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New roots solving algorithms

  1. Jan 23, 2006 #1
    I hope the following webpage on new roots solving algorithms based on the Arithmonic mean (a particularcase of the Rational Mean) could be of some interest for this audience:
    References and links can be found at its home page:
    Indeed, there are very good news here, specially, for young people
    because from now on, by means of simple arithmetic they will be able to
    learn at secondary school, among many other new simple algorithms,
    those which have been classed as the most advanced and superb
    analytical methods: Halley’s, Newton’s, Bernoulli’s and Householder’s.
    Some authors have pointed out that "Arithmetic" was the main obstacle
    ancients should overcome in order to solve problems involving what we
    call nowadays "roots-solving methods of higher degree", and that such
    analytic algorithms could only be found, formulated and explained by
    agency of the modern Cartesian system and infinitesimal calculus. We can
    see now that ancients certainly had at hand the most simple arithmetical
    tool (The Rational Mean, The Fifth Arithmetical Operation) for solving all
    those problems involving higher degree equations. It is really striking to
    realize that since ancient times mathematicians could have easily carried
    out such an elemental operation and roots solving methods but --from all
    the evidences-- they didn't!.
    Based on the extremely simple arithmetical processes and wonderful
    properties of Number shown in the book and its introductory web pages,
    it is so hard to realize these so simple arithmetical methods do not appear
    in any book on numbers since ancient times up to now.
    Last edited by a moderator: Apr 21, 2017
  2. jcsd
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