This is just a leveling of a typical Facebook meme asking about the number of holes in a T-Shirt that has two noticeable holes cut all the with the chest and ago areas. I'm walk to ignore those and also just ask the question "how numerous holes walk a T-Shirt have?"
I think the answer is 3: the neck, the left arm, and the best arm. I think the bottom, the area the surrounds her waist, isn't actually a feet at all. Certain if you flatten the end the surface you finish up with a (rough) circle through the head and arm holes in the middle, and what went roughly the belt is currently the circumference.
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Am I absent something?
A T-shirt is homeomorphic to either:
the surface ar of a round with 4 holes poked in it, or
a 2-dimensional disk with 3 feet poked in it.
So i beg your pardon number you get depends on i m sorry you check out yourself as starting with.
Additionally, if friend think of the T-shirt as having thickness, then it's homeomorphic come a heavy torus through 3 holes: something favor this (though the Wikipedia article is talking around just the surface of this object).
I'm disturbed through the quantity of occupational that must have gone into make every those glass models.
Is over there a video showing exactly how he make them?
Even if you flatten that out, the hole at the bottom is quiet a hole, by my logic. But it appears I'm wrong!
One method I heard of informing how many holes a thing has actually (which is referred to as it's genus) is how countless discrete cut it bring away to reduced through. For example a round is genus 0 and a torus (doughnut) is genus 1. Now a t-shirt will certainly take, by mine reckoning 3 discrete cuts to cut into two. The would typical it has three holes and you're right! Mmm now I'm gonna need to think about that.
Even if girlfriend flatten that out, that hole at the bottom is tho a hole, by mine logic. However it appears I'm wrong!
Take a piece of piping. How plenty of holes are there? Obviously just one, however there space two openings.
Likewise, a shirt has 4 openings, yet three holes.
Conflating "opening" and also "hole" is the trouble here.
We'd should specify the cuts thing more precisely to usage it together a rule. If I reduced the T-shirt in half lengthwise, over there are only two discrete cut (each v an arm hole left). Also, we have the right to shorten the T-shirt with just one cut (though the cut will it is in shaped favor a circle).
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With mine limted because I did applied math knowledge around topology, yes ns think a t-shirt is indistinguishable to S3.