Two spheres and three spheres

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In summary, the conversation discusses the possibility of traveling in one direction and ending up where you started on a curved 2-sphere, as well as the difference between 2-spheres and 3-spheres. It is difficult to grasp the concept of a 3-sphere, but it can be understood by analogy to a 2-sphere and the radial coordinate may only be applicable when embedding the 3-sphere in a higher dimensional space.
  • #1
Baggio
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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? :confused:

Thanks

Raj
 
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  • #2
Baggio said:
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.

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

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? :confused:

Thanks

-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.
 

1. What is the difference between two spheres and three spheres?

The main difference between two spheres and three spheres is the number of spheres involved. Two spheres refer to a system or object consisting of two spheres, while three spheres refer to a system or object consisting of three spheres.

2. How are two spheres and three spheres used in science?

Two spheres and three spheres are commonly used in science as models or systems to study and understand different concepts. They can represent atoms, molecules, planetary bodies, or other physical phenomena.

3. Can two spheres and three spheres interact with each other?

Yes, two spheres and three spheres can interact with each other depending on the specific system or model being studied. For example, in the atomic model, electrons (represented as spheres) interact with the nucleus (also represented as a sphere).

4. What are some real-life examples of two spheres and three spheres?

Two spheres can be seen in a variety of objects, such as marbles, eyeballs, or billiard balls. Three spheres can be found in models of atoms, planetary systems, or soap bubbles.

5. How do two spheres and three spheres relate to each other in terms of size and shape?

In most cases, two spheres and three spheres can have different sizes and shapes. However, they can also be similar in size and shape if they represent the same type of object or system. For example, two atoms modeled as two spheres can have the same size and shape, while three atoms modeled as three spheres can also have the same size and shape.

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