In golf, the act of scoring an eagle on a hole; hitting two strokes under par.
From 'eagle' (verb) + '-ing' gerund/participle suffix, creating a noun that refers to the action of scoring an eagle. Part of golf's bird-themed scoring terminology.
Golf created 'birdie,' 'eagle,' and 'albatross' as an ascending scale of excellence, and 'eagling' is the action—it's a great example of how sports invent vivid, memorable terminology that sticks around.
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