| 1 | If the universe has a positive curvature, it's a closed universe . | |
| 2 | It goes back... Actually, some of you may be able to see the curvature. | |
| 3 | The limit of this ratio as the length of the arc approaches zero. | |
| 4 | Cosmologists call negative curvature models of the universe open universes . | |
| 5 | This allowed them to finely control the curvature of their structures. |