Torus: Mobius Strip Incisions

[addedline8]

whats

 

[lavinia]

Consider the torus, a doughnut-shaped solid that is perfectly circular at each perpendicular cross section, and a Möbius strip, which has a single 180-degree twist and a uniform curvature throughout its length. Suppose a torus is sliced three times by a knife that each time precisely follows the path of such a Möbius strip. What is the maximum number of pieces that can result if the pieces are never moved from their original positions?
Note: Each of the Möbius strips is entirely confined to the interior of the torus.

I don't see the picture. Explain again.

 

[addedline8]

Sorry about that. Here is the attached picture. Thanks for responding.

 

[Jamma]

Are your knife cuts allowed to go over each other?

[Actually, looking at your note, they must be able to- if the strips are all in the interior of the torus then if they weren't you could never separate any pieces].

Are your Mobius strips a set size? (I don't quite understand what you mean by your note on the curvature- do you mean that you just twist the interval around the circle at a constant speed around the Mobius strip to make it, so that they are "uniform" in some sense?)

 

[blue_raver22]

A torus is a three-dimensional shape that resembles a donut with a hole in the middle. A Mobius strip is a two-dimensional surface with only one side and one edge. Incisions on a torus that follow the shape of a Mobius strip would create a unique and interesting shape. This shape would have only one side and one edge, similar to a Mobius strip, but would also have a hole in the middle like a torus. This concept could have potential applications in mathematics and engineering, as it demonstrates the interconnectedness and complexity of geometric shapes. Further research and experimentation could reveal new insights and possibilities for this concept.