Approximating roots. No precedents in math history

Approximating roots. No precedents in math history

Postby arithmetic » Tue Aug 20, 2013 11:01 pm

A new general and unifying arithmetical concept: The Rational Mean, which allows to generate, among many other new algorithms, those celebrated Lucas?s, Bernoulli's, Newton's, Halley's, Householder's root-approximating methods which up to now were considered the exclusive achievement of Infinitesimal Calculus. No derivatives, no trial-and-error checkings, no geometry, no cartesian system, but just Simplest Arithmetic.

Indeed, it is really striking to realize that even ancient mathematicians had at hand the elementary tools for constructing these high-order algorithms. Actually, these new findings compel us to cogitate on the reasons mathematicians were forced to create the "elevated" infinitesimal system that we have inherited.
The book also includes the new Generalized Continued Fractions for approximating the maximum and the minimum modulus root of the general algebraic equation, number Pi, number e, Golden Mean, and others with improved convergence rate.

These new high-order methods also embrace complex roots and the general algebraic equation, and from the solid evidence at hand, these arithmetical methods have no precedents in the mathematics literature.

https://sites.google.com/site/arithmonic/roots
arithmetic
 
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Re: Approximating roots. No precedents in math history

Postby leesajohnson » Fri Mar 25, 2016 5:52 am

Great information, seriously I didn't know about these facts that mathematicians were forced to create the "elevated" infinitesimal system that we have inherited.

leesajohnson
 

Re: Approximating roots. No precedents in math history

Postby Guest » Fri Mar 25, 2016 6:32 am

???????......Who has ever been at infinity, not even to mention "the "elevated" infinitesimal system"........
Guest
 

Re: Approximating roots. No precedents in math history

Postby Raiden Mitchell » Thu Jun 17, 2021 3:18 pm

Thank you very much for sharing this book. I have been looking for books on this topic in paper format for several weeks and cannot find them. Indeed, it is incredibly interesting and amazing that the ancient mathematicians had at hand the rudimentary tools for constructing high-order algorithms.

Raiden Mitchell
 


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