Paper Bag Problem - The Square Teabag

The Square Teabag

In the special case where the bag is sealed on all edges and is square with unit sides, h = w = 1, and so the first formula estimates a volume for this of roughly:

or roughly 0.19. According to Andrew Kepert at the University of Newcastle, Australia, an upper bound for this version of the teabag problem is 0.217+, and he has made a construction that appears to give a volume of 0.2055+.

In the article referred to above A C Robin also found a more complicated formula for the general paper bag. Whilst this is beyond the scope of a general work, it is of interest to note that for the tea bag case this formula gives 0.2017, unfortunately not within the bounds given by Kepert (i.e., 0.2055+ ≤ maximum volume ≤ 0.217+).