Math in… Clothing Holes

Don’t you hate it when you find a hole in your favorite t-shirt? Or, at least a hole that’s not supposed to be there! How many holes should a t-shirt have?

A standard t-shirt seems to have 1 hole for your neck, 2 for your arms, and 1 for your waist. So maybe 4 holes, total?

By that count, a pair of pants has 3 holes, a skirt has 2, and a sock has 1.

If we take a skirt and stretch it out like a washer, does it still have two holes? If not, when did the second hole disappear?

Is there a way to talk about holes where they don’t appear or disappear when we reposition fabric?

One way is to think in terms of boundary. If an ant walks on the surface of a tube or washer, it encounters two circular boundary components.

Here are some items of clothing represented topologically as punctured spheres and disks with highlighted boundary components:

What other topologies can clothing have?

What other kinds of things do we call holes?