Plane
A plane is a flat surface with no thickness.

Our world has three dimensions, but there are only two dimensions on a plane.
Examples:
 length and height, or
 x and y
And it goes on forever.

Examples
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 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.
Imagine
Imagine you lived in a twodimensional world. You could travel around, visit friends, but nothing in your world would have height.
You could measure distances and angles.
You could travel 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?
