People who operate boats or travel by boat for recreation or work, or a type of flat-topped straw hat traditionally worn while boating.
From 'boat' + '-er' (agent suffix meaning 'one who'), with 'boater' as the hat being a separate evolution from the occupational term.
The boater hat—that flat, hard straw hat—became iconic in the late 1800s and was so associated with river boating that the hat itself took the name from the activity; Huckleberry Finn would have worn one!
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