My first two letters can show you my size
My second two are here to clarify
Take my first two, atop my last, alongside my second, add another one and you will find splitting very hard
I will reveal the answer in the first of December if no one gets it. Good luck.
I can make the first two clues work nicely:
if the answer is PIE then we can find the area of a circular pie as pi times radius squared, and "i.e." is often used to introduce a clarification.
However,
I can't then make any sense of the third clue -- if I take "first", "second", etc., to refer to letters of "PIE" I don't get anything that looks meaningful to me.
Perhaps
there's some way to interpret the third clue in terms of digits or something so as to end up with an expression corresponding to a prime number ("you will find splitting very hard"), or something like that.
Angzuril (in comments) makes the suggestion that
perhaps "atop" means "above and to the right of" and "alongside" refers to the bits that are "atop" rather than to the whole thing, in which case it could be a description of the LHS of Euler's famous formula: $e^{\pi i}+1$. This equals zero, which I would describe as especially easy to split since it is an integer multiple of every integer there is, but I suppose you could say it's hard to split because there's no way to divide it into two strictly smaller parts.
I bet this is right; thanks, Angzuril!
The answer is
PIE
The first 2 letters are
pi. It describes the size of a circle's circumference
The second two are
i.e. Often confused with e.g.: i.e. is used to explain, clarify or
rephrase a statement; (i.e used to explain something)
Take my first two, atop my last, alongside my second, add another one and you will find splitting very hard
$e^{i\pi} + 1 = 0$ — that is, e^i*pi plus 1 = 0 ...and you can't split 0
The anser is
Xmas.
My first two letters can show you my size
XM, a common clothes measurement.
My second two are here to clarify
AM, clarifies the time. (As in 12 Am)
Take my first two, atop my last, alongside my second, add another one and you will find splitting very hard
Can't figure how this one fits yet.
