Special Notice (reposted March 1, 2012, with additions/corrections):

This March 10 (2012), MHK will be giving a presentation (1079-03-89) titled

“Does the Banach-Tarski Paradox have an Evil Twin?!” (links to unofficial copy of the official abstract; actual paper )

at the Southeastern Sectional meeting (#1079) of the American mathematical Society, at the University of South Florida in Tampa, FL, USA.

It is scheduled for 8:45 a.m. in the Session for Contributed Papers, I, Room 354, Cooper Hall, USF. See http://www.ams.org/meetings/sectional/2188_progfull.html

(APOLOGIES: if you get/got an  Evil Twin!  flash drive at the 2012 Southeastern Sectional Meeting (#1079) in Tampa, FL, USA, it will/did not contain the best README file, which you can get HERE.)

Here are  4  slideshows,  2 in PowerPoint (ppsx) and  2 in PDF:
Banach_Tarski's_Evil_Twin!_(long_pps).ppsx (more introductory material)
Banach_Tarski's_Evil_Twin!_(short_pps).ppsx (almost no introductory material)
Banach_Tarski's_Evil_Twin!_(short_pps).pdf (almost no introductory material, but if you display comments, you get extra notes)
Banach_Tarski's_Evil_Twin!_(long_pps).pdf (more introductory material, and if you display comments, you get extra notes)

Here is the paper:
Banach-Tarski's_Evil_Twin!_(A4).pdf (this is a short 12 page paper describing the basics; BTW it’s sized for A4 paper)