yearday
A particular day numbered from the first day in the year, without regard to month divisions.
To avoid the idiosyncracies^([sic]) of leap years, we propose, as a first approximation to the actual yearday, a standardized yearday s that is a function of (m, d) only, s = S(m) +dl (6) where 5 is a function of m only.
Where it comes from
From Middle English ȝereday, ȝerdai (“anniversary”), from Old English *ġēardæġ (compare Old English ġeārdagas (“days of yore”)), from Proto-West Germanic *jāradag (“day of the year, yearly day”), from Proto-Germanic *jēradagaz, equivalent to year + day. Cognate with West Frisian jierdei (“birthday”), Dutch jaardag (“anniversary, birthday”), German Jahrtag (“anniversary”).
Adapted from the Wiktionary entry yearday (CC BY-SA 4.0).