Ordinary Point

An ordinary point has distinct meanings in differential equations and incidence geometry.

For a second-order linear ordinary differential equation in normalized form

is an ordinary point if and are analytic functions in a neighborhood of . Every solution then has a convergent Taylor series about . A point that is not ordinary is a singular point (Arfken 1985).

In incidence geometry, a point which lies on at least one ordinary line is called an ordinary point, or sometimes a regular point (Guy 1989).