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The arithmetic-geometric mean of Gauss (1984)

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Abstract

Paper 3: David A. Cox, “The arithmetic-geometric mean of Guass,” L’Enseignement Mathematique, vol. 30 (1984), p. 275–330. Reprinted by permission.

Synopsis: Although the arithmetic-geometric mean (AGM) is now used widely in high-precision computation, it was actually discovered nearly a century earlier, independently by Lagrange, Legendre and, in considerably more detail, by Gauss (although there is no evidence that any of them saw the connection to computing π). As David A. Cox points out in this article, Gauss did numerous computations with the AGM, such as when he numerically discovered that

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  1. Amherst College, Amherst, Massachusetts, USA

    David A. Cox

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  1. David A. Cox
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Cox, D.A. (2016). The arithmetic-geometric mean of Gauss (1984). In: Pi: The Next Generation. Springer, Cham. https://doi.org/10.1007/978-3-319-32377-0_3

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