We are a commune of inquiring, skeptical, politically centrist, capitalist, anglophile, traditionalist New England Yankee humans, humanoids, and animals with many interests beyond and above politics. Each of us has had a high-school education (or GED), but all had ADD so didn't pay attention very well, especially the dogs. Each one of us does "try my best to be just like I am," and none of us enjoys working for others, including for Maggie, from whom we receive neither a nickel nor a dime. Freedom from nags, cranks, government, do-gooders, control-freaks and idiots is all that we ask for.
Has it struck EVERYBODY as absolutely fascinating that difference between the squares of consecutive integers equals the sum of those two integers?
Naturally, it must also have struck everybody – well, maybe not exactly everybody – that the series formed by differences of the squares of consecutive integers is, therefore, simply a series made up of consecutive odd numbers.
If neither of these has struck you, it may be because you have not been stuck, without a book, waiting in long line to get to a bathroom.
Two consecutive integers are X and X+1
(X+1)^2 - X^2 = X^2 + 2X + 1 -X^2 = 2X+1= (X+1) + X
Interesting but hardly fascinating.
Twice any integer is an even number and any even integer plus 1 is an odd number. So, yeah....
Whatever lets you wait in control, I suppose.
That reminds me of some stuff I've been listening to in one of the Great Courses series: Great Theorems, Great Thinkers. I'm not a mathematician - in fact a lot of the math went way over my head, but the professor is engaging and the stories fascinating. I highly recommend it.