[00:00]	The Expansion of the Universe
[00:01]	Visualizing Space
[01:12]	One-dimensional Universe
[02:08]	Two-dimensional Universe
[02:54]	Three-dimensional Universe
[03:56]	Higher-dimensional Shapes
[05:04]	Expansion of the Universe
[07:35]	Two-dimensional Expansion
[08:25]	Does the Universe Have an Edge?
[08:47]	No Edges
[10:09]	Space is Curved
[10:32]	One-dimensional Curvature
[11:48]	Two-dimensional Curvature
[12:03]	One-dimensional Curvature (reprise)
[13:00]	Two-dimensional Curvature (reprise)
[14:45]	Two-dimensional Expansion
[15:56]	The Expansion of the Universe
[18:19]	One-dimensional Complexity
[19:26]	The Fate of the Universe
[21:40]	String Theory

Learning Objectives

1. Visualize one-, two-, three-, and four-dimensional Universes, by analogy to lines (strings), planes (pieces of paper), and so on.

2. Imagine how physical space could have no end, by bending a line into a circle, a plane into a sphere (the surface of a balloon), and so on.

3. Consider how a Universe could expand into a higher dimension. A one-dimensional Universe appears as a straight line from within, but could be a curved space (a circle), expanding into a second dimension. A two-dimensional Universe appears as a flat plane from within, but could be a curved space (the surface of a sphere), expanding into a third dimension. A three-dimensional Universe appears as does our own world, but could be a curved space, expanding into a fourth dimension ...

4. Contrast the Steady State and the Big Band models of the Universe.

5. Connect mean density and gravity to the idea that the Universe is either open, expanding outwards in size forever, or closed, doomed to collapse inward in the end.