I didn’t see this here, but thought people may be interested:
Britney Gallivan has solved the Paper Folding Problem. This well known challenge was to fold paper in half more than seven or eight times, using paper of any size or shape. http://pomonahistorical.org/12times.htm
The largest pieces of paper generally available would be the rolls of newsprint that are used for printing newspapers. These weigh around 25 tonnes – there are pictures here.
According to this page (near the bottom), such pieces of paper are about 65 kilometres in length. Foled in halp 12 times, and the pile would be still be about 16 metres wide. However, one person could not do that folding without the use of mechanical handling equipment, such as a crane capable of lifting around 15 tonnes.
I could think about this problem for weeks and never would it occur to me to use math. I’d be using soup spoons, dictionaries, anvils, driving cars over the damn piece of paper…but an equation? Lands sakes.
Also a rather liberal definition of ‘fold’ - that’s the big thing about the paper folding problem that most people don’t seem to appreciate; it isn’t just that the object you’re trying to manipulate is steadily getting smaller, it’s that the number of sheets you’re trying to fold is doubling every time - more than seven folds and it isn’t really a ‘fold’ any more, it’s a ‘bend’, at least for the sheets on the outside.
A big error on the site (reads like a press release) is that she “was the first person to realize the basic cause for the limits.” This is plainly false. She may be the first person to bother carrying through the calculation, but just because mathematicians haven’t worked out the numbers on a niche problem doesn’t mean they don’t realize the technique that will lead to the answer. She may be able to stretch this into a master’s thesis at a place like Pomona College, but it’s really no more than an exercise nobody had bothered to actually carry out before because there’s nothing to be done with it.
I am always amazed to see new breakthroughs… This probably has some implications for nanotechnology and building stuff at a molecular level, not to mention folding solar sails…thanks for posting! I’ve ordered her book.