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[lordnincompoop]

I have an interesting question that my mathematics teacher posed to me:

Can you cut a torus in half and still have one piece?

Now, as this is for mathematics I's supposing there's no trick answer such as "Cut it normally and eat the other."

So is there a way to cut a torus in half so that instead of two halves, you still have a single piece?


Thanks in advance for any and all answers that you may have.

[Shades]

I believe you need to look at cutting a mobius strip along the length. The halftwist means that the resultant shape is still all connected I think, I don't remember all the details so I might be off on some facts there.

[lordnincompoop]

I believe you need to look at cutting a mobius strip along the length. The halftwist means that the resultant shape is still all connected I think, I don't remember all the details so I might be off on some facts there.

Unfortunately, it wouldn't work for objects such as doughnuts which was the example used by him.

I'd have done this myself if I could, but I jsut couldn't. I spent hours on this before and got nothing. 

[bartavelle]

It might be a trick on the definition of torus. It could not be an euclidian space torus, but either some weird thingie in a weird space that is topologicaly a torus, or an algebraic torus. I have no more clue to offer ...

[Shades]

It might be a trick on the definition of torus. It could not be an euclidian space torus, but either some weird thingie in a weird space that is topologicaly a torus, or an algebraic torus. I have no more clue to offer ...

A mobius strip is a form of torus anyway.

Unfortunately, it wouldn't work for objects such as doughnuts which was the example used by him.

Try visualising cutting the shape of the mobius strip into the doughnut. So the knife you use to cut follows the path of the strip. (does this make sense?)

[Siquo]

What does "cutting in half" mean, mathematically? In my definition, something is cut in half when you end up with two pieces of the same volume, so it's impossible by that definition. You could cut it and end up with two linked rings that cannot be detached from eachother without breaking them, but that counts as two pieces in my book.

[Siquo]

On second thought, just cut it as if the cut were a mobius band and it renders one bigger torus. Twisting twice gives you two interlinked tori.

[Shades]

On second thought, just cut it as if the cut were a mobius band and it renders one bigger torus. Twisting twice gives you two interlinked tori.

This is what I was trying to say

[Siquo]

Yeah, you did

I just confirmed. Although I do not have a donut at hand to try it.

[eerr]

(text)
-Nevermind

[lordnincompoop]

Thank you, all. This helped me greatly.