A Short Riddle!

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.

• This will definitely be solved by December :P – Beastly Gerbil Nov 17 '16 at 16:31
• I know but just in case – Leo Nov 17 '16 at 16:31
• I'm guessing the 'here to clarify' part refers to the letters 'i.e.'? – Tarun Nov 17 '16 at 16:45
• "second two" = letters 2,3 or letters 3,4? (Of course you may prefer not to answer.) – Gareth McCaughan Nov 17 '16 at 20:31
• 2 and 3. It's OK for that one – Leo Nov 17 '16 at 20:32

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!

• You can do the last clue with letters, just Euler`s identity (last)^(2nd)(first two) == e^i*pi , and add 1 is Euler's. – Angzuril Nov 17 '16 at 20:52
• Oh, I see. It would never have occurred to me to describe an exponent as "atop" the thing raised to that power, but I suppose you may well be right. Is zero supposed to be very hard to split? Personally I'd say the exact opposite -- it's an integer multiple of everything. – Gareth McCaughan Nov 17 '16 at 22:09
• Wow that was quick. What I meant by "You will find splitting very hard" was that you can't divide or 'split' by 0. – Leo Nov 17 '16 at 22:19

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

• .... as already given by Gareth's answer plus Angzuril's comment. – Rubio Nov 17 '16 at 21:09
• I know I just thought I'd put it together, no need to upvote this one. – Sam Harrington Nov 17 '16 at 21:10
• Just you try and stop us! – Jasen Nov 18 '16 at 3:48

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.

• Extra medium? Not sure about that one – Leo Nov 20 '16 at 21:34