what do you call the white fibers over the orange after you peeled it.?

Question

and what do you call each segment that separates from the whole?

Answer 1

It's called the pith. It's not good for anything.

And to answer your second question, they are segments, just as you described them.

Answer 2

its called the pith. when a recipe calls for the zest of an orange, you are only supposed to use the orange flesh, not the white part because it is bitter tasting :)

Answer 3

white fibers.

Answer 4

Vicki nailed it.