Two spheres and three spheres

Baggio

Just a couple of questions:

1. If we imagine space to be curved over a sphere is it possible to travel in one direction and eventually end up where you started, assuming that the sphere it self is not expanding.

2. What's the difference between a two sphere and a three sphere? I find it hard to grasp the idea of a three sphere, because if there is now a radial or z coordinate then it's not really a sphere is it?

Thanks

Raj

jcsd

If you're thinking about something analogus to an explorer circumnavigating the globe, then yes certaily.

-The main difference between a 2-sphere and a 3-sphere is their number of diemsnions (this is obvious I suppose).

-The idea of a 3-sphere is hard to grasp, the best way is by analogy to a 2-sphere.

-'the radila coordinate is something that is only really a coordiante when you embed the 3-sphere into a higher dimensional space, in the context of the space of the three sphere itself (assuming enough structure is defined) the 'radius' of the sphere is just a parameter that differentiates it from other simlair spaces.