Re: Hypercube

[Jack Uretsky <jlu@HEP.ANL.GOV>]

In the math literature the dimension of the maximal sphere is one
less than the dimension in which it is embedded. Thus
                1-sphere, a circle, can lie in a plane
                2-sphere is the ordinary sphere in Euclidean 3-space
                ...etc.



Adam was by constitution and proclivity a scientist; I was the same, and
we loved to call ourselves by that great name...Our first memorable
scientific discovery was the law that water and like fluids run downhill,
not up.
                          Mark Twain, <Extract from Eve's Autobiography>

On Sun, 16 Jul 2000, John Denker wrote:
__________________________________________snip____________________________
> matter what the dimensionality.  When necessary, the term "3-sphere" is
> used to designate the special case of D=3.
>
> ====================
>
> As to the importance of considering dimensionalities other than D=3, the
> list is endless.  Here are some examples:

more examples:  phase space for n spinless particles in 3 dimensions
is 6n-dimensional.
        Our universe may have more than 4 dimensions, with the added
dimensions "rolled-up", in some theories, or communicating with us
only through gravity, in other theories (Randall and Sundrum).