[seqfan] Re: n-sphere constants
Neil Sloane
njasloane at gmail.com
Sun Feb 10 23:10:18 CET 2013
The formulas for those two constants involve pi^(n/2) and (n/2)! - see
my book with Conway, Sphere Packings, Lattices and Groups, page 9.
I agree that it would be worth having those two series of
decimal expansions in the OEIS (dec. expansion
of vol of unit sphere, and of surface area of unit sphere).
I suggest they be added for the following key dimensions:
1 through 12, 16, 24 and 32.
Another sequence of decimal expansions that could be added is
Decimal expansion of density of (conjectured) densest sphere packing in
dimension [N].
There are actually two densities that should be added.
I'll do this myself.
Neil
On Sun, Feb 10, 2013 at 4:00 PM, <franktaw at netscape.net> wrote:
> The OEIS does not really support sequences of (real) constants. About the
> best you can do is enter the first few as "const" sequences, and include
> appropriate comments.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: John W. Nicholson <reddwarf2956 at yahoo.com>
>
> The following is from "The Tau Manifesto" section 5:
> "The generalization of a circle to arbitrary dimensions, called a
> hypersphere or
> an n-sphere."
> Later a see:
> "We see from these formulas that the surface area and volume formulas
> define two
> families of constants, which we’ll call τ_n and σ_n" . My question is how
> to
> make a family of constants in the OEIS and add constants like A000796 or
> A019692?
>
> John W. Nicholson
>
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--
Dear Friends, I have now retired from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
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