"Scientists have measured space to be flat to high accuracy"

[sevensages]

TL;DR

Space is three dimensional. So how can space be flat?

In Max Tegmark's book Our Mathematical Universe, Tegmark wrote the following: "As we saw in the last chapter, we've measured our space to be flat to high accuracy" (99). Since space is three dimensional, I am totally baffled by Tegmark's statement that scientists have measured space to be flat to high accuracy. Since space is three dimensional, how can space be flat?

 

[Ibix]

Flat in this context means that it obeys the rules of Euclidean geometry - for example, if you draw a triangle its internal angles will add to 180°. If we lived in a "closed" or "open" universe (the other two possibilities aside from flat) the angles in sufficiently large triangles would add to more than or less than 180°.

 

[sevensages]

Flat in this context means that it obeys the rules of Euclidean geometry - for example, if you draw a triangle its internal angles will add to 180°. If we lived in a "closed" or "open" universe (the other two possibilities aside from flat) the angles in sufficiently large triangles would add to more than or less than 180°.

That definitely makes sense. Thank you for your answer. I would have never figured it out on my own.

 

[sevensages]

Flat in this context means that it obeys the rules of Euclidean geometry - for example, if you draw a triangle its internal angles will add to 180°. If we lived in a "closed" or "open" universe (the other two possibilities aside from flat) the angles in sufficiently large triangles would add to more than or less than 180°.

If the angles of a large triangle added up to more than 180 degrees or less than 180 degrees, meaning that we live in a close or an open universe, would that mean that the universe does not have three dimensions?