Kenneth G. Wilson (1923). The Columbia Guide to Standard American English. 1993.
plain, plane (adjs., nn.)
A plain is a broad, flat expanse of country, and so the corresponding adjective means level, lacking decoration, unpretentious, and uncluttered and obvious. Used of persons, plain means homely or lacking in beauty. A plane is a geometrically flat surface, a tool for smoothing wood to make it flat, a kind of tree, and any of a number of specialized names for surfaces of like qualities, such as the planes of a glider or airplane. Plain and plane are homophones, but confusion can arise when you spell the name of the specialized flat surface you have in mind: is it a plane or a plain? Plain is topographical at the outset, and plane, geometrical, but from there on, your dictionary should be your guide.