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Michael Brooks

The Art of More. How Mathematics Created Civilization



 Michael Brooks 2021

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notes








1


GordonP. Numerical cognition without words: evidence from Amazonia. Science 306. 5695 (2004): 49699.




2


EverettC. Numbers and the Making of Us: counting and the course of human cultures. Cambridge, MA: Harvard University Press, 2019.




3


NuwerR. Babies are born with some math skills. Science, 2013, www.sciencemag.org/news/2013/10/babies-are-born-some-math-skills.




4


DeeJ. The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara, www.gutenberg.org/files/22062/22062-h/22062-h.htm.




5


BrooksR. Bean Counters: the triumph of the accountants and how they broke capitalism. London: Atlantic Books, 2019.




6


MignetF.A. M. A. History of the French Revolution from 1789 to 1814, www.gutenberg.org/files/9602/96028.txt.




7


SollJ. The Reckoning: financial accountability and the rise and fall of nations. New York: Basic Books, 2014.




8


Founders Online. From Alexander Hamilton to Robert Morris, [30 April 1781], http://founders.archives.gov/documents/Hamilton/0102-021167.




9


  ,         .   ,   43  .    , , ,     . ,    ,     ,  ,   ,         .




10


FehrT. et al. Common brain regions underlying different arithmetic operations as revealed by conjunct fMRI-BOLD activation. Brain Research. 1172 (2007): 93102.




11


PikaS. et al. How to order a beer: cultural differences in the use of conventional gestures for numbers. Journal of Cross-Cultural Psychology 40. 1 (2009): 7080.




12


IfrahG. From One to Zero: a universal history of numbers. New York: Penguin Books, 1987.




13


BertelettiI., BoothJ.R. Perceiving fingers in single-digit arithmetic problems. Frontiers in Psychology. 6 (2015).




14


ButterworthB. The Mathematical Brain. London: Macmillan, 1999.




15


H?yrup J. State, justice, scribal culture and mathematics in ancient Mesopotamia: Sarton Chair Lecture. Sartoniana. 22 (2009): 1345.




16


H?yrup J. On a collection of geometrical riddles and their role in the shaping of four to six algebras. Science in Context. 14, no. 12 (2001): 85131. (: 4,874.       ,      .)




17


CrappierJ.-J. et al. The Akan Weighing System restored after 120 years of oblivion. A metrological study of 9301 geometric gold-weights. Colligo 2. 2 (2019): 922.




18


ScriptureE.W. Arithmetical prodigies. American Journal of Psychology. 4, no. 1 (1891): 159.




19


DuvernoyS. Leonardo and theoretical mathematics. Nexus Network Journal. 10,1 (2008): 3949.




20


   ,     . ,   ,           .  , ,     . ,   10   5  .     2 .  ,      2 .        5 .    ,    .  ,     1.    1. ,   10   1/3 .      2 . , 10    2 ,       5 .    ,       5 ? 6 = 30 . ,   10  1/3  30.




21


McNamara J., ShaughnessyM.M. Student errors: what can they tell us about what students DO Understand? Math Solutions, 2011.




22


   : 2/7, 1/2, 5/9.    : 2.        ( 12/13,  7/8   1,      2),       .  12/13  96/104,      8.   7/8  91/104,      13.  . 96 + 91 = 187,  ,     187/104.   1,8,     2.




23


    0  1,           .  12  : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55  89.




24


PascalB. Penses, www.gutenberg.org/files/18269/18269-h/18269-h.htm.  ..




25


WallisJ. A Treatise of Algebra, Both Historical and Practical. Philosophical Transactions of the Royal Society of London. 15, no. 173 (1685): 10951106.




26


SeifeC. Zero: The Biography of a Dangerous Idea. New York: Viking, 2000.




27


   :    -.  . :    , 1983.




28


KaplanR. The Nothing That Is: a natural history of zero. Oxford: Oxford University Press, 2000.




29


Physics by Aristotle, http://classics.mit.edu/Aristotle/physics.html.




30


WengJ. et al. The effects of long-term abacus training on topological properties of brain functional networks. Scientific Reports. 7, no. 1 (2017): 8862.




31


GoldthwaiteR. The practice and culture of accounting in Renaissance Florence. Enterprise & Society. 16, no. 3 (2015): 61147.




32


Gleeson-WhiteJ. Double Entry: how the merchants of Venice created modern finance. New York: W.W.Norton & Co, 2012.




33


SchemmenM. The Rules of Double-Entry Bookkeeping (a Translation of Particularis de Computis et Scripturis). IICPA Publications, 1494.      ..


