On page 0 there were 480 octonion multiplication
tables. Of these there are four that surpass all the rest in symmetry and elegance. Of
these my favorites are the D(+) and C(+) tables, which are refered to as the Dixon
preference and Cederwall preference in the Java applet above (I've been using the former
for years, and Martin Cederwall is the first person I met who uses the latter; I must add
that this C(+) table is far more widely used than mine).
To get an idea how this
Java applet works (and what it has to do with D(+) and C(+)),
click on any of the 28 red and blue boxes in the upper two rows
of boxes (the third row, is determined by the first two rows and gives the product
of those two rows).
I will cover these tables and more on
the following pages, but you might want to take a look at my book, which I have
found listed at the gigantic
site, and on the Springer
site. There are many other books out there: Okubo's "Introduction to Octonion...";
and Lohmus, Paal and Sorgsepp's "Nonassociative Algebras in Physics" being two
that spring to mind. As to the applet, besides for the book, a relevant paper
requested of me 4 years ago has finally appeared in Acta Mathematica Applicanda .
But if you play with the applet long enough you'll figure out what