Here’s a great thing: a trio of Klein bottles nested one inside the other by mathematical glass-blower Alan Bennett (found via BoingBoing, of course.) You can tell it’s three separate bottles by looking at how the layers are interconnected: the long skinny tubes at the bottom each connect a pair of layers, and the folded-over edges at the top connect the same pairs (1+6, 2+5, 3+4). Figuring that out was fun, but then I saw this tantalizing quote from the museum’s website:
“In the series Alan Bennett made Klein bottles analogous to Mobius strips with odd numbers of twists greater than one.”
Darn, I was really hoping to see one of those! Suddenly the math geek in me is sorely disappointed. Given how much labor it must have taken to build this object, he could have made it a lot more interesting just by switching which tubes connect to which bottles! If the tubes linked 2+6, 3+5, and 1+4, this object would be transformed from three separate surfaces into a single surface that turns inside-out three times, the equivalent of a triply-twisted Moebius strip.
Luckily, a little snooping around turns up some photos of Bennett’s other work on display, courtesy of Flickr user Brian Ritchie:
And also here’s a little article discussing some of what Bennett was after when he created these models: he was interested in what happens when you slice them up. Apparently a single slice can turn a Klein bottle into one Moebius strip, or two Moebius strips with an arbitrary number of twists. It all depends on how you slice it. Nice!