Definition:Surface/Plane Surface

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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 $7$)


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.


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 any straight line lying partly in a plane surface lies wholly in that surface (unless intersecting it in just one place).

Also known as

A plane surface is usually referred to just as a plane.

Also see