Displaying similar documents to “The ancient problem of duplication of a cube in high school teaching”

Rational approximations to algebraic Laurent series with coefficients in a finite field

Alina Firicel (2013)

Acta Arithmetica

Similarity:

We give a general upper bound for the irrationality exponent of algebraic Laurent series with coefficients in a finite field. Our proof is based on a method introduced in a different framework by Adamczewski and Cassaigne. It makes use of automata theory and, in our context, of a classical theorem due to Christol. We then introduce a new approach which allows us to strongly improve this general bound in many cases. As an illustration, we give a few examples of algebraic Laurent series...

Solving an indeterminate third degree equation in rational numbers. Sylvester and Lucas

Tatiana Lavrinenko (2002)

Revue d'histoire des mathématiques

Similarity:

This article concerns the problem of solving diophantine equations in rational numbers. It traces the way in which the 19th century broke from the centuries-old tradition of the purely algebraic treatment of this problem. Special attention is paid to Sylvester’s work “On Certain Ternary Cubic-Form Equations” (1879–1880), in which the algebraico-geometrical approach was applied to the study of an indeterminate equation of third degree.

Note on a variation of the Schröder-Bernstein problem for fields

F. S. Cater (2002)

Czechoslovak Mathematical Journal

Similarity:

In this note we study fields F with the property that the simple transcendental extension F ( u ) of F is isomorphic to some subfield of F but not isomorphic to F . Such a field provides one type of solution of the Schröder-Bernstein problem for fields.