Definition:Plane Surface
Definition
In the words of Euclid:
- A plane surface is a surface which lies evenly with the straight lines on itself.
(The Elements: Book $\text{I}$: Definition $7$)
Side
From the definition of surface, it follows that a plane locally separates space into two sides.
Thus the sides of a plane are the parts of that space into which the plane separates it.
The Plane
The plane is the term used for the general plane surface which is infinite in all directions.
Warning
Care needs to be taken with this definition.
It is possible to create non-plane surfaces which can be generated solely by straight lines.
Twist a deck of cards and the edges of the deck will no longer be plane surfaces, although the edges of the individual cards are as straight as before.
The point to this definition is that every straight line lying partly in a plane surface lies wholly in that surface (unless intersecting it in just one point).
Also known as
A plane surface is usually referred to just as a plane.
Also see
- Results about planes can be found here.
Linguistic Note
The word plane can also be used in an adjectival form, with the usual meaning as being embedded in a plane, or lying wholly within a plane.
The example plane curve comes to mind.
Sources
- 1952: T. Ewan Faulkner: Projective Geometry (2nd ed.) ... (previous) ... (next): Chapter $1$: Introduction: The Propositions of Incidence: $1.2$: The projective method
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): plane: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): plane: 1.