The mathematical field of topology—the study of qualitative properties of certain objects that are invariant under certain kind of transformations—has fascinated me ever since I heard the joke that topologists can’t tell the coffee cup from which they are drinking from the doughnut they are eating.
(Okay, I admit it’s not a funny joke. But I’m a sucker for mathematical humor. And donuts.)
Now a professor and artist George Hart has shown how to cut a bagel into a Mobius strip: two congruent, linked halves—they “pass through each other’s holes, like two links of a chain.”
Hart provides step-by-step instructions for how, using a single knife cut, you can transform an ordinary bagel into a topological marvel. And the best part? “[Y]ou get more cream cheese, because there is slightly more surface area.”
(Via: Serious Eats” New York)
Update: In the comments, Beatrix points out that the bagels aren’t a Mobius strip after all but rather “a pair of linked annuli, each with a full twist. a mobius strip has a half-twist only. if this were a mobius strip, one could not spread cream cheese on one side.” Also, over on Postmodern Conservative, uber-math nerd Will Wilson has more topological goodness.
December 8th, 2009 | 10:46 am
sorry to be a spoil-sport, but this is not a mobius strip. this is, as the linked article indicates, a pair of linked annuli, each with a full twist. a mobius strip has a half-twist only. if this were a mobius strip, one could not spread cream cheese on one side.
side note: an annulus without a twist is topologically equivalent (i.e., homeomorphic) to an annulus with any number of full twists.
December 8th, 2009 | 10:58 am
I think of the observation about the homeomorphism between doughnuts and coffee to be proof that those great gifts should be enjoyed together.
December 8th, 2009 | 11:19 am
[...] do Joe Carter and MAKE Magazine point me towards the same online curiosity. The intersection of topology and [...]
December 8th, 2009 | 2:08 pm
I have to concur with Beatrix. Note that a mobius band with cream cheese would be impossible to eat without getting one’s hand messy, since a mobius band has only one side.
When I was in graduate school, I attended a geometry and topology conference for which the continental breakfast was advertised in advance as consisting of “edible torii”. Imagine my disappointment when I arrived in eager anticipation of glazed doughnuts, only to find…bagels.
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