Hmm, what of rolls? Ciabatta, Kaiser rolls? Even croissants? By this definition it seems they'd be burgers, since rolls are cut in half. But then my roast beef sandwich is a lying, cold, sad burger
You have weird Ciabattas if you think that Ciabatta is a kind of bun and not a bigger loaf. Croissants are pastry. And yes, burgers made with Kaiser rolls are totally burgers:
from a topological perspective, wraps and tacos are two different beasts.
in a wrap, the bread completely surrounds (and encloses) the other ingredients, so theres a 2-dimensional hole involved (which basically means the inside is hollow).
in a taco, no such wholes are present.
you can also distinguish sandwiches from tacos and wraps (since sandwiches involve two pieces of bread, like you said). but unfortunately, you can’t topologically distinguish a burger from a sandwich
But tacos traditionally are more like wraps by your definition, with the exception being hard/crunchy tacos which are on what i would technically call a chip, this making crunchy tacos just portable nachos
Additionally walking tacos are supported by a chip bag, making them neither a taco nor nachos.
A chicken sandwich is a sandwich when the chicken meat is between two slices of bread cut from a bigger loaf. It's a chicken burger when it's between two halves of a bun.
And as you said, hamburger derives from the German city of Hamburg, so Germans, not Americans, have the authority here.🤪