5 ms·
Ho can a coffee cup be transformed into a doughnut? is the "hole" they are referring to the handle?
by samwhiteUK 8y ago
Ho can a coffee cup be transformed into a doughnut? is the "hole" they are referring to the handle?
- avip 8y agoWell the cup is essentially a point, and the handle... is essentially a torus (AKA doughnut).
- intuitionist 8y agoYes, the hole is the handle -- imagine the cup part "melting" into the handle and you get a sense of how the transformation works.
- mnw21cam 8y agoIs it disturbing that when I read "coffee cup", I thought of those paper disposable things with no handle?
- msla 8y ago> Is it disturbing that when I read "coffee cup", I thought of those paper disposable things with no handle? No, because the usual term for the ceramic thing with the handle is a coffee mug.
- jerf 8y agohttps://youtu.be/zc8rKvxedrA?t=18 https://youtu.be/zc8rKvxedrA?t=18 In Topology, you're allowed to move surfaces around much more freely than you can in the real world, so don't use your intuition from there, which says that coffee cups are too hard to move around. The point is that you can move the surface around in ways that in topology are considered to be no change to the surface, and get from one shape to another. If you do want to use your physical intuition, a play-dough coffee cup can be squished into a donut without ever poking a new hole through the playdough and without ever closing one up. That's probably not great mathematical intuition since it still keeps some constraints that topology doesn't, but if you're not planning on studying topology, it's harmless enough.