A good answer might be:

A point is a location in space.

Picture of a Point

A geometrical point is a location in space. It has no other characteristics. It has no length, width, or thickness. It is pure location.

The above answer would not help you if you somehow did not have the concept of "point." The phrase "location is space" designates the same concept as the word "point." The definition cannot convey a concept you do not already have.

In geometry texts the word point is usually not defined. It is regarded as one of the undefined primitives that are used to define other objects. Instead of defining "point" books give examples and hope that you somehow build up the concept from them.

At right is a picture that I hope will clarify this. The picture shows two spires atop a building. The picture is 2D, but think about the actual 3D building. Focus on the spike at the top of the closest spire.

What is the location of the very top of the spike? On the scale of the building, the end of the spike defines an exact location. We can conceptualize that location as a point.


If you had the spike lying in front of you on your desk, would you consider its end to be a point?