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:(adsbygoogle = window.adsbygoogle || []).push({});

http://mipagina.cantv.net/arithmetic/rmdef.htm

References and links can be found at its home page:

http://mipagina.cantv.net/arithmetic

Comments:

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.

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# New roots solving algorithms

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