# What is a flat Universe?

**What is a flat Universe? **

First a word of caution: we physicists are using everyday words with a slightly different (or sometimes more precise) meaning. This helps at first because it sounds vaguely familiar but, when you go deeper (as we do in this course), this may make things more difficult.

For example, in everyday language, a flat surface is a 2-dimensional surface which is not curved.

For physicists, flat space could have more dimensions than 2 (actually 3 in our case). Flat space is a space where the familiar laws of ordinary geometry (the geometry of Euclid) apply: parallel lines never meet, the three inner angles of a triangle sum up to 180°, etc. In the case of a non-flat or curved space, all this has to be reconsidered: parallel lines meet, the angles of the triangle do not add up to 180°. Now you might think that we know that we are in a flat space because we learn all these rules at school. Well, Einstein tells us that this is true only locally, in our close vicinity. The question is whether this is true at the scale of the full universe. And it appears to be so!

As I understand we describe the universe, where big distances al involved, as a four dimension space, in the case we chose rectangular references, they are ct,x,y,z. When you refer that the universe is curved, means that the four dimension space is curved?

In other words, if we consider two events in the space time universe (ct1,x1,y1,z1) and (ct2,x2,y2,z2) then the shortest path from one event to the other is not necessary a rectilinear path in the four dimension space.

It is a strange concept, indeed, that the universe is flat but I suppose it is flat in relation to something much grander. I look up and i look down. This hardly lends itself to the concept of flat but if I were looking at the entirety of it from another perspective… Perhaps…