Bøger af Franz Rothe

The geometric construction of the regular 17, 257 and even the 65 537-gon are given in complete details, including programming codes. The theory of geometrical constructions and its connection to Galois theory is treated in detail. Later parts deal with totally positive real numbers as sums of squares, cyclotomic polynomials,Chebychev polynomials, Gaussian periods, Galois theory, and more related topics. The solvability of equations is treated as far as it is related to geometric constructions, and tailored to prove the steps needed is that context, as simple as possible. Much less known is the relation between the lunes of Hippocrates and transcendental numbers to which the final section is dedicated.

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This book has been growing over the years out of several resources. Firstly, the courses in number theory and modern algebra I had occasionally been teaching at UNC Charlotte. Secondly, my interest to invent mathematical problems for competitions, and invent and pose problems for individual work with gifted students.After being forced to retire about two years ago because of health reasons, I did continue to occupy myself with these topics, and I learned more substantially from the work of Gauss on quadratic reciprocity and on the construction of Fermat polygons. Too, I did take up numerical computation with the computer language of Dr. Racket, which is based on Lisp and freely available on the internet.