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A ‘lost’ chapter in the calculation of \(\pi\): Baron Zach and MS Bodleian 949. (English) Zbl 1325.01013
From the summary we learn that: “The Bodleian library holds a manuscript containing mathematical tables and a calculation of \(\pi\) to 154 decimal places, last described (in part) in 1802.”
The paper under review provides an outline of the manuscript’s contents and relates it to developments in the computation of \(\pi\), not only to those from the 19th century but also with a glance to that of the 20th century. The contents of the paper yield a vision on an (almost forgotten) way how to calculate digits from the decimal expansion of \(\pi\). A rich list of references closes the paper. Due to Baron Franz Xaver von Zach (1754–1832), Hungarian astronomer and scientific intelligencer, the hidden manuscript came to live. There is much to get from the author’s investigations.
01A50 History of mathematics in the 18th century
01A55 History of mathematics in the 19th century
11Y60 Evaluation of number-theoretic constants
Full Text: DOI
[1] Agarwal, R. P.; Agarwal, H.; Sen, S. K., Birth, growth and computation of pi to ten trillion digits, Adv. Differ. Equ., 100, (2013) · Zbl 1380.01012
[2] Albree, Joe; Brown, Scott H., “A valuable monument of mathematical genius”: the ladies’ diary (1704-1840), Hist. Math., 36, 10-47, (2009) · Zbl 1163.01014
[3] Babbage, Charles, Passages from the life of a philosopher, (1864), Longman, Green, Longman, Roberts, and Green London · Zbl 0861.01026
[4] (Balázs, Lajos G., The European Scientist: Symposium on the Era and Work of Franz Xaver von Zach (1754-1832), (2004), Wissenschaftlicher Verlag Harri Deutsch GmbH Frankfurt am Main)
[5] Bradley, James, Astronomical observations, (1798), Clarendon Press Oxford
[6] Bradley, James, Miscellaneous works and correspondence, (1823), Oxford University Press Oxford
[7] Clapinson, Mary; Rogers, T. D., Summary catalogue of post-medieval western manuscripts in the Bodleian library Oxford, vol. 2, (1991), Clarendon Press Oxford
[8] De Morgan, S. E., Memoir of augustus De Morgan, (1882), Longman, Green, and Co. London
[9] Despeaux, Sloan Evans, Mathematical questions: a convergence of mathematical practices in british journals of the eighteenth and nineteenth centuries, Rev. Hist. Math., 20, 1, 5-71, (2014) · Zbl 1307.01024
[10] Halley, Edmond, A most compendious and facile method for constructing the logarithms, Philos. Trans., 19, 58-67, (1695)
[11] Hobson, E. W., Squaring the circle: A history of the problem, (1913), Cambridge University Press Cambridge · JFM 45.1215.12
[12] Jones, W., Synopsis palmariorum matheseos, (1706), J. Matthews for J. Wale London
[13] (Kidd, John, Catalogue of the Works in Medicine and Natural History Contained in the Radcliffe Library, (1835), S. Collingwood Oxford)
[14] Lister, Anne, The secret diaries of miss anne lister, (2010), Virago London, ed. Whitbread, Helena
[15] (Long, G., The Penny Cyclopædia, vol. 19, (1841), Charles Knight and Co. London)
[16] Madan, Falconer, A summary catalogue of western manuscripts in the Bodleian library at Oxford, vol. 3, (1895), Clarendon Press Oxford
[17] McConnell, Anita, 2004. Franz Xaver von Zach in England. In: Balázs [2004], 34-44.
[18] Montucla, Jean-Étienne, Histoire des mathématiques, vol. 4, (1802), Henri Agasse Paris
[19] Montucla, Jean-Étienne, Histoire des recherches sur la quadrature du cercle, (1831), Bachelier Père at Fils Paris
[20] ODNB, Oxford dictionary of national biography, (2004), Oxford University Press Oxford, online edn., 2011
[21] Paris, Aimé, Principes et applications diverses de la mnémotechnie, (1834), Mansut Fils Paris
[22] Peaucelle, Jean Louis, Personnes ayant participé aux travaux du bureau du cadastre de octobre 1791 à Mars 1802, (2011)
[23] Peaucelle, Jean Louis, Le détail du calendrier de calcul des tables de prony de 1791 à 1802, (2012)
[24] Razpet, Marko, Več kot 150 decimalk krožne konstante pred letom 1800, Obzornik za matematiko in fiziko, 60, 129-136, (2013)
[25] Roegel, Denis, The great logarithmic and trigonometric tables of the French cadastre: a preliminary investigation, (2010)
[26] Rutherford, William, Computation of the ratio of the diameter of a circle to its circumference to 208 places of figures, Philos. Trans., 131, 281-283, (1841)
[27] Sandifer, Ed., Why 140 digits of pi matter, (Pisanski, Tomaž, Jurij Baron Vega in njegov čas: Zbornik ob 250-letnici rojstva/Baron Jurij Vega and his times: Celebrating 250 years, (2006), DMFA - Založništvo: Arhiv Republike Slovenije Ljubljana), 240-254
[28] Schulz Strasznicky, Leopold von, Der kreis-umfang für den durchmesser 1 auf 200 decimalstellen berechnet von herrn Z. dahse [sic] in wien, J. Reine Angew. Math., 27, 198, (1844)
[29] Sherwin, H., Sherwin’s mathematical tables, (1706, 1771), J. Mount and T. Page London
[30] Taylor, E. G.R., The mathematical practitioners of Hanoverian england, (1966), Cambridge University Press Cambridge · Zbl 0156.24505
[31] Thibaut, Bernhard Friedrich, Grundriß der reinen Mathematik, (1822), Bandenhoef und Ruprecht Göttingen
[32] Vargha, Magda, Franz xaver von zach (1754-1832): his life and times, (2005), Konkoly Observatory of the Hungarian Academy of Sciences Budapest, Trans. Csaba, József
[33] Vega, Jurij, Thesaurus logarithmorum completus, (1794), Weidmann Leipzig
[34] Wallis, Ruth, 2004. Hornsby, Thomas (1733-1810), astronomer. In: ODNB [2004].
[35] Willmoth, Frances, 2004. Sharp, Abraham (bap. 1653, d. 1742), mathematician and scientific instrument maker. In: ODNB [2004].
[36] WolframAlpha
[37] Zach, Franz Xaver, freiherr von, Letter to ‘M. le Général D….’ dated 1 September 1818, (Correspondance astronomique, géographique, hydrographique et statistique, vol. 1, (1818), A. Ponthenier Gênes), 205-226
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