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Ah, I see. Yes, I agree that given that fact you get the desired inequality. But this fact is, as you say, nontrivial. It's certainly false for various non-b
by bzbarsky 10y ago
Ah, I see. Yes, I agree that given that fact you get the desired inequality.
But this fact is, as you say, nontrivial. It's certainly false for various non-box-like shapes afaict, so there's something special to boxes that needs proving here.
- cousin_it 10y agoJust note that all combinations ±a±b±c can be realized by paths on the box. I'm sorry, I see now that my original comment glossed over tons of stuff that was clear only to me. Instead of saying "easy to check" I should've posted my napkin sketch with the easy check. Anyway, my solution is still simpler and more natural than the one in that pdf :-)