Two Balls
I used SketchUp for parts of a general audience talk last spring. Here’s one where I tried conveying the idea that the 3-sphere can be viewed as the one-point compactification of ordinary 3-space and as the union of two balls.
Of course I first walked the audience through the analogous constructions of lower dimensional spheres, but this one’s more fun. The animated gif above doesn’t capture it that well. Download the model and play with it yourself.
this blog kicks ass.
And it takes names.
fantastic!
can you please explain us whats its role in geometry…i am unable to get the role it plays
Well I was going to link you to the wikipedia article on the 3-sphere (looks like I just did), but maybe it’s not got the answer you’re looking for. Perhaps you could elaborate. Or maybe it would be useful for you to think about how the 2-sphere is obtained from two disks. Or how the 1-sphere (the circle) is obtained from two line segments.