Plain and plane are distinct in most of their definitions, but they almost converge where plain refers to a flat, treeless area of land and plane refers to a flat, level surface. But even here, the distinction is simple: A plain is a land formation, while plane is abstract, mainly appearing in mathematics and other specialized fields.
Outside those definitions, plain and plane are not as easily confused. Plane most often appears as an abbreviation of airplane. Its other definitions relate to levels of achievement (e.g., a higher plane), skimming over water (short for hydroplane), and flat tools used to smooth surfaces. Plain has a range of adjectival meanings, including free from adornment, free from obstructions, and evident to the mind.
The Serengeti plain in Tanzania and Kenya is renowned for sights such as this one. [Los Angeles Times]
Mrs. Cleere and Mrs. Kimball’s fifth-grade classes also studied plotting points on a Cartesian plane. [AL.com]
We are currently heading through a region called Pali-Aike, a wide plain of wispy grassland. [Telegraph]
Or you can position it so that both screens rest along the same plane. [USA Today]