Tau looks like r, which is used for radius length, which is relevant to some equations that use the circle constant. Of all possible letters, why use tau? Are they trying to mess with students and teachers whose handwriting makes it ambiguous whether a symbol is tau or r? Maybe it was just because it's half the pi symbol.
I'm pretty sure people only care about Pi Day because it sounds like pie. Tau Day will never be as celebrated, unless you call it 2Pi Day, which defeats the point, but is still a good excuse to eat pie.
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I'd love an explanation of the technique.
FWIW, among my friends--whom I might describe as "polite askers" or "assertive guessers"--it's common to ask "does anybody want to split this with me?" That way, you're both asking for what you want (more of the thing) and making an offer in a guess-culture-compatible way. It's easy for other people to accept, because now by taking it they're not preventing you from having it. If no one does, you can be reasonably confident no one else actually wanted it.
A variant on the same thing is: "Would anyone else like this?" which is a shorter version of the offering ritual that TheOtherDave described. Because it's skipping most of the ceremony, it's much askier, but it's still not polite to say "yes" and take the thing, because you'd be taking it out of the hands of someone who clearly wanted it. (An exception might be made if you hadn't actually had any of the thing yet, and said so.) But you can say "I'll split it with you," achieving the same result as the above.
Of course, this only works for plausibly divisible things. I've had a friend laugh at me--good-naturedly--for offering to split something bite-sized. Surprise, surprise: he's much askier, I'm much guessier.