| Paper Bag Problem |
Article Index for Paper Bag |
Website Links For Paper |
Information AboutPaper Bag Problem |
| CATEGORIES ABOUT PAPER BAG PROBLEM | |
| geometric shapes | |
| optimization | |
|
The problem is made even more difficult by assuming that the bag is made out of a material like Paper or PET Film which can neither stretch nor Shear . According to Anthony C. Robin , an approximate formula for the capacity of a sealed expanded bag is: : where ''w'' is the width of the bag, ''h'' is the height, and ''V'' is the maximum volume. A very rough approximation to the capacity of a bag that is open at one edge is: : (This latter formula assumes that the corners at the bottom of the bag are linked by a single edge, and that the base of the bag is not a more complex shape such as a Lens ). 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 , the 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, but significantly nearer. REFERENCES EXTERNAL LINKS
|
|
|