How could we tell (in principle)whether we live in a universe in which space is flat or in a universe in which space is positively curved?
A)Find out if the universe has a center
B)Find out if the universe has boundaries
C)Determine whether there is cosmic background radiation
D)Measure the sum of the angles of a very large triangle

Question

Quizplus · Accepted Answer

The sum of the angles of a triangle in a flat universe is always 180 degrees, while the sum of the angles in a positively curved universe will be greater than 180 degrees. Therefore, by measuring the sum of the angles of a very large triangle, we can determine whether the universe is flat or positively curved. Choices A and B are not useful because the universe does not necessarily have a center or boundaries regardless of its curvature. Cosmic background radiation exists in both flat and curved universes, so choice C is not specific to either geometry.

How Could We Tell (In Principle)whether We Live in a Universe