A place for majestic STEMLORD peacocking, as well as memes about the realities of working in a lab.
Rules
This is a science community. We use the Dawkins definition of meme.
a torus is not homotopic to a straw though unless you take the straw and glue it at its ends. a straw is homotopic to a circle, a torus is homotopic to product of two circles, Baldur's gate is homotopic to a disk which is homotopic to a point unless we are talking about the game storage medium which used to be a CD which is also homotopic to a circle
Wouldn’t a straw be the product of a circle and a line?
What you said is stronger than being homotopic. homotopic is weaker, for instance a line is homotopic to a point, By taking the straw (even if it has thickness) and just shrinking it along its longer axis you eventually arrive at a circle. If it has thickness you will arrive at a band and then you can also retract radially to arrive at a circle.
A CD is clearly homotopic to a torus, though...
And the walls of a straw do have thickness...
A straw goes:
Gas - solid - gas - solid - gas
If solid torus yes, if just the regular torus (surface of the solid torus) no. CD is homotopic to a circle and so is a solid torus.
OK, that's my ignorance. I didn't realise toruses were usually hollow.
Thank you for letting me know, you're right and I've learnt something.
Zero
The true answer involves integrals imo (my calc is rusty so I'm not gonna bother trying lol)