Alex's Adventures in Numberland - Alex Bellos [180]
Glaser, A., History of Binary and Other Nondecimal Numeration, Southampton, PA, 1971
Kawall Leal Ferreira, M. (ed.), Idéias Matemáticas de Povos Culturalmente Distintos, Global Editora, São Paulo, 2000
Suzuki, K., Lectures on Soroban, Institute for English Yomiagezan
Dowker, A., and Lloyd D., ‘Linguistic influences on numeracy’, Education Transactions, University of Bangor, 2005
Wassmann, J., and Dasen, P.R., ‘Yupno Number System and Counting’, Cross-cultural Psychology Journal, 1994
Hammarström, H., ‘Rarities in Numeral Systems’, 2007
CHAPTER TWO
Proofs Without Words is a gem, and was my source for the different Pythagoras proofs. Thanks to Tom Hull for much of the background about origami. The illustrations of how to make business-card tetrahedrons and cubes are inspired by his book. Another remarkable Japanese religio-geometric practice is sangaku, which didn’t fit in the chapter but is too fascinating not to mention here. A sangaku is a wooden tablet hung at a Buddhist or Shinto shrine that has a proof of a geometric prlem painted on it. Between the seventeenth and nineteenth centuries, thousands of sangaku were made by Japanese who had worked out geometrical problems but could not afford to publish them in books. Drawing the solutions on a tablet and hanging them at a shrine was a way of making a religious offering while also advertising their results.
Shortly before going to press, I learnt that Jerome Carter had died in a motorcycle accident in 2009.
Balliett, L.D., The Philosophy of Numbers, L.N. Fowler, 1908
Bell, E.T., Numerology, Century, 1933
Dudley, U., Numerology, Mathematical Association of America, 1997
du Sautoy, M., Finding Moonshine, Fourth Estate, London, 2008
Ferguson, K., The Music of Pythagoras, Walker, New York, 2008
Hull, T., Project Origami, A.K. Peters, Wellesley, MA, 2006
Kahn, C.H., Pythagoras and the Pythagoreans, a Brief History, Hackett, Indianapolis, IN, 2001
Loomis, E.S., The Pythagorean Proposition, Edwards Bros, Ann Arbor, MI, 1940
Maor, E., The Pythagorean Theorem, Princeton University Press, NJ, 2007
Mlodinow, L., Euclid’s Window, Free Press, New York, 2001
Nelsen, R.B., Proofs Without Words, Mathematical Association of America, Washington DC, 1993
Riedwig, C., Pythagoras, His Life, Teaching and Influence, Cornell University Press, Ithaca, NY, 2002
Schimmel, A., The Mystery of Numbers, Oxford University Press, New York, 1993
Simoons, F.J., Plants of Life, Plants of Death, University of Wisconsin Press, Madison, WI, 1998
Sundara Rao, T., Geometric Exercises in Paper Folding, Open Court, Chicago, IL, 1901
Bolton, N.J., and MacLeod, D.N.G., ‘The Geometry of the Sri Yantra’, Religion, vol. 7, 1977
Burnyeat, M.F., ‘Other Lives’, London Review of Books, 2007
CHAPTER THREE
Even though the Liber Abaci was first published in 1202, its first English translation did not appear until its 800th anniversary, in 2002. Vedic mathematics is not the only type of speed arithmetic in the market. There are several ‘systems’ and many of them share the same tricks. The best known is the Trachtenberg System, devised by Jakow Trachtenberg while a political prisoner in a Nazi concentration camp. Self-styled ‘mathemagician’ Arthur Benjamin is an entertaining, recent purveyor of the speed arithmetician’s art.
Fibonacci, L., Fibonacci’s Liber Abaci, Springer, New York, 2002
Joseph, G.G., Crest of the Peacock, Penguin, London, 1992
Knott, K., Hinduism: A Very Short Introduction, Oxford University Press, 1998
Seife, C., Zero, Souvenir Press, London, 2000
Tirthaji, Jagadguru Swami S. B. K., Vedic Mathematics, Motilal Banarsidass, Delhi, 1992
Dani, S.G., ‘Myths and reality: On “Vedic mathematics”’
CHAPTER FOUR
The least dweeby contestant in Leipzig was Rüdiger Gamm, a former bodybuilder who failed maths at school. After a career with exaggeratedly large biceps, he now has an exaggeratedly large brain. Gamm, whose calculation skills have made him a minor celebrity in Germany, told me that memory is his greatest asset: