It's a common approximation(*) of the Fourier transform, used to estimate frequency components in time series data.

It was an Easter egg for Master Po, who may have missed implied time when I said rhythm.

(*)The even more common one is to use Euler's and just directly evaluate from there, but it was just easier to copy from wikipedia than spell out the eq'n. A great deal of what I've done and published started with that eq'n. (Stated for Po's benefit, just to beat him to that punch. )

Ok Bob - once again 1,1,1,2,__ or 1,1,2,1,3,1,4,__

It's funny how people used a mnemonic to justify an answer.

That's like saying Math is the way it is because I tied this string around my finger

Multiplication and division are equal im PEMDAS it's actually P E MD AS. It could have just as easily be written PEDMSA.

The only argument for the answer being 1 is if you interpret the 2 being a function of the parenthesis. Since it's genreally considered shorthand for multiplication and not a function the answer is 9. (Unless your talking computer science or a different type of math like calculus where x and * dont mean the same thing anymore). Basically what EarlyMon said.

Of course, but you'd be surprised at the number of educated people who will be stumped. Maybe not the ones used to work specifically with Mathematics though.

For example, the CEO of a consulting engineering firm that I know didn't find it.

It was a Malcolm Gladwell "Blink" answer. I didn't ponder my decision at all. Doesn't make my answer correct, but it does prevent me from getting sucked into a self debate. Here's my logic:

We make the equation a bit more algebraic without changing the operators and parens:

c/2(a+b) where a=1, b=2, and c=6

If you assume c/2 comes after evaluating (a+b), you are essentially putting (a+b) in the numerator of your division:

c/2 * (a+b)/1 --> c(a+b)/2

So if the equation was written as c(a+b)/2 ((a+b) is in the numerator), your final answer is 9. But the equation was definitely not written in this way. So 9 is wrong.

As the original equation was written, (a+b) is clearly in the denominator because I proved above it can't be in the numerator without a drastic re-write of the equation. In other words, c/2(a+b) can only imply that (a+b) is in the denominator without re-writing the equation. Therefore, as the original equation was written, the answer is the following:

eval parens first: (a+b) = 3
3 is part of the denominator, so 6/2(3) = 6/6 = 1

Ah yer right sorry, but it was a mistake of quoting the wrong part of your post, not misreading what you said.

Your proof is still wrong though because it rests on the "because it was written this way, I can perform the order of operations this way"

This is what I should have put in the second quote:

That's where you make an assumption and rewrite the equation yourself.

You're basically saying because there are parenthesis, you can do the multiplication of 2 * (a+b) before c/2 even though that's not how the order of operations work. After the parenthesis, you're supposed to go back to division/multiplication and left->right. x(y) is just another way of writing x*y, it doesnt change the rules

Well there's debate on how order of operations work as it pertains to M and D. But I was trying to eliminate that debate entirely by focusing on the OP's statement in one of his posts: