the.com/hatband

The only part of a hat that admits a head is a tragic approximation of a circle.

means The strip of material—ribbon, leather, or cord—that wraps around the base of a hat's crown, either to decorate it or to help it fit.

from Straightforward compound of 'hat' plus 'band,' band here carrying its old sense of a binding strip or encircling ring, the same sense that gives us wristbands and wedding bands. English has been cinching things with 'bands' since medieval times, so pairing it with 'hat' once hats became common headwear was less invention than inevitability.

original purpose
absorbed sweat before anyone invented deodorant
idiom
tight as a hatband means stingy, not snug
status marker
feathers and bands once signaled rank, not fashion
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