Approximations of irrationalities by using linear recurrent sequences - Couverture souple

Murru, Nadir

 
9783659479694: Approximations of irrationalities by using linear recurrent sequences
Couverture souple
ISBN 10 : 3659479691 ISBN 13 : 9783659479694
Editeur : LAP LAMBERT Academic Publishing, 2013

Synopsis

The book is devoted to the approximation and periodic representation of algebraic numbers, like quadratic and cubic irrationalities. Continued fractions surely provide rational approximations and periodic representation for quadratic irrationals. Here, new kinds of representation for square roots are exploited with the aid of linear recurrent sequences. A beautiful connection with the solution of the Pell equation is highlighted, finding an original way to solve it through a group structure over the Pell hyperbola. Moreover, similar results are obtained and illustrated for cubic irrationals, approaching the Hermite problem, i.e., the problem of finding a way to write algebraic numbers (irrational numbers that are solution of some algebraic equation with rational coefficients) as a periodic sequence of integers.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The book is devoted to the approximation and periodic representation of algebraic numbers, like quadratic and cubic irrationalities. Continued fractions surely provide rational approximations and periodic representation for quadratic irrationals. Here, new kinds of representation for square roots are exploited with the aid of linear recurrent sequences. A beautiful connection with the solution of the Pell equation is highlighted, finding an original way to solve it through a group structure over the Pell hyperbola. Moreover, similar results are obtained and illustrated for cubic irrationals, approaching the Hermite problem, i.e., the problem of finding a way to write algebraic numbers (irrational numbers that are solution of some algebraic equation with rational coefficients) as a periodic sequence of integers.

Biographie de l'auteur

In 2007, I graduated in mathematics with honors. In 2011, I have obtained a PhD in mathematics with a thesis in the beautiful field of the number theory. Presently, I still do research in this field at the University of Turin and CNR of Pisa. As Gauss said: "Mathematics is the queen of sciences and number theory is the queen of mathematics".

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2013
Langue
anglais
ISBN 10 
3659479691
ISBN 13 
9783659479694
Reliure
Broché
Nombre de pages
68
Coordonnées du fabricant
non disponible
Personne responsable
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