As the general definition of a legally significant quantity for Mitzvot/Transgressions involving amounts of food: Yoma 80a, Eruvin 4b; Succah 5b-6a; Pesachim 49b-50a
As the legal minimum of a prohibited item one ingests, to require a Chatat [sin offering]: Yoma 80a
Only considering an olive eaten within the time it takes to eat a "Peras" to be like eating an olive-sized amount, biblically or rabbinically: Pesachim 44a, 114b