Alex's Adventures in Numberland - Alex Bellos [183]
CHAPTER ELEVEN
While it is still an open question whether the universe is flat, spherical or hyperbolic, the universe is certainly pretty flat; if its curvature does indeed deviate from zero, it does so only very slightly. An irony of testing the universe for its curvature, however, is that it can never be conclusively proved that the universe is flat since there will always be measurement error. By contrast, it is theoretically possible to prove that the universe is curved, which would happen if the results produce a curvature, accounting for measurement error, that is non-zero.
The Hilbert Hotel sometimes goes by the name of Hotel Infinity, and the story has many different versions. The guests wearing T-shirts is my own adaptation.
Aczel, A.D., The Mystery of the Aleph, Washington Square Press, New York, 2000
Barrow, J.D., The Infinite Book, Jonathan Cape, London, 2005
Foster Wallace, D., Everything and More, W. W. Norton, New York, 2003
Kaplan, R., and Kaplan, E., The Art of the Infinite, Allen Lane, London, 2003
O’Shea, D., The Poincaré Conjecture, Walker, New York, 2007
Taimina, D., and Henderson, D.W., ‘How to Use History to Clarify Common Confusions in Geometry’, Mathematical Association of America Notes, 2005
INTERNET
It’s impossible to research anything to do with maths without referring to Wikipedia and Wolfram MathWorld (www.mathworld.wolfram.com), which I conferred with on a daily basis.
GENERAL
The number of books I looked through is too long to list all of them here, but these ones directly contributed in one way or another to the material in this book. Anything by Keith Devlin, Clifford A. Pickover or Ian Stewart is always worth a read.
Bell, E.T., Men of Mathematics, Victor Gollancz, London, 1937
Bentley, P.J., The Book of Numbers, Cassell Illustrated, London, 2008
Darling, D., The Universal Book of Mathematics, Wiley, Hoboken, NJ, 2004
Devlin, K., All the Math That’s Fit to Print, Mathematical Association of America, Washington DC, 1994
Dudley, U. (ed.), Is Mathematics Inevitable?, Mathematical Association of America, Washington DC, 2008
Eastaway, R., and Wyndham, J., Why Do Buses Come in Threes?, Robson Books, London, 1998
Eastaway, R., and Wyndham, J., How Long is a Piece of String?, Robson Books, London, 2002
Gowers, T., Mathematics: A Very Short Introduction, Oxford University Press, Oxford, 2002
Gullberg, J., Mathematics, W. W. Norton, New York, 1997
Hodges, A., One to Nine, Short Books, London, 2007
Hoffman, P., The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth, Fourth Estate, 1998
Hogben, L., Mathematics for the Million, Allen & Unwin, London, 1936
Mazur, J., Euclid in the Rainforest, Plume, New York, 2005
Newman, J. (ed.), The World of Mathematics, Dover, New York, 1956
Pickover, C.A., A Passion for Mathematics, Wiley, Hoboken, NJ, 2005
Singh, S., Fermat’s Last Theorem, Fourth Estate, London, 1997
Acknowledgements
Firstly, thanks to Claire Paterson at Janklow & Nesbit, without whose encouragement this book would never have been written, and to my editors Richard Atkinson in London and Emily Loose in New
York. I’m also very grateful to Andy Riley for his wonderful illustrations.
The success of my trips relied on the support of friends old and new: in Japan, Chieko Tsuneoka, Richard Lloyd Parry, Fiona Wilson, Kouzi Suzuki, Masao Uchibayashi, Tetsuro Matsuzawa, Chris Martin and Leo Lewis. In India, Gaurav Tekriwal, Dhananjay Vaidya and Kenneth Williams. In Germany, Ralf Laue. In the US, Colm Mulcahy, Tom Rodgers, Tom Hull, Neil Sloane, Jerry Slocum, David Chudnovsky, Gregory Chudnovsky, Tom Morgan, Michael de Vlieger, Jerome Carter, Anthony Baerlocher and Ed Thorp. In the UK, Brian Butterworth, Peter Hopp and Eddy Levin.
The manuscript is much improved thanks to comments from Robert Fountain, Colin Wright, Colm Mulcahy, Tony Mann, Alex Paseau, Pierre Pica, Stefanie Marsh, Matthew Kershaw, John Maingay, Morgan Ryan, Andreas Nieder, Daina Taimina, David Henderson,