The projective line is a fundamental example of an algebraic curve. From the point of view of algebraic geometry, P1("K") is a non-singular curve of genus 0. If "K" is algebraically closed, it is the unique such curve over "K", up to rational equivalence. In general a (non-singular) curve of genus 0 is rationally equivalent over "K" to a conic "C", which is itself birationally equivalent to projective line if and only if "C" has a point defined over "K"; geometrically such a point "P" can be used as origin to make explicit the birational equivalence..