From: mulcybr@AZStarNet.com (Stephen Harris)
Newsgroups: sci.physics.research,sci.physics,sci.math
Subject: Re: The union of all the onions
Date: Mon, 28 Aug 1995 22:12:26 LOCAL
Keywords: Tony Smith Homepage

In article <41gcdr$mp5@zermelo.mit.edu> baez@math.mit.edu (John Baez) writes:
>I imagine it's something algebraists know all about.

>Before anyone gets too serious about onionology, better known as the
>Cayley-Dickson process, they should probably read the literature on
>the subject.  MIT has a book with a title something like "Mutation of
>alternative algebras", which begins with some interesting results on
>this process, together with references.  I can't seem to find this
>book in the electronic catalog I'm now searching, alas, so I can't
>quickly give a more precise reference.

  Since I don't have a degree I seldom post. I spent an hour on the homepage
  of Tony Smith http://www.gatech.edu/tsmith/home.html who knows about
  fractals and Penrose tiles and B Fuller. I suppose you know him since he
  has a mirror for your files. But if not he knows a lot about octinions.

  What I know is so basic you probably have forgotten it but its short.
   The tetrahedron is the closest packing of spheres (78%) The % drops
   as the dim goes up. At dim 7 the gap equals the volume of a tetrahedron
   and dim 8 is the gap filled in. I think this applies to 720degrees working
   but the 360 not. I read about this in information theory(same type math)

   Best Regards,
   Stephen

==============================================================================

Newsgroups: sci.physics,sci.math
From: mkinyon@peabody.iusb.indiana.edu (Michael Kinyon)
Subject: Re: The union of all the onions
Date: Tue, 29 Aug 1995 13:33:53 GMT

[Follow-up to sci.physics.research deleted.]

In article <41gcdr$mp5@zermelo.mit.edu>, John Baez <baez@math.mit.edu> wrote:
>Before anyone gets too serious about onionology, better known as the
>Cayley-Dickson process, they should probably read the literature on
>the subject.  MIT has a book with a title something like "Mutation of
>alternative algebras", which begins with some interesting results on
>this process, together with references.  I can't seem to find this
>book in the electronic catalog I'm now searching, alas, so I can't
>quickly give a more precise reference.

I would suggest the following references:

_Introduction to Nonassociative Algebras_ by R.D. Shaffer, P.A.M.S. Series 22,
Academic Press, 1966.

_Malcev-admissable Algebras_ by H.C. Myung, Progress in Math. Series 64,
Birkhauser, 1986.

(Every alternative algebra is Malcev-admissable)

_Mutations of Alternative Algebras_ by A. Elduque and H.C. Myung, M.I.A. 
Series 278, Kluwer Academic Publishers, 1994.
-- 
Michael Kinyon                  | email: mkinyon@peabody.iusb.edu
Dept of Mathematics & Comp. Sci.| phone: (219)-237-4240
Indiana University South Bend   | fax:   (219)-237-4538
South Bend, IN 46634 USA        | "The quote in my .sig is false." - M. Kinyon