The Spark of a Palindrome
As a child, when I couldn’t sleep, my wonderful father would do something we called “boring me to sleep”. It wasn’t and isn’t an insult to him, but he is very good at talking about something mundane for as long as needed. Most of the time, he would discuss a single number for as long as it took to get me to sleep. It would go something like this:
What about the number seven? It’s prime, which is pretty cool. It’s also one more than six, which is divisible by most of the numbers smaller than it. Seven is also two less than nine, which is a square number…
He could (and probably still can) go on like this for as long as necessary. Maybe this is why I feel so calm and happy when it comes to numbers.
Palindromes have also been important to me, partially because my name, Hannah, is the same forwards and backwards. I vividly remember learning about palindromes in elementary school. I felt pretty darn special!
Today is January 24, 2021 and, like some of the other days in January this year, it’s a palindrome! So, let’s discuss 12421 as a number. First of all, it’s 20 21 22 21 20, which is kind of cool. With a base of two, the exponents go 0, 1, 2, 1, 0. But, that’s just the beginning!
If you consider the numbers within 12421, you’ll notice some cool “stuff”, too. First let’s look at 12421 (aka 12) and 12421 (aka 24). Twelve is half of twenty-four. They are both divisible by four. When divided by four, we are left with three and seven. 37 is prime. Kind of cool. More importantly, twelve and twenty-four are both divisible by twelve, which leaves one and two. That gives us 12, bringing us right back to the twelve we started with, the first two digits of 12421.
If you consider the second half of 12421 in the same way, we can find more greatness. For 12421 (aka 42) and 12421 (aka 21), twenty-one is half of forty-two. They are both divisible by seven. When we divide by seven, we are left with six and three. 63 is not prime, but has 3, 7, 9, 21 as factors (when we ignore one and itself). That’s four factors, and four is the middle number of this palindrome (and my lucky number, more importantly).
What does all of this mean? Absolutely nothing. Nothing above will become the next famous math theorem. Somehow, though, it made me smile. Confused and bored? That’s okay! Math is my calming topic, the thing I love to think about. It’s a sort of “spark” for me. But the real question is… what’s yours?