Alex’s Adventures in Numberland (79 page)

Hooper, W.,
Rational Recreations, in which the principles of Numbers and Natural Philosophy are clearly and copiously elucidated by a series of easy, entertaining, interesting experiments, among which are all those commonly performed with the cards
, London, 1774

Loyd, S.,
The 8th Book of Tan Part I
, 1903; new edition Dover, New York, 1968

Maor, E.,
Trigonometric Delights
, Princeton University Press, NJ, 1998

Netz, R., and Noel, W.,
The Archimedes Codex
, Weidenfeld & Nicolson, London, 2007

Pasles, P.C.,
Benjamin Franklin’s Numbers
, Princeton Universityess, NJ, 2008

Pickover, C.A.,
The Zen of Magic Squares, Circles and Stars
, Princeton University Press, NJ, 2002

Rouse Ball, W.W.,
Mathematical Recreations and Problems
, Macmillan, London, 1892

Slocum, J.,
The Tangram Book
, Sterling, New York, 2001

Slocum, J., and Sonneveld, D.,
The 15 Puzzle
, Slocum Puzzle Foundation, California, 2006

Swetz, F.J.,
Legacy of the Luoshu
, Open Court, Chicago, IL, 2002

Dudeney, H., ‘Perplexities’, column in
Strand Magazine
, London, 1910–30

Singmaster, D., ‘The unreasonable utility of recreational mathematics’, lecture at the First European Congress of Mathematics, Paris, July 1992

CHAPTER SEVEN

The
On-Line Encyclopedia of Integer Sequences
(www.research.att.com/~njas/ sequences/) looks quite daunting at first to the non-specialist, but once you get the hang of it, is fascinating to surf. I found Chris Caldwell’s online encyclopedia of primes,
The Prime Pages
(www.primes.utm.edu) an excellent resource.

Doxiadis, A.,
Uncle Petros and Goldbach’s Conjecture
, Faber & Faber, London, 2000

du Sautoy, M.,
The Music of the Primes
, Fourth Estate, London, 2003

Reid, C.,
From Zero to Infinity
, Thomas Y. Crowell, New York, 1955

Schmelzer, T., and Baillie, R., ‘Summing a curious, slowly convergent series’,
American Mathematical Monthly
, July 2008

Sloane, N.J.A., ‘My Favorite Integer Sequences’, 2000

CHAPTER EIGHT

It’s a curious quirk that pi, phi and Fibonacci sound related when their etymologies are all completely different, although conspiracy theorists might not be convinced. Separating the cranks from the non-cranks when it comes to the golden ratio is not always easy. One definite non-crank is Ron Knott, whose website: www.computing.surrey.ac.uk/personal/ext/ R.Knott/Fibonacci/ has all you ever wanted to know about 1.618…

Livio, M.,
The Golden Ratio
, Review, London, 2002

Posamentier, A.S., and Lehmann, I.,
The (Fabulous) Fibonacci Numbers
, Prometheus Books, New York, 2007

McManus, I.C., Cook, R., and Hunt, A., ‘Beyond the Golden Section and normative aesthetics: why do individuals differ so much in their aesthetic preferences for rectangles?’,
Perception
, vol. 36, 2007

CHAPTER NINE

The Kelly strategy is a lot more than just remembering the fraction
, since gambling situations are usually more complex than the very simple one I described. I apologize to Ed Thorp, who asked hopefully during our interview if I would be able to spell out Kelly in proper detail. Sorry, Ed, it’s just too complicated for the scope of this book! William Poundstone’s terrific book was a guiding light and I’m grateful he supplied me with data for the graph chapter 9.

Aczel, A.D.,
Chance
, High Stakes, London, 2005

Bennett, D.J.,
Randomness
, Harvard University Press, Cambridge, MA, 1998

Devlin, K.,
The Unfinished Game
, Basic Books, New York, 2008

Haigh, J.,
Taking Chances
, Oxford University Press, Oxford, 1999

Kaplan, M., and Kaplan, E.,
Chances Are
, Penguin, New York, 2006

Mlodinow, L.,
The Drunkard’s Walk
, Allen Lane, London, 2008

Paulos, J.A.,
Innumeracy
, Hill & Wang, New York, 1988

Poundstone, W.,
Fortune’s Formula
, Hill & Wang, New York, 2005

Rosenthal, J.S.,
Struck by Lightning
, Joseph Henry Press, Washington DC, 2001

Thorp, E.O.,
Beat the Dealer
, Vintage, New York, 1966

Tijms, H.,
Understanding Probability
, Cambridge University Press, 2007

Venn, J.,
The Logic of Chance
, Macmillan, London, 1888

CHAPTER TEN

Statistics is the one field of maths covered in this book that I never studied at school or college, so much of this was very new to me. Some mathematicians don’t even consider statistics proper maths, occupied as it is with messy things like measurement. I enjoyed getting my hands dirty, although I’m not going back to Greggs for a very long time.

Blastland, M., and Dilnot, A.,
The Tiger That Isn’t
, Profile, London, 2007

Brookes, M.,
Extreme Measures
, Bloomsbury, London, 2004

Cline Cohen, P.,
A Calculating People: The Spread of Numeracy in Early America
, University of Chicago Press, IL, 1982

Cohen, I. B.,
The Triumph of Numbers
, W. W. Norton, New York, 2005

Edwards, A.W.F.,
Pascal’s Arithmetical Triangle
, Johns Hopkins University Press, Baltimore, MD, 1987

Kuper S., and Szymanski S.,
Why England Lose
, HarperCollins, London, 2009

Taleb, N.N.,
The Black Swan
, Penguin, London, 2007

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.), T
he 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