A plane is a flat surface with no thickness.


Our world has three dimensions, but there are only two dimensions on a plane:

length and width make a plane

x and y also make a plane

A plane has no thickness, and goes on forever.



It is actually hard to give a real example!

When we draw something on a flat piece of paper we are drawing on a plane ...

... except that the paper itself is not a plane, because it has thickness! And it should extend forever, too.


So the very top of a perfect flat piece of paper
that goes on forever is the right idea!


Also, the top of a table, the floor and a whiteboard are all like a plane.

Here you can spin part of a plane:



A plane has 2 Dimensions (and is often called 2D):


Point, Line, Plane and Solid

A Point has no dimensions, only position
A Line is one-dimensional
A Plane is two dimensional (2D)
A Solid is three-dimensional (3D)


Plane vs Plain

In geometry a "plane" is a flat surface with no thickness.

But a "plain" is a treeless mostly flat expanse of land ... it is also flat, but not in the pure sense we use in geometry.

Both words have other meanings too:

  • Plane can also mean an airplane, a level, or a tool for cutting things flat
  • Plain can also mean without special things, or well understood


2d world

Imagine you lived in a two-dimensional world. You could travel places, visit friends, but nothing in your world has height.

You could measure distances and angles.

You could go fast or slow. You could go forward, backwards or sideways. You could move in straight lines, circles, or anything, so long as you never go up or down.

What would life be like living on a plane?