Archimedes: The Sand-Reckoner
DOI:
https://doi.org/10.13102/sscf.v18i.8567Keywords:
Aristarchus of Samos, History of Science, AstronomyAbstract
We present the commented translation of the famous treatise written by Archimedes of Syracuse “The Sand-Reckoner”. Archimedes set out to determine an upper limit to the number of grains of sand that would fit in the 'Universe' of his time. He used two definitions of 'Universe': the common definition and the definition of Aristarchus of Samos. It is precisely in this treatise that we have the oldest allusion of the Aristarchus' heliocentric proposal. Archimedes concluded that the maximum number of grains of sand that could fit in the 'Universe' would be, in modern notation, 1051 in the common definition and 1063 in Aristarchus' definition. We believe that “The Sand-Reckoner” can be used in Physics, Mathematics and/or Astronomy classes, discussing: the Universe conception in antiquity, the Archimedes experimental procedure to determine the angular diameter of the Sun and the problem of representing extremely large numbers before the invention of the Indo-Arabic numeral system.
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G. Ifrah, Os Números: A História de Uma Grande Invenção. 11a Edição. São Paulo: GloboLivros (2005).
C.B. Boyer, Fundamental Steps in the Development of Numeration. Isis 35, (2) 153 (1944).
J.P. Baptista, L. Ferracioli, Os Grandes Números. Rev. Bras. Ens. Fís. 23, (1) 130 (2001).
R. Netz, W. Noel, Códex Arquimedes. Rio de Janeiro: Record (2009).
G.L. Grudtner, F.M. Bertato, I.M.L. D’Ottaviano, A Medida do Círculo: Uma tradução do texto KΥKΛOΥ METPHΣIΣ de Arquimedes. Rev. Bras. Hist. Mat. 21, (42) 1 (2021).
A.K.T. Assis, Arquimedes, o Centro de Gravidade e a lei da Alavanca. Sâo Paulo: Livraria da Física (2011).
T. Heath, The Copernicus of Antiquity: Aristarchus of Samos. London: Macmillan (1920).
L.V. Freitas, R.M. Santucci, I.A. Marques, Reinventando o método de Aristarco. Rev. Bras. Ens. Fís. 43, e20210062 (2021).
T.L. Heath, The Works of Archimedes. Cambridge: Cambridge University Press (1897).
E.J. Dijksterhuis, Archimedes. Princeton: Princeton University Press (1987).
O. Neugebauer, Archimedes and Aristarchus. Isis 34, (1) 4 (1942).
R. von Erhardt, E. von Erhardt-Siebold, Archimedes’ Sand-Reckoner: Aristarchos and Copernicus. Isis 33, (5) 578 (1942).
A. Diller, The Ancient Measurements of the Earth. Isis 40, (1) 6 (1949).
A.M. Velásquez-Toribio, M.V. Oliveira, Primeiro modelo matemático da cosmologia: as esferas concêntricas de Eudoxo. Rev. Bras. Ens. Fís. 41, e20180096 (2019).
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Copyright (c) 2023 Davi M. Cataneo, Ivo A. Marques
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