Or a scythe, but the Latin root falx originally meant a sickle. Curving and tapered to a point, is the main idea. The word was coined in English either in the 18th or 19th century (dictionaries disagree) from said root, and is used nowadays mainly in medical contexts. Falcons are named after the same root, from the shape of their talons.
He had sharp eyes and a falciform nose over a thin, insinuating mustache.