The hard feet of animals like horses, sheep, goats, and cattle.
From Old English 'hōf', related to German 'Huf' and Old Norse 'hóf'. The word comes from Proto-Germanic *hofaz. Interestingly, 'hoof' is one of the few English words where the plural is NOT formed regularly—it's 'hooves' or 'hoofs', making it a living artifact of older English grammar.
A horse's hoof is actually a single giant toenail made of keratin (the same material as your fingernails), and it grows continuously throughout the horse's life—farriers have to trim them regularly or they'll grow too long and cause lameness!
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