.. index:: plane


.. _plane:

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.