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A point is a location in space.

Picture of a Point

Cupola atop a building

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 already understand the concept of "point". The phrase "location in space" designates the same concept as the word "point". The definition cannot convey a concept you do not already have.

In geometry, the word point is not defined. It is 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 cupolas on top of a building. The picture is 2D, but think about the actual 3D building. Focus on the spike (finial) at the top of the closest cupola.

What is the location of the very top of the spike? On the scale of the building, the sharp 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?