plane

A surface is that which has length and breadth only.

The extremities of a surface are lines.

A plane surface is a surface which lies evenly with the straight lines on itself.

—Euclid

A plane is a flat field with two dimensions.

A plane is flat when is contains a line projected by two points on the plane.

The plane is the primary context for the constructions we will create until we venture into 3 dimensions much later.

Euclid’s 5th postulate concerning parallel lines has created consternation amongst mathematicians because it does not hold up for non flat surfaces.

Non-planar surfaces, such as the surface of a sphere, will be defined later.