• CARMA SEMINAR
  • Speaker: Prof. Richard Brent, CARMA, The University of Newcastle
  • Title: Jonathan Borwein and Pi
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 1:59 pm, Wed, 14th Mar 2018
  • Abstract:

    The late Professor Jonathan Borwein was fascinated by the constant $\pi$. Some of his talks on this topic can be found on the CARMA website.
    This homage to Jon is based on my talk at the Jonathan Borwein Commemorative Conference. I will describe some algorithms for the high-precision computation of $\pi$ and the elementary functions, with particular reference to the book Pi and the AGM by Jon and his brother Peter Borwein.
    Here "AGM" is the arithmetic-geometric mean of Gauss and Legendre. Because the AGM has second-order convergence, it can be combined with FFT-based fast multiplication algorithms to give fast algorithms for the \hbox{$n$-bit} computation of $\pi$.
    I will survey a few of the results and algorithms that were of interest to Jon. In several cases they were either discovered or improved by him. If time permits, I will also mention some new results that would have been of interest to Jon.


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