Euclidean Geometry

One recent day on the way home from school D and I had a conversation that went like this:

S: So, how was your day?
D: Pretty good, except for I had to take a lot of time to explain to Zachary about how the lines at the top point of a triangle have a little bit of flatness.
S (confused): They do?
D: Yes! See, if you think about it in your brain, and look at those lines, you can see that at the TOP of the lines where they come together there is the little flat space that is the end of the line, because the line is really like a skinny skinny rectangle.
S: Oh, okay, I understand now. But I can see why it would take some convincing.
D: Yes, I had to tell him and tell him. That point would always have some flatness. Unless you had a robot, maybe.
S: Now I don’t understand again. How would a robot change things?
D: Well, it might. If it was big enough, and you could get inside and make it do what you wanted, and the robot could draw a very very very very super skinny line, then it would maybe really be a point.
S: Yes, that might work, I think you’re right.

(I’m calling this story, “D’s spontaneous discovery of our inability to represent Euclidean space satisfactorily with the limited tools at our disposal.” Holy cow!)