### Galois Group lecture on Paradoxical Decompositions

Dear All,

You are invited to attend Professor Richard Sharp's Galois Group lecture about 'Paradoxical Decompositions' this Wednesday 18th March 2009, at 1:10pm in the Alan Turing Building Room G.207. Free refreshments will be available at the end. (You would be mad to miss this lecture!)

Please feel free to email me if you have any questions or comments.

Best wishes, Beans

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Wednesday 18th March 2009 at 1:10-2pm

Alan Turing Building, room G.207

Professor Richard Sharp

Abstract - Paradoxical Decompositions

It is possible to decompose a solid sphere into a finite number of pieces, which may be rearranged to make two spheres each with the same volume as the original one. Put more informally, it is possible to cut an orange into a finite number of pieces and reassemble them into two oranges of the same size. This is called the Banach-Tarski paradox and is perhaps the most counterintuitive of a family of so-called "paradoxical decompositions".

This talk will explain some of the mathematics involved, exploring concepts of volume, non-measurability and self-similarity.

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PS: I'm still alive - but I've lost my voice and memory it seems, as I have no idea whatsoever as to what I did this Saturday! I'm straining to remember but my minds drawing blanks! (On Sunday some cousins came over though...).

## 2 comments:

Sounds

veryinteresting!I know it will be as Professor Sharp is a brilliant lecturer. His lectures are the only reason as to why I passed Measure Theory last semester, as I unfortunately didn't find the time to read the extra material on my own!

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