Random Math Ideas

This is where I’ll be posting random mathematical ideas I may have from time to time. They may or may not be of any particular use, and more often than not are just curiosities that I explore from time to time.

For example:

Did you know that ?

Of course you did. Now ?
Of course! That’s basic everyday multiplication tables!

Now how about ?
That’s .

Seeing a pattern yet?

If you’ve seen it, it goes out to which yields .

It breaks down beyond that because then you get 10, which messes up the order of things, and you can account for that and predict values beyond that, but it’s not nearly as pretty.

Really cool in my book.

Another question: what is the sum of an infinite number of infinitesimally small areas?