# The Undefined Terms in Geometry (i.e. points, lines & planes)

As I understand it, there are three undefined terms (alternatively they are sometimes called primitive notions) in Geometry:

1. Point: A point has 0 dimensions and merely denotes a location.
2. Line: A line has only 1 dimension (that of length, but no others) and spans infinitely in both directions.
3. Plane: A plane has 2 dimensions (length and width, but no height) in which it extends indefinitely in all directions.

However, it seems incongruous with my understanding of the world. A graphical representation of a line for example appears to also have width, however negligible (and my observations about points and planes are similar). And then, these elements are supposed to combine to form 3D solids! I suppose my question is then:

How do you understand and/or think about these concepts? How robust should your understanding be to utilise them effectively?

Additionally, I am also wondering what purpose it serves to describe lines and planes as limitless. Everywhere I have looked prescribes this same quality to them, but it doesn't explain why.

Thank you guys so much!

• "A graphical representation of a line" is not a line. Ceci n'est pas une pipe.
– Blue
Nov 9, 2015 at 0:32
• Of course! After having studied Magritte, I can't believe I didn't make that connection. But of course, that begs the question: What constitutes a 'true' line? Is it a set of real numbers? Something else? How about a 'true' point or plane for that matter? It seems for now we shall have to make do with imperfect real world analogues and graphical representations of these concepts, while we ponder how they may truly exist theoretically. Anyway, It's all very interesting to think about. Thanks for weighing in! :D Nov 10, 2015 at 4:41