I Case My Rest

Since moving to France, I've noticed many small cultural differences. Among the more unexpected is the shape of pillows here – They're square, rather than rectangles. It might seem like this is irrelevant to getting a good night's sleep, but it actually changes the way the pillow inflates, and initially I found it incredibly uncomfortable. I was curious if I could find a way to model how the different dimensions lead to different pillow shapes.

It turns out this is a well-studied problem, usually called the paper bag or teabag problem. Unfortunately, it's a problem with no simple solution. There are approximations of the total volume contained, but I was more interested in the shape of the pillow. That can be modeled with a computer program, but I failed in my attempts to get that one to work.

However, the original post on that page suggested a different way to make the comparison – Inflate some paper bags myself! The French pillowcases are 65 x 65 cm, and according to this site, American ones are 20 x 26 in or about 51 x 66 cm. I cut out 1/5 scale replicas of the two sizes, and blew them up as best I could:

The area for the French pillows is only about 25% larger, but this leads to much thicker pillows! It seems after a few months here, my spine has reshaped itself, and I'm sleeping much better now. Still a funny bit of culture shock though.