(plān) noun
1. Geom. A surface such that a straight line joining any two of its points lies wholly within the surface.
2. Hence, any flat or uncurved surface.
3. A grade of development; stage; level, as of thought, knowledge, rank, etc.
4. Aeron. A supporting surface of an airplane: often used in combination: monoplane.
5. An airplane.
—adjective
1. Lying in a plane; level; flat.
2. Having a flat surface; dealing only with flat surfaces: plane geometry. See synonyms under HORIZONTAL, LEVEL, SMOOTH. ♦ Homophone: plain. [Var. of PLAIN², noun; refashioned after L planus flat]

(plān) noun
1. A tool used for smoothing boards or other surfaces of wood.
2. A trowel–like tool for striking off clay that projects above the mold.
—v. planed, plan·ing v.t.
1. To make smooth or even with or as with a plane.
2. To remove with or as with a plane.
—v.i.
3. To use a plane.
4. To do the work of a plane. ♦ Homophone: plain. [<MF plane <OF plain <LL plana a plane <planare plane <L planus flat]

(plān) noun
A plane tree. ♦ Homophone: plain. [<OF plane <plasne <L platanus <Gk. platanos <platys broad; because of its broad leaves]

(plān) v.i. planed, plan·ing
1. To rise partly out of the water, as a power boat when driven at high speed.
2. To glide; soar.
3. To travel by airplane. ♦ Homophone: plain. [<F planer <plan a plane <L planus flat]