Hermite problem is:
"Peut-être parviendra-t-on à déduire de là, un système complet de caractères pour chaque espèce de ce genre de quantités, analogue par exemple à ceux que donne la théorie des fractions continues pour les racines des équations du second degré"
Another way to state this concern is:
"Find methods for expressing real numbers as sequences of positive integers so that the sequence is eventually periodic precisely when the initial number is a cubic irrational."
Another description of the problem is:
"In 1848, Hermite asked Jacobi for methods of expressing a real number as a sequence of integers such that the algebraic properties of the real number are reflected in the periodicity of its sequence. In other words, Hermite wanted a generalization to cubic and higher degree algebraic numbers of the fact that the decimal expansion of a real number is periodic if and only if the real is rational and, more importantly, of the fact that the continued fraction expansion of a real number is periodic if and only if the real is a quadratic irrational. Such attempts are called multidimensional continued fractions."
Jacobi tried unsuccessfully to solve this problem.
"Peut-être parviendra-t-on à déduire de là, un système complet de caractères pour chaque espèce de ce genre de quantités, analogue par exemple à ceux que donne la théorie des fractions continues pour les racines des équations du second degré"
Another way to state this concern is:
"Find methods for expressing real numbers as sequences of positive integers so that the sequence is eventually periodic precisely when the initial number is a cubic irrational."
Another description of the problem is:
"In 1848, Hermite asked Jacobi for methods of expressing a real number as a sequence of integers such that the algebraic properties of the real number are reflected in the periodicity of its sequence. In other words, Hermite wanted a generalization to cubic and higher degree algebraic numbers of the fact that the decimal expansion of a real number is periodic if and only if the real is rational and, more importantly, of the fact that the continued fraction expansion of a real number is periodic if and only if the real is a quadratic irrational. Such attempts are called multidimensional continued fractions."
Jacobi tried unsuccessfully to solve this problem.
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