Definition talk:Sphere

are $$x$$ and $$y$$ really elements of $$\mathbb{R}^{n+1}$$? It seems like a three dimensional sphere has its points specified in $$\mathbb{R}^3$$. --Cynic (talk) 21:44, 21 January 2009 (UTC)
 * The sphere we are most familiar with, that which we think of as the surface of the Earth or skin of an orange, is the two dimensional sphere. Think of it like this: the surface of the Earth requires only two coordinates to describe a point, longitude and latitude, hence, (and this is very unrigorous, intuitional) the surface of the Earth is two-dimensional and we call it a two-sphere.
 * We describe a surface like an orange's skin or the Earth's surface as $$\mathbb{S}^2 = \left\{{ x \in \mathbb{R}^{3} : |x|=1   }\right\} \ $$.   Hope that clears up any questions.  Zelmerszoetrop 21:54, 21 January 2009 (UTC)