 (difference from 492: 99)
512 = 2,601 (difference from 502: 101)
522 = 2,704 (difference from 512: 103)
If there is a pattern, 532 should be 522 plus 105. It is—2,809.
After this, Mom went back to 1 and wrote down the squares of the first 12 numbers, to see if they followed the same pattern.
They do. Each difference is precisely two numbers greater than the last one. Incredible, isn’t it? And while it’s amazing, we also realize that God has known all along and He made it that way for a reason.
So there’s your math lesson for the day. A terribly impractical, but undeniably fascinating pattern.