THE FIFTH ARITHMETICAL OPERATION

 

         

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                                            

The Rational Mean: The fifth arithmetical operation. All means as particular cases of the Rational Mean (Generalized Mediant). The new Arithmonic Mean as an essential arithmetical operation for roots solving. New Properties and observations on Number.

 

Roots Solving: Bernoulli´s, Newton´s and many other new algorithms --converging even faster than Halley´s-- trivially found just by agency of arithmetic (The Rational Mean),  no Cartesian system, no decimals, no derivatives. No precedents, at all.

 

Generalized Continued Fractions: Traditional continued fractions as particular cases of a new general concept "Generalized Continued Fractions". (Fractal Fractions)

 

These pages are just a brief introduction to the book:

“LA  QUINTA  OPERACION  ARITMÉTICA, Revolución del Número”

(Translation: The Fifth Arithmetical Operation, Number Revolution)

ISBN:980-07-6632-4. 200 pages, spanish language.

Copyright ©. All rights reserved under international Copyright Conventions.

 Author: D. Gómez.

 

 

 

Linked pages:

 

 

Comments

 

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. Now, the facetious response to such statements is: "Number beats Axes. Arithmetic beats Fluxions", mainly because, 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 of higher degree. The implausible fact that ancients and many modern mathematicians could have easily carried out such an elemental operation but --from all the evidences-- they didn't, bring to light an astonishing testimony of something wrong about the whole story of roots-solving and the definition of irrational numbers and their arithmetical operations. Worst, all these observations throw many doubts about the so-called "rigorousness" of modern mathematics.

Based on the extremely simple arithmetical processes and wonderful properties of Number shown in the book and its introductory web pages: Rational Mean Definition-&-Evaluation, Roots Solving and Continued fractions) and considering the incomprehensible and astonishing  absence of any precedent on this matter all through the history of Arithmetic and roots solving, one can realize now that it is certainly a ridiculous arrogance to think that the artificial and personal creations (i.e.: Cartesian system; decimal fractions; imaginary numbers, etc.) of any individual could ever exceed the natural order determined by God in accordance with the harmonies of Number. Indeed, 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. No matter  all the absurd attacks and troubles these comments have caused to me in the Usenet since long time ago,  these very simple arithmetical web-pages will continue their task: Bringing to light the true story on roots solving and the irrational numbers.

Nowadays, people of modern societies are suffering the consequences of social leaderships that have been thoroughly affected (mainly, since the rise of Cartesian system and mechanistic philosophy) by egotistic conceptions of people who use to consider about themselves as better planners than God. Many bizarre "scientific" conceptions have certainly inspired people with confusedness, atheism, chaos and dehumanisation.

These are not pessimistic conclusions, at all, but an encouraging message based on all those elemental and natural principles of Quantity which have been passed over by many "great mechanistic" minds.

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 primary or secondary school the "most advanced" analytic methods (Halley’s, Newton’s, Bernoulli’s, Power series expansions) which have been brought to us as exclusive superb products of the "divine" Cartesian system and its fluxions.

 

Some other works:

Other useful web sites:

 

 

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Copyright © 1993-2002

All rights reserved under international Copyright Conventions.

No part of this page may be reproduced, stored or transmitted in any form or by any means without the prior permission of the author: D. Gómez.

Last revision: 2002