Etymology
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granny (n.)

also grannie, 1660s, according to OED, most likely a diminutive and contraction of grannam, shortened form of grandame, rather than from grandmother. The sailor's granny knot (by 1803), originally granny's knot, readily jammed and insecure, is a reef or square knot with the second part crossed the wrong way, so called in contempt because "it is the natural knot tied by women or landsmen" [Smyth, "Sailor's Word-Book," 1867]. Granny Smith apples (1895) are said to have been named for Maria Ann Smith (d. 1870) of Australia, who originated them. Granny glasses attested from 1966.

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Definitions of granny

granny (n.)
the mother of your father or mother;
Synonyms: grandma / grandmother / grannie / gran / nan / nanna
granny (n.)
an old woman;
granny (n.)
a reef knot crossed the wrong way and therefore insecure;
Synonyms: granny knot
From wordnet.princeton.edu