Re: Imaginary numbers - most interesting points

*To*: mathgroup at smc.vnet.net*Subject*: [mg98664] Re: [mg98647] Imaginary numbers - most interesting points*From*: "David Park" <djmpark at comcast.net>*Date*: Thu, 16 Apr 2009 04:11:01 -0400 (EDT)*References*: <23154843.1239787862080.JavaMail.root@n11>

The most extraordinary thing to me is that complex numbers are built into ordinary space - of any dimension! They are not something you have to import from the outside. How do you find out about that? Read about 'geometric algebra'. ('New Foundations for Classical Mechanics: Second Edition' by David Hestenes or 'Geometric Algebra for Physicists' by Chris Doran & Anthony Lasenby. And, as it happens, there is a very powerful Mathematica package for this called GrassmannAlgebra written by John Browne: http://www.grassmannalgebra.info/ David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: robert prince-wright [mailto:robertprincewright at yahoo.com] I have (perhaps unwisely!) decided to do a 'Pecha Kucha' on imagination .... or at least imaginary numbers. The audience are all engineers with hazy recollection of undergrad maths. If you are not familiar with Pecha Kucha, then its worth checking Youtube and doing some googling. Simplistically the concept is to share understanding of something using 20 slides. Each slide should convey as much as possible with as few words as possible, with the message limited to 20 seconds! So, what is the most interesting thing about the imaginary number 'i' that you can think of, and how can it most simply be conveyed using Mathematica 7 in Slide presentation form? I've started with the notion of polynomial roots, de Moivre, reflections etc. but would appreciate a wider view. R