Definition of a plane - Math Open Reference

Plane

From Latin: plantum - "flat surface,"

An imaginary flat surface that is infinitely large and with zero thickness

Clearly, when you read the above definition, such a thing cannot possibly really exist. Imagine a flat sheet of metal. Now make it infinitely large in both directions. This means that no matter how far you go, you never reach its edges. Now imagine that it is so thin that it actually has no thickness at all. In spite of this, it remains completely rigid and flat. This is the 'plane' in geometry.

It fits into a scheme that starts with a point, which has no dimensions and goes up through solids which have three dimensions:

point	line	Plane	Solid
Zero dimensions	One dimension	Two dimensions	Three dimensions

It is difficult to draw planes, since the edges have to be drawn. When you see a picture that represents a plane, always remember that it actually has no edges, and it is infinitely large.

Parallel planes

Two parallel falt surfaces, one above the other

You can think of parallel planes as sheets of cardboard one above the other with a small gap. Parallel planes are the same distance apart everywhere, and so they never touch. Since a plane has zero thickness, we could stack up an infinite number of these planes

Intersecting planes

Two flat surfaces, with a line where one penetrates the other.

If two planes are not parallel, then they will intersect (cross over) each other somewhere. Two planes always intersect at a line, as show on the right.

This is similar to the way two lines intersect at a point.

Coordinate Geometry

In another branch of mathematics called coordinate geometry, points are located on the plane using their coordinates - two numbers that show where the point is positioned. To achieve this, the plane is thought to have two scales at right angles. Using a pair of numbers, any point on the plane can be uniquely described.

For more on this, see