| 1 | The upper bound will be given by the sphere. | |
| 2 | Here it is more like we are parameterizing the sphere. | |
| 3 | Let's do a second example with the same sphere. | |
| 4 | Now, what is the best way to figure out where you are on the sphere? | |
| 5 | But, that spherical thing with a little slit going twisting into it will actually have boundary my loop. |