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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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Math. Comp. 5 (1951), 133-160 Request permission
References
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    • Not only the publications of Goodwyn to which we refer, but others, have been discussed in thorough fashion by J. W. L. Glaisher: (i) Report of the Comm. on Mathematical Tables, 1873, p. 31-33, 150; (ii) “On circulating decimals with special reference to Henry Goodwyn’s ’Table of circles’ and ’Tabular series of decimal quotients’ (London 1818-1823),” Cambridge Phil. Soc., Proc., v. 3, 1878, p. 185-206; (iii) “On a property of vulgar fractions,” Phil. Mag., s. 5, v. 7, 1879, p. 321-336. We have already quoted DeMorgan’s Statement of 1861 [MTAC, v. 2, p. 87] concerning Goodwyn: “His manuscripts, an enormous mass of similar calculations, came into the possession of Dr. Olinthus Gregory, and were purchased by the Royal Society at the sale of his [Gregory’s] books in 1842.” In the above publications of Glaisher it is stated that no trace of the papers could be found at the Royal Society. Neville’s statement, p. xi, “Goodwyn left a mass of papers, no one knows what became of them,” is therefore slightly misleading. K. G. J. Jacobi, “Über die Kreistheilung und ihre Anwendung auf die Zahlentheorie,” Jn. reine angew. Math., v. 30, 1846, p. 166-182. K. G. Reuschle, Mathematische Abhandlung, enthaltend: Neue Zahlentheoretische Tabellen, Stuttgart, 1856. A. J. C. Cunningham, Quadratic Partitions. London, 1904; Quadratic and Linear Tables. London, 1927. B. van der Pol, Verslagen van de Maatschappij Diligentia, The Hague, 1946. A copy of this diagram woven in red and white squares hangs on the wall of the reviewer’s study, a gift from the author. The curve $t = {x^t}$ has been frequently studied before. For example: (a) J. F. C. Hessel, “Über das merkwürdige Beispiel einer zum Theil punctirt gebildeten Curve das der Gleichung entspricht $y = \sqrt [x]{x}$,” Archiv Math. Phys., v. 14, 1850, p. 169-187; H. Scheffer, “Über die durch die Gleichung $y = \sqrt [x]{x}$ dargestellten Curven,” Archiv Math. Phys., v. 16, 1851, p. 133-137. The role which $\xi = {\omega ^\xi }$ plays in Cantor’s theory of transfinite numbers will be recalled; see, for example, G. Cantor, Math. Annalen, v. 49, 1897, p. 242-246 (also the English translation of P. E. B. Jourdain, Open Court, 1915, p. 195-201).
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Additional Information
  • © Copyright 1951 American Mathematical Society
  • Journal: Math. Comp. 5 (1951), 133-160
  • DOI: https://doi.org/10.1090/S0025-5718-51-99428-8